## Kerala Plus One Maths Model Question Paper 3

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 score each. Answer any 6.

Question 1.
a. Write set is the subset of all the given sets?
(a) {1,2,3,….}
(b) {1}
(c) {0}
(d) {}
b. Write down the power set of A = {1,2,3}

Question 2.
In any triangle ABC, prove that
a(SinB- sinC) + b(sinC- sinA) +c(sinA- sinB) = 0

Question 3.
a. Solve x2 + 2 = 0
b. Find the multiplicative inverse of 2-3i
a. x2 + 2 = 0

Question 4.
a. Solve

b. Find the graphical solution of the above inequality.

Question 5.
a. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of atmost 3 girls,
b. Find n if 2nC3: nC3 = 12 : 1

Question 6.
a. The new coordinates of the points (2, 5) if the origin is shifted to the point (1, 1) by translation of axes.
A) (3, 1) B(1, 3) C (-1, 3) D (3, -1)
b. Find what the equation x+ xy – 3y2– y + 2 = 0 becomes when the origin is shifted to the point (1,1)?

Question 7.
Evaluate :

Questions from 8 to 17 carry 4 score each. Answer any 8.

Question 8.

Question 9.
Consider the statement 1.3 + 2.32 + 3.33

a. Verify whether the statement is true for n =1.
b. Prove the result by using principle of mathematical induction.

Question 10.
a. Express (1 + i)3 + (1 – i)3 in a + ib form.
b. Find the polar form of the complex number – 1 – i.

Question 11.
solve the following linear inequalities graphically:

Question 12.
a. “P=

b. The letters of the word FATHER be permuted and arranged in a dictionary, find the rank of the word FATHER?

Question 13.
a. The distance of the point P(1,-3) from the line 2y – 3x = 4 is
A) 13
B)  $$\frac { 7 }{ 13 } \sqrt { 3 }$$
C) √13
D) None of these
b. Reduce the equation√3x + y + 8 = 0 in to normal form. Find the values of P and ω
imagee

Question 14.
a. A conic with e = 0 is known as
A) a parabola
B) an ellipse
C) a hyperbola
D) a circle
b. Consider the circle x+ y+ 8x + 10y – 8 = 0
i) Find the centre C and radius ‘r’.
ii) Find the equation of the circle with centre at C and passing through the point (1, 2)

Question 15.
a. What is the perpendicular distance from the point P(6,7,8) from XY plane.
A) 8
B) 7
C) 6
D) 9
b. Find the equation of the set of points P, the sum of whose distances from A(4,0,0) and B(-4,0,0) is equal to 10.

Question 16.
a. Convert 20°40‘ into radian measure.
b. If sin x = $$\frac { 12 }{ 13 }$$ and x is an acute angle, find the value of cos 2x.
c. Prove that
$$\frac { sinx-sin\quad 3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x }$$
= 2 sin x.

Question 17.
a. Write the component statements of the following statement: All prime numbers are either even or odd
b. Verify by the method of contradiction, p = √7 is irrational

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. Write the interval (6,12) in the set-builder form.
b. Draw the Venn diagram of the following sets :
i) A’ ∩ B’
ii)A – B
c. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis? How many like tennis only and not cricket?

Question 19.
a. Write the number of terms in the expansion of (a – b)2n
b. Find the general term in the expansion of (x2– yx)12, x ≠ 0
c. Find the coefficient of xy3 in the expansion of (x + 2y)9

Question 20.
a. The common ratio of the G.P is $$\frac { -4 }{ 5 }$$ and the sum to infinity is $$\frac { -80 }{ 9 }$$. Find the first term.
b. Evaluate:

c. Find the sum of first n terms of the series : 0.6+0.66+0.666+…….to n terms.

Question 21.
a. Find the derivative of xn from first principles.

Question 22.
a. Find the point of intersection of the lines 2x + y = 5 and x + 3y + 8 = 0.
b. Find the equation of a line passing through the point of intersection of the above lines and parallel to the line 3x + 4y =7.
c. Find the distance between these two paralle lines.

Question 23.
a. Find the Mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from mean is ………

b. Calculate mean, variance and standard deviation of the following distribution:

Question 24.
a. In aleap year the probability of having 53 Sundays is ……..

b. Events E and F are such that P (not E or not F) = 0.25, state whether E and F are mutually exclusive.
c. How many points are there in a sample space, if a card is selected from a pack of 52 cards.

a. d) { }
b. P(A)={{1,2,3}, {1,2}, {2,3}, {1,3}, {1}, {2}, {3}, ø}

LHS = a (sinB-sinC) + 6(sinC-sinA) +c (sinA-sinB)
= 2R sin A(sinB-sinC) + 2R sin B (sinC-sinA)+2R sinC (sinA – sinB)
= 2R [sin A sin B – sinAsinC + sinB sinC – sinBsinA + sinCsinA – sin C sinB]
= 2R x 0 = 0 = RHS

a. B) (1, 3) since [2 – 1, 5 – 2]
b. Let the coordinates of a point P changes from (x,y) to (X,Y) when origin is shifted to (1,1)
∴ x = X + 1, y = Y + 1 Substituting in the given equation, we get
(X+1)2 + (X + 1) (7 + 1) -3 (7 + 1)2 -(7 + 1) + 2 = 0
⇒ X2+2X + 1 + XY + X+ Y+ 1-3 (P + 27 + 1) – (7+ 1) + 2 – 0
⇒ X2 – 3Y2 + XY + 3X- 6Y = 0
∴ Equation in new system is
X– 3Y2 + XY + 3X -6Y = 0

a. D
b. The alphabetical order of the word ‘ FATHER are A, E, F, H, R, T No. of words beginning with

a. D
b. Comparing x2 + y1 – 8x +10 y – 12 = 0 with

a. A. 8 [ || perpendicular distance of a point from XY plane = z coordinate
b. Let P(x, y, z) be the point such that PA + PB = 10

a. p: All prime numbers are even. q: All prime numbers are odd
b. Let us assume that √7 is a rational number
∴ √7 = , where a and b are co-prime, i.e. a and b have no common factors, which implies that 7b– a2 ⇒ 7 divides a.
∴ there exists an integer ‘k’ such that a = 7k
a= 49k2 ⇒ 7b= 49k2⇒b2= 7k2 7 divides b.
i.e., 7 divides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition √7 is wrong, is an irrational number.

a. {x : x ∈ R, 6 < x ≤ 12}

a. Number of terms in expansion can be given by 2n + 1
b. General term can be given by

a.  2x + y =5 ……………. (1)
x + 3y = -8………………….. (2)
(1) x 3 – (2) ⇒
6x + 3y = 15 x + 3y = -8
(-) (-) (+)
————-
5x  = 7 7
∴ x = 7/5

b. Slope of the required line, m = $$-\frac { 3 }{ 4 }$$
|| slope of the parallel line Equation of the line is y – y = m (x – x1)

a. b

c. The parallel lines 15x + 20y – 57 = 0 and
3x + 4y – 7 = 0 ⇒15x + 20y – 35=0 x ing by 5
Parallel distance

a. (b) 7/3
b. (not E or not F)
= P(E ‘∪ F’) = P(E ∩ F)’ = 1 = 1P(E ∩ F)
⇒ 0.25 = 1 -P(E n F) ⇒ p(E ∩ F) = 1 -0.25 = 0.75 ≠ 0
⇒ E and F are not mutually exclusive
c. 52

## Kerala Plus One Maths Model Question Paper 2

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any six from question numbers 1 to 7. Each carries three scores.

Question 1.
Find 7+ 77 + 777 + 7777 +…. to n terms.

Question 2.

Question 3.
a. If A and B are two events in a random experiment, then
P(A) + P(B) – P(A ∩ B)
b. Given P(A) = 0.5, P(B) = 0.6 and P
(A ∩ B) = 0.3. Find P( A ∪ B) and P(A’).

