Kerala Plus One Question Paper 2024 Math Science

Kerala Board

Question Paper
2024

Reg. No. : ......................................
FY-427 Name : ...........................................

FIRST YEAR HIGHER SECONDARY EXAMINATION, MARCH – 2024

Part – III Time : 2 Hours
MATHEMATICS (SCIENCE) Cool-off time : 15 Minutes
Maximum : 60 Scores

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 questions and to plan your answers.
 Read questions carefully before answering.
 Read the instructions carefully.
 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.

  :
    15  ‘  ’ .
 ‘  ’    
 .
      .
    .
  , , ,   
.
   .
    .
     
    .

FY-427 1 P.T.O.

Answer any 6 questions from 1 to 8. Each carries 3 scores. (6  3 = 18)
1. (i) If A = {1, 2, 3} and B = {1, 4}, then the number of subsets of A  B is (1)
(a) 52 (b) 62
(c) 25 (d) 26
x 2  2 2
(ii) If   1, y –    – ,  , then find x and y. (2)
3 3  3 3

2. (i) cos (x + y) + cos (x – y) = _________. (1)
 3   3 
(ii) Prove that cos   x  + cos  – x  = – 2 cos x. (2)
 4   4 

x x x
3. (i) Solve the inequality x + +  10 + . (2)
2 3 6
(ii) Mark the solution in a number line. (1)

4. (i) nC = _________. (1)
r
n! n!
(a) (b)
r! (n – r)!
n! n(n – 1)
(c) (d)
r! (n – r)! r!
(ii) In how many ways a committee consisting of 3 men and 2 women, can be chosen
from 7 men and 5 women ? (2)

5. (i) Sum of all coefficients in the Binomial expansion of (1 + x)n is _________. (1)
4
 x 3
(ii) Using Binomial theorem expand    . (2)
3 x

6. Consider the line L1 : 3x – 4y + 12 = 0 and a point A(2, –3).
(i) Find the equation of the line passing through A and parallel to the given line L1. (2)
(ii) Find the distance from the origin to the given line L1. (1)

7. Find the coordinates of focus, equation of directrix and length of latus rectum of the
parabola x2 = 12y.

FY-427 2

1  8    6  .
3  . (6  3 = 18)
1. (i) A = {1, 2, 3}, B = {1, 4}  A  B    (1)
(a) 52 (b) 62
(c) 25 (d) 26
x 2  2 2
(ii)   1, y –    – ,  ,  x, y  . (2)
3 3  3 3

2. (i) cos (x + y) + cos (x – y) = _________. (1)
 3   3 
(ii) cos   x  + cos  – x  = – 2 cos x  . (2)
 4   4 

x x x
3. (i) x+ +  10 +    . (2)
2 3 6
(ii)   . (1)

4. (i) nC = _________. (1)
r
n! n!
(a) (b)
r! (n – r)!
n! n(n – 1)
(c) (d)
r! (n – r)! r!
(ii) 7  5     3  2 
     ? (2)

5. (i) (1 + x)n     
_________ . (1)
4
 x 3
(ii)       . (2)
3 x

6. L1 : 3x – 4y + 12 = 0   A(2, –3)   .
(i) A    L1  
   . (2)
(ii) L1       . (1)

7. x2 = 12y   ,  , 
   .

FY-427 3 P.T.O.

n n
8. (i) lim x – a = ________. (1)
xa x –a

lim x n – 2n
(ii) If x  2 = 32, then find the value of n. (2)
x–2

Answer any 6 questions from 9 to 16. Each carries 4 scores. (6  4 = 24)
9. (i) A  A' = __________. (1)
(ii) If U = {1, 2, 3, 4, 5, 6}, A = {2, 3, 4} and B = {2, 3, 4, 6}, then verify that
(A  B)' = A'  B'. (3)

