Plus One Maths Model Question Paper 2

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.
  • Read instructions carefully .
  • Read questions carefully before you answering.
  • 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.

Plus One Maths Previous Year Question Papers and Answers

Answer any six from question numbers 1 to 7. Each carries three scores.
Plus One Maths Model Question Papers Paper 2A

Question 1.
Find 7+ 77 + 777 + 7777 +…. to n terms.
Plus One Maths Model Question Papers Paper 2Q1

Question 2.
Plus One Maths Model Question Papers Paper 2Q2

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’).
Plus One Maths Model Question Papers Paper 2Q3

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
Plus One Maths Model Question Papers Paper 2Q4

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 =
\(\frac { -\sqrt { 3 } }{ 2 } \)
Plus One Maths Model Question Papers Paper 2Q5

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.
Plus One Maths Model Question Papers Paper 2Q6

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).
Plus One Maths Model Question Papers Paper 2Q7

Answer any six from question numbers 8 to 17. Each carries four scores.
Plus One Maths Model Question Papers Paper 2B

Question 8.
Consider the following statement :
Plus One Maths Model Question Papers Paper 2Q8
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.
Plus One Maths Model Question Papers Paper 2Q8.1

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”
Plus One Maths Model Question Papers Paper 2Q9

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
Plus One Maths Model Question Papers Paper 2Q10
Plus One Maths Model Question Papers Paper 2Q10.1

Question 11.
a. In a random experiment, 6 coins are tossed simultaneously. Write the number of sample points in the sample space.
Plus One Maths Model Question Papers Paper 2Q11
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).
Plus One Maths Model Question Papers Paper 2Q11.1

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.
Plus One Maths Model Question Papers Paper 2Q12

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}}
Plus One Maths Model Question Papers Paper 2Q13

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.
Plus One Maths Model Question Papers Paper 2Q14

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.
Plus One Maths Model Question Papers Paper 2Q15

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?
Plus One Maths Model Question Papers Paper 2Q16

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.
Plus One Maths Model Question Papers Paper 2Q17

Answer any five from question numbers 18 to 24. Each carries six scores.
Plus One Maths Model Question Papers Paper 2C

Question 18.
a. Match the following:
Plus One Maths Model Question Papers Paper 2Q18
b. Find the derivatives of tan x using the first principles.
Plus One Maths Model Question Papers Paper 2Q18.1

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.
Plus One Maths Model Question Papers Paper 2Q19

Question 20.
a. If x is the mean and c is the standard deviation of a distribution, then the coefficient of variation is……..
Plus One Maths Model Question Papers Paper 2Q20
b. Find the standard deviation for the following data:
xi : 3   8    13    18    23
f:  7   10  15    10    6
Plus One Maths Model Question Papers Paper 2Q20.1

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.
Plus One Maths Model Question Papers Paper 2Q21
Plus One Maths Model Question Papers Paper 2Q21.1

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.
Plus One Maths Model Question Papers Paper 2Q22

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
Plus One Maths Model Question Papers Paper 2Q23

Question 24.
a. In how many ways can the letters of the word, PERMUTATIONS be arranged if:
i. the words start with P and end with S?
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?

Answers

Plus One Maths Model Question Papers Paper 2Q24

Answer 1.
Plus One Maths Model Question Papers Paper 2A1

Answer 2.
Plus One Maths Model Question Papers Paper 2A2

Answer 3.
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

Answer 4.
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

Answer 5.
Plus One Maths Model Question Papers Paper 2A5

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

Answer 7.
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.
Plus One Maths Model Question Papers Paper 2A7

Answer 8.
Plus One Maths Model Question Papers Paper 2A8

Answer 9.
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.

Answer 10.
Plus One Maths Model Question Papers Paper 2A10

Answer 11.
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

Answer 12.
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.

Answer 13.
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)}

Answer 14.
Plus One Maths Model Question Papers Paper 2A14

Answer 15.
Equation of hyperbola is
Plus One Maths Model Question Papers Paper 2A15

Answer 16.
Plus One Maths Model Question Papers Paper 2A16

Answer 17.
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

Answer 18.
Plus One Maths Model Question Papers Paper 2A18
Plus One Maths Model Question Papers Paper 2A18.1

Answer 19.
Plus One Maths Model Question Papers Paper 2A19
Plus One Maths Model Question Papers Paper 2A19.1

Answer 20.
Plus One Maths Model Question Papers Paper 2A20

Answer 21.
a. ii. x-2y-4 = 0; x-2y – 5 = 0
b. 3x – 4y + 10 = 0; 3x – 4y = -10
Plus One Maths Model Question Papers Paper 2A21
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

Answer 22.
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.
Plus One Maths Model Question Papers Paper 2A22

Answer 23.
a. ii (-2, 3)
b. 2x + y = 4
Plus One Maths Model Question Papers Paper 2A23
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.

Answer 24.
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.
Plus One Maths Model Question Papers Paper 2A24
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
Plus One Maths Model Question Papers Paper 2A24.1

Plus One Maths Previous Year Question Papers and Answers

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