Question 4.
Let A = {x:x is an integer, 1/2 < x < 7/2}
B = {2, 3, 4}
a. Write A in the roster form.
b. Find the power set of (A ∪ B)
c. Verify that (A – B )∪ (A ∩ B)=A

Question 5.
(i) Find the value of sin
$$\left( \frac { 3l\pi }{ 3 } \right)$$
(ii) Find the principal and general solutions of the equation cosx =
$$\frac { -\sqrt { 3 } }{ 2 }$$

Question 6.
A committee of 3 persons is to be constituted from a group of 2 men and 3 women.
a. In how many ways can this be done?
b. How many of these committees would consist of 1 man and 2 women.

Question 7.
a. Which one of the following points lies in the sixth octant?
i. (-4, 2, -5)
ii. (-4, -2, -5)
iii. (4, -2, -5)
iv. (4, 2, 5)
b. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

Answer any six from question numbers 8 to 17. Each carries four scores.

Question 8.
Consider the following statement :

a. Prove that P(1) is true.
b. Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n.

Question 9.
a. Write the negation of the statement: “Every natural number is greater than zero”
b. Verify by the method of contradiction : “P : √13 is irrational”

Question 10.
a. The 8th term in the expansion of (√2+√3)
is
i. 27 √2
ii. 27 √3
iii. 72 √2
iv. 72 √3
b. Find the term independent of x in the expansion of

Question 11.
a. In a random experiment, 6 coins are tossed simultaneously. Write the number of sample points in the sample space.

b. Given that P(A’)=0.5. P(B) = 0.6, P
(A ∩ B) = 0.3. Find P(A’) , P(A ∪ B), P(A ∩ B)and P(A ∪ B).

Question 12.
Let U={1,2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 4, 7} and B = {1, 3, 5, 7}
a. Find A ∪ B.
b. Find A’, B’ and hence show that (A ∪B)’ = (A’∩ B’)
c. The power set P(A ∪ B) has elements.

Question 13.
a. Let A= {7, 8} and B = {5, 4, 2} Find A x B.
b. Determine the domain and range of the
relation R defined by R = {(x, y): y = x + 1, x ∈ {0, 1,2, 3,4, 5}}

Question 14.
a. Find the distance between the points (2,-1, 3) and (-2, 1, 3)
b. Find the co-ordinates of the point which divides the line segment joining the points
(-2, 3, 5) and (1, -4,6) internally in the ratio of 2:3.

Question 15. A hyperbola whose transverse axis is X – axis, center (0,0) and the foci (±√10,0) passes through the point (3, 2)
a. Find the equation of the hyperbola.
b. Find its eccentricity.

Question 16.
a. Solve for the natural number n;
12. (n+1) p3 =5. (n+1) p3
b. In how many ways can 7 athletes be chosen out of 12?

Question 17.
Consider the statement: “n(n +1) (2n + 1) is divisible by 6”
a. Verify the statement for n = 2.
b. By assuming that P(k) is true for a natural number k, verify that P(k + 1) is true.

Answer any five from question numbers 18 to 24. Each carries six scores.

Question 18.
a. Match the following:

b. Find the derivatives of tan x using the first principles.

Question 19.
a. Find the equation of the line passing through the points (3, -2) and (-1,4).
b. Reduce the equation √3x + y – 8 = 0 into normal form.
c. If the angle between two lines is π/4 and slope of the line is 1/2, find the slope of the other line.

Question 20.
a. If x is the mean and c is the standard deviation of a distribution, then the coefficient of variation is……..

b. Find the standard deviation for the following data:
xi : 3   8    13    18    23
f:  7   10  15    10    6

Question 21.
a. Which one of the following pair of a. Which one of the following pair of straight lines are parallel?
i. x – 2xy-4 = 0; 2x – 3y – 4 = 0
ii. x – 2y – 4 = 0; x – 2y – 5 = 0
iii. 2x – 3y – 8=0; 3x – 3y – 8 = 0
iv. 2x – 3y – 8 = 0; 3x – 2y – 8 = 0
b. Equation of a straight line is 3x – 4y + 10 = 0.Convert it into the intercept form and write the x-intercept and y-intercept.
c. Find the equation of the line perpen dicular to the line x – 7y + 5 = 0 and having x-intercept 3.

Question 22.
a. If (x+1, y-2) = (3,1), write the values of x and y.
b. Let A={ 1, 2, 3, 4, 5} and B={4, 6, 9} be two sets. Define a relation R from A to B by R={(x, y): x-y is a positive integer}. Find A X B and hence write R in the Roster form.
c. Define the modulus function. What is its domain? Draw a rough sketch.

Question 23.
a. Which among the following is the interval corresponding to the inequality -2 < x ≤ 3 ?
i. [-2, 3]
ii. [-2, 3)
iii. (-2, 3]
iv. (-2, 3)
b. Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3
2x – 3y ≤ 6

Question 24.
a. In how many ways can the letters of the word, PERMUTATIONS be arranged if:
ii. there are always 4 letters between P and S?
b. In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together.
c. How many chords can be drawn through 21 points?

a. P(A) + P(B) – P (A ∩ B) = P (A ∪ B)
b. P(A ∪ B) = P(A) + P(B) – P (A ∩ B)
= 0.5+ 0.6=0.3 = 1.1-0.3 = 0.8
P(A)’= 1- P (A) = 1-0.5 = 0.5

a. Let A = {1, 2,3}
b. A ∪ B = {1, 2, 3,4}
P(A ∪ B)= {1}, {2}, {3}, {4},
{1, 2}, {1, 3}, {1, 4}, {2, 3},
{2, 4}, {3, 4}, {1, 2 ,3}, {1, 2, 4},
{2, 3,4}, {1,3,4}, {1,2, 3, 4},
{(j)} = 24 = 16 elements
c. A-B= {l}, A ∩ B = {2, 3}
(A – B) ∪ (A ∩ B) = {1, 2, 3} = A

a. Required number of ways = 5C3 = 10
b. Number of committees =
2C1 x 3C2 = 2 x 3 = 6

a. i. (-4, 2,-5)
b. Let YZ plane divides the line joining the points A (-2, 4, 7) and B (3, -5, 8) at R (x, y, z) in the ratio k: 1.
Then x coordinates of R = 0.

a. Let p : “Every natural number is greater than zero”. ~p: “ Every natural number is not greater than zero”.
b. Let us assume that √13 is a rational number.√13=a/b, where a and b are co-pnme, i.e., a and b have no common factors, which implies that 13b2= a2 ⇒ 13 divides a. There exists an integer ‘k’ such that a= 13k a2= 169 k2 ⇒ 13b2= 169k2 ⇒ 13k2 ⇒ 13 divides b.
i.e., 13 dvides both a and b, which is contradiction to our assumption that a and b have no common factor. ∴ Our supposition is wrong. ∴ √13 is an irrational number.

a. 26
b. P(A) = 0.5; P(B) = 0.6; P(A ∩ B) = 0.3
P(A’ ) = 1 – P(A) = 1 – 0.5 = 0.5
P(A ∪ B)=P(A)+P(B)-P(A ∩ B)
= 0.5 + 0.6 – 0.3 = 0.8
P( A ∩ B)=l-P P(A ∪ B)= 1-0.8 = 0.2
P(A ∪ B)=l-P(A ∩ B)= 1-0.3 =0.7

U = {1,2, 3, 4, 5,7},
A = {1,2, 4, 7} and B = {1,3, 5, 7}
a. A ∪ B = {1,2, 3, 4, 5, 7}
b. A’ = {3, 5, 6, 8, 9}
B’ = {2, 4, 6, 8, 9}
A ∪ B = {1,2, 3, 4, 5, 7}
(A ∪ B)’ = {6, 8, 9}
A’∩ B’ = {6, 8, 9},
So (A ∪ B)’ = A’∩B’
c. The power set P(A ∪B) has 26 or 64 elements.

a. A = {7, 8} and B = {5, 4, 2}
A x B = {(7, 5), (7, 4), (7,2), (8, 5), (8, 4), (8, 2)}
b. Domain = {0,1, 2, 3, 4, 5}
Range = {1,2, 3, 4, 5, 6}
R = {(0,1). (1, 2), (2, 3), (3, 4),(4, 5), (5, 6)}

Equation of hyperbola is

a. When n = 2,
2 (2+1) (2×2 + 1) = 2 x 3 x 5 = 30 is divisible by 6
b. P(k) = k(k + l)(2k + 1) is divisible by 6
P (k + 1) = (k + l)(k + 2) (2k + 1)
+ (k + 1) (k + 2)2 = (k + 1) (2k +1) k + (k + 1)
(2k + 1) x 2 + (k + 1) (k + 2)
= k (k + 1) (2k + 1) + 2 (k + 1)
[2k + 1 + k + 2]
= k (k + 1) (2k + 1) + 6(k + 1)2
is divisible by 6
∴ P(k + 1) is true

a. ii. x-2y-4 = 0; x-2y – 5 = 0
b. 3x – 4y + 10 = 0; 3x – 4y = -10

c. Slope of the given line is
$$\frac { -A }{ B } =-\frac { 1 }{ -7 } =\frac { 1 }{ 7 }$$
Slope of the required line is -7
Given x intercept of the required line is 3, the point is (3,0).
Hence equation of the required line is
y – 0= -7 (x – 3); y + 7x = 21 or 7x + y – 21 = 0

a. (x+1, y-2) = (3, 1) x+l=3; x=2 y-2 = i; y=3
b. AxB = { (1,4),( 1,6),( 1,9), (2,4), (2,6), (2,9),(3,4),
(3,6), (3,9), (4,4), (4,6) ,(4,9), (5,4), (5,6), (5,9)}
R = {(5,4)}
c. A real function R is to be a modulus function, if f (x) = | x |, x ∈ R, is known as modulus function.

a. ii (-2, 3)
b. 2x + y = 4

Solution region:
2x + y ≥ 4
⇒ 0 ≥ 4, which is false. || by putting x = 0, y = 0
Hence shade the half plane, which does not contain the origin. x + y < 3
⇒ 0 ≥ 3, which is true.
Hence shade the half plane, which contains the origin.
2x – 3y < 6
⇒ 0 ≤ 6, which is true.
Hence shade the half plane, which contains the origin. The common region shown in the figure ’ is the solution region.

a. i. When word start with P and end with S, then there are 10 letters to be arranged of which T appears two times.

ii. When there are always 4 letters between P & S
P & S can be at
1st and 6th place
2nd and 7th place
3rd and 8th place
4th and 9th place
5th and 10th place
6th and 11th place
7th and 12th place
So, P & S will placed in 7 ways & can be arranged in 7 x 2 ! = 14
The remaining 10 letters with 2T’s 10!
can be arranged in$$\frac { 10i }{ 2i }$$=1814400 ways
The required number of arrangements = 14 x 1814400 = 25401600
b. Can be done in 5 ! ways, such that xGxGxGxGxGx
where G represents the seats for girls and cross mark represents the seats for boys = Total number of ways

## Kerala Plus One Maths Model Question Paper 1

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 score each. Answer any 6.

Question 1.
Write the set $$\left\{ \frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } ,\frac { 6 }{ 7 } \right\}$$ r in the set- builder form.
a. If A and B are two sets such that A ⊂ B , then what is A ∪ B
b. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C1 50 to the chemical C2, and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to Chemical C1 but not chemical C2.

Question 2.
A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m CA = 8m, AB = 9m. Lamp post subtends an angle 15° at the poiny B. Determine the height of the lamp post.

Question 3.
Find square root of the complex number 8- i6.

Question 4.
Arathi took 3 examinations in an year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is at least 80 find the minimum mark that she should get in the first examination?

Question 5.
a. A die is thrown until a six comes up. Write down the sample space for this experiment.
b. What is the probability of getting a doublet in throws of a pair of dice.

Question 6.
(a) A hyperbola with a = b is known as…………..

A. rectangular hyperbola
B. isosceles hyperbola
C. equilateral hyperbola
D. None of these

(b) Find the equation of an ellipse whose length of major axis is 26 and foci (± 5, 6)

Question 7.

Questions from 8 to 17 carry 4 score each. Answer any 8.

Question 8.

Question 9.
Let P(n) be the statement : 13 + 23 + 33 +………+n3
$$={ \left[ \frac { n(n+1) }{ 2 } \right] }^{ 2 }$$
a.Verify whether the statement is true for n = 1
b. Prove the result by using mathematical induction

Question 10.
a. Express (5 – 3i)3 in the form a + ib
b. Solve the equation -x+ x – 2 = 0

Question 11.
Solve the folowing linear inequalities graphically:

Question 12.
a. How many 3 digit even number can be formed form the digits 1,2,3,4,5 and 6, if the digits can be repeated?
b. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Question 13.
a. The base of an equilateral triangle with side 2 a lies along they-axis such that the mid-point of the base is at the origin. Find vertices of the triangle….
b. Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6)

Question 14.
a. find the centere and radius of the circle x2+ y– 8x + 10y – 12 = 0
b. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Question 15.
a. If p is the length of perpendicular from the origin to the line whose intercepts on the exes are a and b, then show that

b. If the lines 2x + y-3=0, 5x + ky -3=0 and 3x – y-2=0 are concurrent, find the value of k.

Question 16.
a. Find the octant in which the points (-3,1,2) and (-3,1,-2) lie.
b. Find the coordinates of a point on y-axis which are a distance of 5√2 from the point P (3,-2,5)

Question 17.
a. Write the negation of the following statement: If you do all the exercises in this book, you get an A grade in the class,
b. Verify by the method of contradiction, p: √2 is irrational.

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. Draw the graph of the function f: R→ R defined by f(x) = xx ∈ R
b. If set A has 2 elements and set B has 3 elements, then the number of function from A to B is
(i) 64
(ii) 6
(iii) 9
(iv) 8

Question 19.
a. If sec x = 13/5, x lies in fourth quadrant, find other t-functions.
b. Prove that show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x
c. Find the value of tan π/8

Question 20.
a. Find the sum of the sequence 7, 77, 777,  7777, ………….. to n terms.
b. Find the sum of first n terms of the series: 3 12 + 5 x 22 + 7 x 32+…….

Question 21.
a. Find the middle term in the expansion of

b. Find the term independent in the expansion of

Question 22.
a. Find the derivative of x sin x form first principles.

Question 23.
a. Find mean deviation about median for the following data.

b. Calculate mean, variance and standard deviation of the following distribution:

Question 24.
Four cards are drawn from a well shuffled pack of 52 cards. Find the probability that it contains
a. all aces
b. atmost 2 aces
c. atleast two aces

– 15 – 8i
Let $$\sqrt { 8-6i }$$ = x + iy……….. (1)
Squaring we have,
8 – i6=(x + iy)2 = x2 + i2xy + i2y2 = (x– y2)  +i2xy
Equating the real and imaginary parts, we have
x– y2= 8 ………….. (2)
2xy = – 6 ……………….. (3)
We know that (x+ y2)2
= (x– y2)2 + 4xy2
= (8)2+(-6)2= 64+36 = 100
∴ x+ y= 4m = √100 = 10 ………….. (4)
(2) + (4) we have,
x2 -y = 8 x2 + y= 10 2x2 = 18
x2 = 9 ⇒ x = ± 3
In (4), we have, 32+y2=10 ⇒ y2
=10 – 9 = 1 ⇒ y = ± 1
Since 2xy = -6,
When x = 3, y = -1 and when x = -3, y = 1
3-i and -3 + i are the square roots.

Let the mark in the first exam = x
Mark in the second exam = x+5
Mark in the third exam = x + 10 x + x + 5 + x + 10.

x >75
Minimum mark Arathi should get in the first exam = 75.

a. s = {6,(1,6),(1, 1, 6),….,(2, 6),(2, 1, 6),…. }
b. n (s) = 36
doublets are (1,1), (2,2), (3,3),
(4,4),(5,5) and (6,6)
∴ P (getting a doublet) =  $$\frac { 6 }{ 36 }$$ = $$\frac { 1 }{ 6 }$$

a. C.
b. 2a = 26 => a = 13
foci = (±5,0) => c = 5
But c2 = a2– b2 ⇒ b=a– c= 132-5= 144

a. (5 – 3i)= 5– 3 x 52(3i)+3 x 5(3i)2– (3i)3
= 125 – 225i+ 135i2 – 21 i3
= 125 – 225i+ 135(-1)-27(-i)
= 125 – 225i – 135 + 27i
= -10 – 198i
b. -x+ x + 2 = 0
a = 1 ; b = 1 ; c = 2
D = b2 – 4ac = (1)2 – 4 (-1) (2)
= 1 – 8 = -7 < 0

The shaded region is the solution region.

a. Here unit place can filled in three ways (i.e. by 2, 4, 6), whereas tens and hundred place can be filled in 6 ways.
b. Out of available nine courses, two are compulsory, Hence the student is free select 3 courses out of 7 remaining courses. Then the number if ways of selecting courses out of 7 courses

(a) Let ABC be the given equilateral triangle with side 2a. Assume that base BC lies along the y-axis such that the mid-point of BC is at the origin. i.e., BO = OC = a, where O is the origin Now, it is clear that the coordinates of point B are (-a, 0) and C are (a,0), while the coordinates of point. Using Pythagoras theorem to ΔAOC, we obtain
AC2 = OA2 + OC(2a)2
= OA2+ a2 4a2– a2 = OA2
⇒ OA=3a2 ⇒ OA = √3a

∴ co-ordinates of A are (±√3a ,0). Thus, the vertices of the given equilat­eral triangle are (0, a),(0,-a), and (√3a,0) or (0, a), (0, -a), and (-√3a ,0)
(b) Any line through (-3,5) is y-5 = m(x-(-3)) = m(x + 3) Slope of line joining (2, 5) and (-3, 6) =

∴  slope of a line⊥ to it = 5
∴reqd. line is y-5 = 5(x+3)
⇒ 5x – y + 20=0

a. centre = (-g, -f) = (4, -5)

b. Equation is
(x1 – x) (x – x2)+(y1 – y) (y – y1)
(x – a)(x – 0)+(y – 0)(y – b) = 0
x2-ax + y2 – by = 0
x2 + y2 – ax -by = 0

a. The equaton of line making intercepts a and b on the axes is

(intercept from) ….(i)
Given p = perpendicular distance from

b. Three lines are said to be concurrent, if they pass through a common point, i.e., point of intersection of any two lines lies on the third line. Here given lines are
2x + y – 3 = 0 ……….. (1)
5x + ky – 3 = 0……….. (2)
3x – y – 2 = 0 …………. (3)
Solving (1) and (3) by cross – multipli­cation method, we get,

Therefore, the point of intersection of two lines is (1, 1). Since above three lines are concurrent, the point (1, 1) will satisfy equation (2) so that
5.1+k.1- 3 = 0 ⇒ k = -2.

a. (-3,1,2) – 2nd octant
(-3,1,-2) – 6th octant
b. Let A (0,y,0) be a point on y-axis having distance 5 √2 from (3,-2,5)

⇒ y+ 4y – 12 = 0
⇒ (y + 6) (y-  2) =0
⇒ y = -6,2
∴ A(0,-6,0) and ,4(0,2,0) are the required points

a. If you do not do all the exercises in this book, you will not get an a grade in the class.
b. Let us assume that be rational.
∴ √2 = a/b, where a and b are co-prime,
i.e., a an b have no other common factors except 1.
Then 2b2 = a2 ⇒ 2 divides a.
∴ there exists an integer tk> such that a – 2k
∴ 2b2 = 4k2 ⇒ 4k= 2b= 2k2 = ⇒ b2=⇒ 2 divides b.
i.e., 2 devides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition is wrong.
∴  √2 is an irrational number.

a.

b. (iii) n(b)n(A) =3= 9

a. This is not a G.P., however, we can relate it to a G.P by writing the terms as Sn =7 + 77 + 777 + 7777 + …….. to n terms

b. Let Tn denote the nth term of the given series

a. Here n = 10 is even
Middle term $$\frac { 10 }{ 2 }$$ +1 = 6th term

Since we have to find a term indepen­dent of x, i.e., term not having x, so

a. We have

b. We first make the data continuous by making classes as below :

## Kerala Plus One Maths Improvement Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any 6 questions from question numbers 1 to 7. Each carries 3 scores

Question 1.
a. If A= {2, 3, 4, 5} and B = {4, 5, 6, 7}, then write :
i. A ∪ B ii. A ∩ B
b. Which one of the following is equal to {x : x∈ R, ∂< x ≤ 4 }?
i. {2,3,4}
ii. {3,4}
iii. [2, 4]
iv.(2, 4]

Question 2.
Consider the set
A = {x : x is an integer, 0 ≤ x < 4}
a. Write A in Roser form
b. If B = {5, 6}, then write A x B
c. Write the number of possible relations from A to B

Question 3.
Prove that

Question 4.

Question 5.
Find the polar from of the complex number

Question 6.
How many terms of the GP, 3, 3/2, 3/4,…………………..are needed to give the sum
$$\frac { 3069 }{ 512 }$$ ?

Question 7.
Consider the real valued function

a. Find the domain of f(x).

Question 8.
a. If U = {1, 2, 3,4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}
B = {2, 3, 5, 7}
Verify (A ∪B) = A’ ∩ B’
b. If A and B are two disjoint sets with n(A) = 4 and n(B) = 2, then n (A-B) = …………

Question 9.
Consider the statement P(n) : 1-3 + 32 +……….. $${ 3 }^{ n-1 }=\frac { { 3 }^{ n-1 } }{ 2 }$$
a. Show that P(1) is TRUE
b. Prove by principle of Mathematical induction, that P(n) is TRUE for all n ∈ N

Question 10.
Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3 and
2x – 3y ≤ 6

Question 11.
Find the square roots of the complex number 3 – 4i.

Question 12.
a. Insert five numbers between 8 and 26 such that the resulting sequence is an AP. b. Find the sum to n terms of the series
1 x 2 + 2 x 3 + 3 x 4+…………..

Question 13.
a. Find the equation of the perpendicular bisector of the line joining the points (0, 0) and (-3, 4).
b. Find the coordinates of the point on the line y = 3x-2 that is equidistant from (0,0) and (-3 -4)

Question 14.
a. Reduce the equation x – y = 4 into normal form.
b. Write the distance of this line from origin

Question 15.
a. Find the derivative of f(x) = x Sin x with respect to x.
b. Find the derivative of the function y = √x with respect to x by using first principles.

Question 16.
Consider the points A (3, 8, 10) and B (6, 10, -8).
a. Find the ratio in which the line segment joining A and B is divided by the YZ coordinate plane.
b. Find the coordinates of the point of division.
c. Which coordinate plane divides the line segment AB internally? Justify your answer.

Question 17.
a. Write the contrapositive of the statement: “If the integer n is odd, then n2 is odd”,
b. Prove by the method of contradiction ‘ √7 is irrational’

Answer any 5 questions from question numbers 18 to 24. Each carries 6 scores

Question 18.

find the valueof x and y.
b. Consider the function f (x) = |x| = 3, draw the graph of f (x)
c. Write the domain and range of (x)

Question 19.
a. Find the value of Sin (75°)

b. In the given figure. ∠AOB = 30° and radius of the circle is d units. Find the length of are APB.
c. Find the length of chord AB

Question 20.
a. Find the number words with or without meaning, which can be made by using all the letters of the word GANGA.
b. If these words are written as in a dictionary, what will be the 26th word?
c. A group consists of 4 girls and 7 boys. In how many ways, can a team of 5 members be selected if the team should have at least 3 girls?

Question 21.
a. Write the expansion of (a + b)n.
b. Find the coefficient of xy7in the expansion of (x-2y)12
c. Show that 9n-1 – 8n – 9 is divisible by 64.

Question 22.
Focii of the ellipse in the given figure are (± √12,0) and vertices are (± 4, 0).
a. Find the equation of the ellipse.
b. Write the equation of a circle with centre (0, k) and radius r.
c. The circle in the figure passes through the points A, B and C on ellipse. Find the equation of a circle.

Question 23.
Consider the following table

a. Find the arithmatic mean of marks given in the above data

b. Find the standard deviation of marks in the above data.

c. Find the coefficient of variation.

Question 24.
a. Consider the experiment in which a coin is tossed repeatedly until a head comes up. Write the sample space.
b. If A and B are two events of a sample space with P (A) = 0.54, (P(B) = 0.69 and P (A ∩ B) = 0.35. Find P (A’ ∩ B’).
c. 3 cards are drawn from a well shuffled pack of 52 cards. Find the prohibility that
i. all the 3 cards are diamond.
ii. at least one of the cards is non diamond
iii. one card is king and two are jacks.

a. A ∪ B = {2, 3, 4, 5, 6, 7}
A∩B = {4, 5}
b. iv) (2, 4]

a. A = {0, 1,2,3}
b. A x B = {(0, 5),(0, 6),(1, 5),(1, 6),(2, 5), (2, 6),(3, 5),(3, 6)}
c. No. of possible relations from A to B
= 2mn = 24 x 2 = 256

∴ n = 10

a. A ∪ B = {2, 3, 4, 5, 6, 7, 8}
(A ∩ B)’ = {1, 9}………….(1)
A’= {1, 3, 5, 7, 9}, B’={1, 4, 6, 8, 9} A’∩B’= {1, 9}…………….(2)
From (1) and (2), we have (A + B)’ = A’ ∩ B’
b. n (A – B) = n (A) = 4

a. Let the required line l is perpendicular bisector of the line joining A(0,0) and B (-3, 4).

Since l is perpendicular bisector of AB, it passes through the midpoint of AB.

a. Since the line joining A and Bis divided by the YZ plane, x = 0

∴ the points divides the YZ plane in the ratio 1 : 2 externally.
b. R divides AB in the ratio 1:2 externally,

Since m:n = – z1 : z2 = -10 : -8 = 5:4
XY plane divides the line segment internally.

a. If n2 is not even, then the integer n is not even.
b. Let us assu,e that √7 is a rational number.
√7 =a/b, where a and b are co-prime, i.e., a and b have no common factors. Squaring we have,
7b2 = a2 ⇒ 7 divides a.
∴ Let a = lk
∴a2= 49k2  ⇒ 7b2= 49k2 ⇒ b= 7k⇒7  divides b.
i.e., 7 divides both a and b, which is contradition to our assumption that a and b have no common factor. our supposition is wrong.
∴ √7 is an irrational number.

a. sin 75 = sin (45 + 30) = sin 45 cos 30 + cos 45 sin 30

=1.05 units
The radius of the circle is not given
properly. Type mismatching happened,
c. OA = OB = 2 units.

a. Number of words = $$\frac { 5! }{ 2!2! }$$
= 30
b. If A is fixed, the remaining 4 letters can 4!
be permuted in $$\frac { 4! }{ 2! }$$ = 12 ways.
If G is fixed, the ramaining 4 letters
can be permuted in $$\frac { 4! }{ 2! }$$ = 12 ways.
∴ the 25th word is NAAGG.
∴ the 26th word is NAGAG
c. No. of selections
= 4C7C4C7C4 = 4 x 21 + 1 x 7 = 84 + 7 = 91

a. (± c ,0) = (±√2 , 0) ; (± a, 0) = (± 4, 0)
c= a– b2 ⇒ b2 = a2– c= 16 – 12 = 4
Equation of the ellipse is $$\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 4 }$$ = 1
b.. (x – 0)2+(y – k)2= r2 ⇒ x+ y– 2ky + k– r= 0
c. The co-ordinates of the points are :
A(-4,0), B(4,0) and C(0, -2).
Equation of the circle is
x+ y+ 2gx + 2fy + c = 0 ………….. (1)
(1) passes through A(-4, 0)
: 16 + 0 – 8g + c = 0 …………… (2)
(1) passes through B (4, 0)
: 16 + 0 + 8g + c = 0…………. (3)
passes through C (0, -2)
: 4 + 0-4f + c = 0 ……………… (4)
(2) + (3) ⇒ 32+2c=0
⇒ 2c = -32
⇒ c = -16 when c= -16
⇒ 16 + 0-8g – 16 = 0
⇒- 8g=0 ⇒ g=0
when c=-16 ⇒ 4 + 0-4f – 16 = 0
⇒- 4f = 12 ⇒ f = -3
Equation of the circle is
x+ y+ 2 (0) x + 2(-3) y+ – 16 = 0
⇒ x2 + y2-6y – 16 = 0

24.
a. Sample space = {H, TH, TTH, TTTH, …………………… }
b. P(A’∩B’)= 1-P(A ∪ B)=1 -[P(A) + P(B)-P(A ∩ B)]
=1 – [0.54 + 0.69-0.35] =1-0.88=0.12
c. i. P(all cards are diamond)

## Kerala Plus One Maths Previous Year Question Paper 2017

Time Allowed: 2 hours
Cool off time: 15 Minutes
Maximum Marks: 60

General Instructions to Candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2 hrs.
• Your are not allowed to write your answers nor to discuss anything with others during the ‘cool off time’.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• All questions are compulsory and only internal choice is allowed.
• When you select a question, all the sub-questions must be answered from the same question itself.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Question 1.
Worker population ratio is……………
a. Population / Worker
b. Worker / Population
c. Population / Worker X 100
d. Worker/Population X 100

Question 2.
List any four effects which ‘the miracle seeds’ created in Indian agriculture.

Question 3.
For a classroom discussion, Ashna collected the following information about present In­dia.
a. Infant, mortality rate – 45
b. Life expectancy-66.4
c. Overall literacy level 74.04
d. Compare them with the British period and comments.

Question 4.
Demographic data on birth and death rates in India, a collected and published by………………
a. RG
b. NSSO
c. CSO
d. Labour Bureau

Question 5.
Distinguish between bar diagram and histo­gram. (Hint: Not to draw diagrams)

Question 6.
The various ranks secured by Merin and Kanchana in four medical entrance examinations are

Calculate the rank correlation and interpret the result.

Question 7.
Find the one which is NOT measured for im­proving agricultural market system.
b. Assurance of minimum support price
c. Maintenance of buffer stock
d. Public distribution system

Question 8.
a. Name the system of farming that restores, maintain and enhance Ecological balance,
b. Point out any three merits of it.

Question 9.
Prepare an essay on various policies and pro­grams towards poverty alleviation in India. Do you find any faults in the implementation of these programs? Substantiate.

Question 10.
A value of correlation coefficient (r) =+1.2 in­dicates
a. Perfect+ve correlation
b. High degree of +ve correlation
c. Low degree of +ve correlation
d. Error in calculation

Question 11.
Identify the names of the steps in a project to which you can include the following statisti­cal tools you have studied.

Question 12.
State the two senses in which the word ‘sta­tistics’ is used. Elucidate.

Question 13.
An import substitution policy.
a. Increase in the tax on imported goods
b. Fixing of quotas
c. Enlarge domestic production
d. All of these

Question 14.
a. Name the outcome of the two policy strat­egies of liberalization and privatization,
b. Do you think that Indian agriculture sec­tor was adversely affected by the reform process? Justify.

Question 15.
State to which country the following demo­graphic features belongs to.
(Hint: India, China or Pakistan)
a. Highest annual growth of population
b. Lowest population density.
c. Less urbanization
d. High fertility rate

Question 16.
Observe the graph. It is……..
a. Uni-modal data
b. Bi-model data
c. Multi-modal data
d. None of these

Question 17.
Calculate the Consumer Price Index (CPI)

Question 18.
“Most of the surveys conducted in India are sample surveys”.
Prepare any three reasons to support the above statement.”

Question 19.
Which is NOT a pair?
a. Tapas Majumdar Committee’ – Education
b. Brundtland Commission – Sustainable de­velopment
c. Karve Committee-Agriculture
d. VKRVRao-National income estimation

Question 20.
a. Name the relative measure of standard de­viation.
b. Define SD.
c. Calculate the standard deviation from the following data:

Question 21.
Do India faces challenges in the power sec­tor? Elucidate.

Question 22.
For conducting a survey among 200 house­holds, Anumitha has written the names of all 200 households on pieces of paper, mixed well and 20 names are selected one by one. It is
a. Census method
b. Random sampling
c. Nonrandom sampling
d. None of these

Question 23.
While preparing a frequency distribution from the raw data, name the questions we have to address. Briefly, explain in 1 % pages. (Hint: Four steps in the construction of a frequency distribution)

Question 24.
The heights (in cm) of 11 plants in a garden are

a. Choose the mode.
b.Calculate the mean and median height of the plants, by using the equations.

Question 25.
Which one of the following statements is NOT TRUE about the employment sector in India?
a. 93% workers are in the informal sector.
b. 50% of the workers are self- employed.
c. Disguised and seasonal unemployment exist in the Indian farm sector.
d. During 1972-2010 there was a movement of workers from casual wage to self-empl­oyment.

Question 26.
Define the term, ‘Sustainable development’. Suggest various strategies for attaining it in two pages.

Question 27.
Express your view in the following aspects with reference to the present human capital formation in India.
a. Education for all
b. Gender equity
c. Higher education

Question 28.
The current and base year prices of a group of commodities are Rs. 180 and Rs. 135 re­spectively. It shows
a. price is said to have risen by 38.33%
b. price is decreased by 33.33%
c. price is increased by 133.33%
d. none of these

Worker /population X 100

• Enable India to attain sufficiency in food grains.
• Increased market surplus
• Large-scale increase in production
• Price of food grains declined.
• Government procured surplus products for future use.

a. 218/1000
b. 32 years
c. Less than 16 %

RGI (also give merits for NSSO)

 Bar diagram Histogram Bar diagram comprised agro up of equispaced A histogram is a two dimen­sional diagram Equal width rectangular bars The width may be different Space is left between adjent bar No space is left Draw for discrete and con­tinues variables. Drawn for continuous vari­able only Not help to determine any average Help to determine made

 R1 Exams R2 Rank of Merin Rank of Kanchana (D = R1 R2) d2 KEAM 1 2 -1 1 AIPMT 3 4 -1 1 JIPMER 2 4 -1 1 ALLMS 4 1 3 9 12

a. Organic farming
b. Substitute with locally produced and or­ganic inputs

• More nutritional value
• Pesticide-free
• Highly international demand
• Environment-friendly

1. Rural Employment Generation Programme.
It is implemented through the Khadi and vil­lage Industries Commission (KVIC), To help eligible enterpreneurs to set up village indus­try units. Under this programme, enterpre­neurs can establish village industries by avail­ing of margin money assistance from KVIC and loans from public sector scheduled com­mercial banks, selected regional rural banks. Under REGP, bank appraises the projects as per the scheme and take credit decision.

2. Prime Minister’s Rozgar Yojana (PMRY): In this programme help to set up any kind of enterprise that generates employment to the educated unemployed from low income fami­lies in rural and urban areas.

3. Swarna Jayanthi Shahari Rozgar Yojana (SJSRY)
The urban self-employment Programme and the urban Wage Employment Programme are two special scheme of the SJSRY, initiated in December 1997.

4. National Food for Work Programme (NFWP)
This Programme was introduced February 2001 for five months and was further extend­ed. This programe aims at augmenting food security through wage employment in droug­ht affected rural areas.

5. Swarna Jay at hi Gram Swarozgar Yojana (SJGSY)

It was launched with effect from 1999. As a result of amalgamating certain erstwhile prog­rammes into a single self-employment pro­gramme. This programme aims at promoting micro-enterprises and helping the rural poor into Self Help Groups(SHG). This scheme cov­ers all aspect of self-employment.

6. Mid Day Meals Scheme: In this programme involves provision for free lunch on working days for children in primary and upper primary classes in government education centers. The primary objective of the scheme is to provide hot cooked meal to children of primary and upper primary.

7. National Social Assistance Programme (NSAP): It was introduced on 15 August 1995 as a 100% centrally sponsored scheme for social assistance to poor household affected by old age, death of primary bread earner and mater­nity.

8. Pradhan Mantri Gramodya Yojana (PMGY): It was started in 2001. It aims at improving the standard of living of the rural people by de­veloping five important area health primary education, drinking water, housing and roads.

9. Pradhan Mantri Gram Sadak Yojana (PMGSY): It was nationwide plan in india to provide good all-weather road connectivity to unconnected villages. The scheme has started to change the lifestyle of many villagers.

10.Sampoorna Gramin Rozgar Yojana (SGRY): It was introduced in 2001. Jawahar Gram Samridhi yojana and Employment Assurance Scheme were intergrated into a single yojana. The objective of this yojana is to provide em­ployment opportunity to the surplus Workers. Through the policy towards poverty alleviati­on has evolved in a progressive manner but over the last five and a half decades it has not undergone any radical transformation.

The three major area of concern which preve­nt the successful implementation of the progra­ms, they are:

• These program depend mainly on govern­ment and bank officials for their implementa­tion since such officials are ill motivated, the resources are inefficiently used and wasted.
• Unequal distribution of land and other as­sets due to the benefits have been availed by the non-poor.
• In comparison to the magnitude of poverty, the amount of resource allocated for these programmes is not sufficient.

Error in calculation

b. Analysis on interpretation
c. organisation or presentation of data

In the plural sense:- statitics refers to the sys­tematic collection of numerical facts. It indic­ated information in terms of numbers or nume­rical data such as employment statistics and population statistics.
In the singular sense:- statistics refers to the science of studying statistical methods. It indic­ates the techniques or methods of collecting organising, presenting analysing and inter­preting data.

d. All of these

a. Globalisation
b. Yes, Reduction of public investment. There has been a drastic decrease in the volume of public investment. In the agricultural sector. There has been an acute outback from the Indian government to provide. Sufficient irri­gation facilities, electricity information sys­tem, market linkages and roads.

Removal at subsidies removal subsidies on fertilisers pushed up the cost of production of agriculture. This made forming more expen­sive, thereby, adversely affecting the poor and marginal farmers. Shift towards cash crops and lack of food grai­ns. The export-oriented production strategies led to the shift of agricultural production from food grains to the production of cash crops like cotton jute etc.

Liberalisation and reduction in impart duties on agricultural products. Due to adherence to the to commitment, Indian government re­duced impart duties on agricultural products that forced the poor and marginal farmers to complete with their foreign countries part in international markets.

a. Pakistan
b. China
c. India
d. Pakistan

b. Bi-modaldata

 Item Weight(4%) Base year price Current year price food 50 2000 3000 cloth 15 1000 1200 fuel 25 400 700 Rent 10 500 600
 Item Weight W Base year Price Current year Price R p1/p0l00 WR food 50 2000 3000 150 7500 cloth 15 1000 1200 120 1800 fuel 25 400 700 175 4375 Rent 10 500 600 120 1200 Total 100 14875

Consumer price index = $$\cfrac { \Sigma WR }{ \Sigma W } =\cfrac { 14875 }{ 100 } =148.75$$

• A sample can give recomable, reliable and accurate informations.
• Lower cost
• Shorter time
• More detailed information can be collected as sample is less than population.
• Need smaller loan of enumerators
• Easier to trains and supervise the enum­erators

c. Karve Committee – Agriculture

a. Coefficient of variables
b. Standard Deviation
Standard Deviation: is the positive square root of the mean of squared deviations from mean.
So if there are five values X1, X2, X3,X4and X5, first their mean is calculated. Then devia­tions of the values from mean are calculated. These deviation are then squared. The mean of these squared deviations is the variance. Positive square root of the variance is the standard deviation.
c.

 Marks No. of students X d(x-5) fd fd2 (Fd x d) 0-10 3 5 -30 -90 2700 10-20 5 15 -20 -250 2000 20-30 6 25 -10 100 600 3040 8 35 0 0 0 40-50 10 45 10 100 1000 50-60 1 55 20 20 400 60-70 5 65 30 360 10800 70-80 5 75 40 200 8000 50 430 25,500

Yes.

1. Installed capacity to generate electricity is not sufficient to feed the annuval demand of7%
2. State electricity board are running is losses of Rs,’ 500 billion transmission and distri­bution loss, wrong price, inefficiency etc.
3. Challenge from the part of the private sector and foreign power generates.
4. General public interest due to high tariff and long power

b. Random sampling

• Find the range of data
• Decide the approximate number of classes
• Determine the approximate class interval size
• Decide the starting point
• Determine the remaining class limits
• Distribute the data into respective classes.

During 1972 -2010 there was a movement of workless from casual wage to self-empl­oyment.

It refers to the development strategy to inte­rruption till the resource extraction was not above the rate of regeneration of the resource and the wastes generated were within the assimilating capacity of the environment But today, environment fails to perform its third and vital function of the substance resulting in an environmental crisis. The rising popula­tion of the developing countries and the af­fluent consumption and production stand­ards of the developed world have placed huge stress on the environment in terms of its first two functions.

Strategies for sustainable Development.

1. Use of a non-conventional source of energy: – India heavily, depends on the hydropower plants to meet its power needs. Both of the­se have adverse environmental impacts. Thermal power plants emit large quantities of carbon dioxide, which is a greenhouse gas. It is not used properly.

2. Bio-Composting:-Inorder to increase pro­duction, we have started using chemical fertilisers which are adversely affecting the waterbodies, groundwater system, etc. But again farmers in large numbers have started using organic fertilisers for production.

3. Mini-Hydel Plants:- Mountainous region have streams everywhere, Most of such streams are perennial. Mini-hydel plants use the energy of such streams to move small turbines which generates electrici­ty. Such power plants are more or less envi­ronment friendly.

4. Traditional Knowledge and Practices:- Traditionally, Indian people have close to their environment. If we look back at our agriculture system, healthcare system, ho­using, transport, etc we find that all prac­tices have been environment-friendly.

5. Biopest Control:-With the advent of Gre­en Revolution, the country entered into the use of chemical pesticides to produce more which laid the adverse impacts on soil, wa­ter bodies, milk, meat, and fishes. To meet this challenge, better methods of pest control should be brought. One step is pesti­cides based on plants like neem. Even many animals also help in controlling pests like snakes, peacocks, etc.

6. CNG in Urban Areas:- In Delhi, the use of Compressed Natural Gas as fuel in the public transport system has significantly low­ered air pollution and the air has become cleaner in the last few years.

a. It is still a dream
b. Better than before
c. A few takes

d.None of these

## Kerala Plus One Maths Previous Year Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any six from question nunbers 1 to 7. Each carries three answers.

Question 1.
Find the sum to n terms of the sequence
4 + 44 + 444 +…………

Question 2.
Solve : Sin 2x – Sin 4x + Sin 6x = 0

Sin 2x – Sin 4x + Sin 6x = 0

Question 3.
If A and B are events such that P(A)= 1/4;
P(B) =1/2; P(A ∩ B) = 1\6 then find: 2 6
(a) P(A or B)
(b) P(not A and not B)

Question 4.
In a A ABC, prove that

Question 5.
(a) The maximum value of the function f(x) = Sin x is………
(i) 1
(ii) √3/2
(iii) 1/2
(iv) 2
(b) Prove that,
(Sin x + Cos x)2 = 1+Sin 2x.
(c) Find the maximum value of Sin x + Cos x.

Question 6.
$$\underset { x\rightarrow 2 }{ Lim }$$ [x] = …….
i. 2
ii. 3
iii. 0
iv. does not exist
(b) Evaluate: $$\underset { x\rightarrow 2 }{ Lim }$$ $$\frac { { x }^{ 3 }-\quad { 4x }^{ 2 }+\quad 4x }{ { x }^{ 2 }-4 }$$

Question 7.
Once card is drawn at random from a pack of 52 playing cards . Find the probability that,
(a) the card drawn is black.
(b) the card drawn is a face card.
(c) the card drawn is a black face card

Answer any eight from question numbers 8 to 17. Each carries four scores.

Question 8.
(a) If A={a, b, c}, then write Power Set P(A).
(b) If the numbed of subsets with two elements of a set P is 10, then find the total number of elements in set P.
(c) Find the number of elements in the power set of P.

Question 9.
Consider Venn diagram of the Universal Set
U = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

(a) Write sets A, B in Roster form.
(b) Verify (A ∪ B)=A ∩ B
(c) Find n(A ∩ B).

Question 10.
Consider the following graphs :

(a) Which graph does not represent a function?
(b) Identify the function f(x)=1/x. from the above graphs.
(c) Draw the graph of the function f(x)=(x-1)2 .

Question 11.
The figure shows the graph of a function f(x) which is a semi circle centred at origin.

(a) Write the domain and range of f(x).
(b) Define the function f(x).

Question 12.
a. If 32n+2 – 8n – 9 is divisible by ‘k’ for all n ∈ N is true, then which one of the following is a value of ‘k’ ?
i.8
ii. 6
iii. 3
iv. 12
b. Prove by using the principle of Math­ematical Induction
P(n) = 1+3+32+…………….. +3n-1 = $$\frac { { 3 }^{ n }-1 }{ 2 }$$ is true for all n ∈ N.

Question 13.
(a) Solve the inequality

(b) Represent the solution on a number line.

Question 14.
(a) Find the nth term of the sequence 3,5,7……………..
(b) Find the sum to n terms of the series. 3xl2 + 5 x22 + 7×32+ ……..

Question 15.
Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Question 16.
Consider a point A(4, 8, 10) in space.
(a) Find the distance of the point A from XY – plane.
(b) Find the distance of the point A from X – axis.
(c) Find the ratio in which the line segm­entjoining the point A and B (6,10, -8) is divided by YZ -plane.

Question 17.
(a) Which one of the following sentences is a STATEMENT?
i. 275 is a perfect square.
ii. Mathematics is a difficult subject.
iv. Today is a rainy day.
(b) Verify by method of contradiction: ‘√2 is irrational’.

Answer any five from question numbers 18 to 24. Each carries six scores.

Question 18.
Consider the quadratic equation x2 + x + 1 = 0
(b) Write the polar form of one of the roots.
(c) If the two roots of the given quadratic are α and β . Show that α2 = β .

Question 19.
The graphical solution of a system of linear inequalities is shown in the figure.

(a) Find the equation of the lines L1, L2, L3
(b) Find the inequalities representing the solution region.

Question 20.
(a) Which one of the following has its middle term independent
i.$${ \left( x+\frac { 1 }{ x } \right) }^{ 10 }$$
ii. $${ \left( x+\frac { 1 }{ x } \right) }^{ 9 }$$
iii. $${ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 9 }$$
iv. $${ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 10 }$$
(b) Write the expansion of $${ \left( { x }^{ 2 }+\frac { 3 }{ x } \right) }^{ 4 }$$
(c) Determine whether the expansion of  $${ \left( { x }^{ 2 }+\frac { 2 }{ x } \right) }^{ 18 }$$  will contain a term containg x10.

Question 21.
The figure shows an ellipse $$\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 9 }$$= 1 and a line

(a) Find the eccentricity and focus of the ellipse.
(b) Find the equation of the line
(c) Find the equation of the line parallel to line L and passing through any one of the foci.

Question 22.
(a) Find the derivative of y = Sin x from the first principle.

Question 23.
Find n, if
(a) 12 x (n-1) p3 =5 x (n+1) p3
(b) If npr = 840; nCr = 35 find r.
(c) English alphabet has 5 vowels and 21 consonants. How many 4 letter words with two different vowels and two different consonants canbe formed without repetition of letters?

Question 24.
Consider the following data:

(a) Find the standard deviation of the distribution.
(b) Find the coefficient of variation of the distribution.

S = 4 + 44 + 444 + 4444+ …. to n terms

sin2x – sin4x + sin6x = 0
sin6x + sin2x – sin4x = 0

(a) 1
(b)   (sin x + cosx)2
= sin2x + cos2x + 2sinx cosx
= 1 + sin2x
(c)   Maximum value of sin2x = 1
Maximum value of sinx + cosx
= $$\sqrt { 1+1 } =\sqrt { 2 }$$

(a) A= {3,4,6,10} B = {2,3,4,5,11}
(b) (A∪B)’ = { 1, 7, 8, 9, 12, 13}
A’ = { 1, 2, 5, 7, 8, 9, 11, 12, 13}
B’ = {1, 6, 7, 8, 9, 10, 12, 13 }
A’∩B’ = {1,7, 8, 9, 12, 13}
∴ (A∪B)’ =A’ ∩B’
(c) n(A∩B)’ = n(U)-n(A∩B)=13-2=11

a. (b) or (c)
b. (a)

(a) Domain = [-4,4]
Range = [0,4]
(b) x2 + y2=16
y2= 16-x2
y= $$\sqrt { 16-{ x }^{ 2 } }$$
i.e.,f (x)= $$\sqrt { 16-{ x }^{ 2 } }$$

(a) 8
(b) P(n):1 + 3 + 32 + ……..3n-1 =$$\frac { { 3 }^{ n }-1 }{ 2 }$$
Let P(1): 1 =$$\frac { { 3 }^{ 1 }-1 }{ 2 }$$=2/2=1
Hence, P(1) is true.
P(k): 1 + 3 + 32 +…… + 3k-1=$$\frac { { 3 }^{ k }-1 }{ 2 }$$
To prove that P(k+1) is true. P(k+1):
1 + 3 +32 + + 3i_1 +3k+1-1 =$$\frac { { 3 }^{ k+1 }-1 }{ 2 }$$
⇒ P(k)+3k = $$\frac { { 3 }^{ k+1 }-1 }{ 2 }$$
⇒ $$\frac { { 3 }^{ k }-1 }{ 2 }$$ + 3k= $$\frac { { 3 }^{ k+1 }-1 }{ 2 }$$
= $$\frac { { 3 }^{ k }-1 }{ 2 }$$ + 3k= $$\frac { { { 3 }^{ k } }-1+2\times { 3 }^{ k } }{ 2 }$$
Now, LHS = $$\frac { { { 3\times 3 }^{ k } }-1 }{ 2 }$$ =  $$\frac { { 3 }^{ k+1 }-1 }{ 2 }$$ = RHS
Hence, P(k+1) is true.
Hence, P(n) is true for all n∈N

$$\frac { 2x-1 }{ 3 } \ge \frac { 5(3x-3)-4(2-x) }{ 20 }$$
40x-20 ≥ (15x-10-8+4x)3
40x-20 ≥ -54
40x-57x ≥ -54 + 20
-17x ≥-34
x ≤ 2 ⇒ x∈(-∞, 2)

(a) tn= 3+(n-1)2 = 2n+1
(b) Let Tn denotes the nth term of the given series.
Tn = (nlh term of 3, 5, 7……….. )(nth term of 12, 22, 32…….. )
= [3+(n-1)2].n2 = (2n+1)n2 = 2n3 + n2

Let the equation of the circle be
(x – h)2 + (y – k)2 = r2
Since the circle passes through (4, 1) and (6,5), we have
(4-h)2 + (1 -k)2 = r2……….. (1)
and (6 -h)2 + (5 – k)2 = r2………… (2)
Also since the centre lies on the line 4x + y = 16, we have
4h + k = 16…………. (3)
Solving the equations (1), (2) and (3), we get
h = 3 and k = 4
(4 – 3)2 + (1 – 4)2 = r2
r2=10
Hence, the equation of the required circle is
(x-3)2+1 (y-4)2= 10
x2-6x + 9 + y2-8y + 16-10 = 0
x2 + y– 6x –  8y + 15 = 0

(a) 10 [Z coordinate of the point]
(b) Let P(4,0,0) be a line on the X-axis.
distance = $$\sqrt { { (4-4) }^{ 2 }+{ (8-0) }^{ 2 }+{ (10-0) }^{ 2 } }$$
= $$\sqrt { 64+100 } =\sqrt { 164 } =2\sqrt { 41 }$$
(c) Since the line segment divided the YZ plane, its x coordinate is zero.
So =$$\frac { { mx }_{ 1 }+{ nx }_{ 1 } }{ m+n }$$
⇒ mx2 + nx1=0
$$\frac { m }{ n } =\frac { { -x }_{ 1 } }{ { x }_{ 2 } } =\frac { -2 }{ 3 }$$
⇒m : n=-2 : 3

(a) 275 is a perfect square,
(b) Let -√2 is rational.
$$\sqrt { 2 } =\frac { p }{ q }$$ , p and q have no common factor.
p2 = 2q2
i.e., 2 divides p2 is 2 divides p
∴ p = 2k, p2 = 4k2
2q2 = 4k2, q2 = 2k2
2 divides q2 is 2 divides q.
p and q have a commonfactor 2.

b. The inequalities are: x + y ≤ 4, y ≥ 1, y ≤ x

In (1),3x + 5y-12 = 0

a. Let f[x) = sinx
f(x + h) = sin(x + h)
f (x + h) – f(x)= sin(x + h) – sinx

(a) 12 x (n-1)P3 = 5 x (n+1)P3
12 x (n-1 )(n – 2)(n – 3) = 5 x (n+1 )n(n-1)
12n2 – 6Qn + 72 – 5n2 – 5n = 0
7n2-65n+72 = 0
$$\frac { 65+\sqrt { 4225-2016 } }{ 14 } =\frac { 67647 }{ 14 }$$
$$\frac { 112 }{ 14 } ,\frac { 18 }{ 14 } =8,\frac { 9 }{ 7 }$$
But n cannot be a fraction. n = 8
(b) nP = r! x nCr   840=r! x 35
r! = 24 ⇒ r = 4
Two different vowels can be selected in 5C2 ways .Two different consonents can be selected in 2ICWays.
Total selection 4 letters = 5C2 x 21C2
Total words = 4! x 5C2 x21C2
= 10 x 210 x 24 = 50400