1
10. (i) Draw the graph of the function, f :  – {0}   defined by f(x) = . (2)
x

(ii) Find the domain and range of f(x) = 9 – x2 . (2)

11. (i) Express (1 – i)6 in x + iy form. (2)
1– i
(ii) Find the coordinates that represent the complex number in the argand plane. (2)
1 i

12. (i) If nPr = 840 and nCr = 35, then find the value of r. (2)
(ii) Find the number of permutations of the letters of the word ATTITTUDE. (2)

13. The vertices of PQR are P(l, 0), Q(5, 4) and R(–l, 4).
(i) Find the equation of the line representing the side PQ. (2)
(ii) Find the equation of the line through R and perpendicular to the side PQ. (2)

14. An ellipse has its foci on ( 4, 0) and vertices at ( 5, 0)
(i) Find the length of the minor axis. (1)
(ii) Find the length of the latus rectum and eccentricity of the ellipse. (2)
(iii) Also write the equation of the ellipse. (1)

15. (i) Give an example of any one point which lie in second octant. (1)
(ii) Show that the points A(0, 7, 10), B(–l, 6, 6) and C(–4, 9, 6) are the vertices of a
right angled triangle. (3)

FY-427 4

n n
8. (i) lim x – a = ________. (1)
xa x –a

lim x n – 2n
(ii) If x  2 = 32  n   . (2)
x–2

9  16    6  .
4  . (6  4 = 24)
9. (i) A  A' = __________. (1)
(ii) U = {1, 2, 3, 4, 5, 6}, A = {2, 3, 4}, B = {2, 3, 4, 6} 
(A  B)' = A'  B'  . (3)

1
10. (i) f :  – {0}  , f(x) =    . (2)
x
(ii) f(x) = 9 – x 2    . (2)

11. (i) (1 – i)6  x + iy   . (2)
1– i
(ii)       
1 i
 . (2)

12. (i) nPr = 840  nCr = 35   ‘r’   . (2)
(ii) ‘ATTITTUDE’     
  . (2)

13. PQR P(l, 0), Q(5, 4), R(–l, 4) 
(i) PQ      . (2)
(ii) R  PQ      
. (2)

14.    ( 4, 0)   ( 5, 0)  .
(i)    . (1)
(ii)     . (2)
(iii)   . (1)

15. (i)       
. (1)
(ii) A(0, 7, 10), B(–l, 6, 6), C(–4, 9, 6)    
 . (3)

FY-427 5 P.T.O.

16. A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the
probability that
(i) All the three balls are white (1)
(ii) All the three balls are red (1)
(iii) One ball is red and two balls are white (2)

Answer any 3 questions from 17 to 20. Each carries 6 scores. (3  6 = 18)
1 – tan 2 15º
17. (i) = ________. (1)
1  tan 2 15º
1 3
(a) (b)
3 2

(c) 2 (d) 3
sin 3x – sin x
(ii) Prove that = 2 sin x. (2)
cos2 x – sin 2 x
1 1 
(iii) If tan  = and tan  = , then show that  +  = . (3)
2 3 4

18. (i) Which term of the G.P. 2, 8, 32, ...... is 32768 ? (2)
(ii) The sum of first three terms of a G.P. is 14 and sum of next three terms is 112.
Find the common ratio, first term and the sum to first n terms of the G.P. (4)

1
19. (i) Using first principle find the derivative of f(x) = . (3)
x

d  x 2  1 
(ii) Find . (3)
dx  x 2  1 
 

20. (i) Find the mean deviation about mean of the following data :
4, 7, 8, 9, 10, 12, 13, 17. (2)
(ii) Find the variance of the following frequency data : (4)

Class 4–8 8 – 12 12 – 16 16 – 20

Frequency 3 6 4 7

______________

FY-427 6

16.   8  , 5   .  
     .
(i)    . (1)
(ii)   . (1)
(iii)       . (2)

17  20    3  .
6  . (3  6 = 18)
1 – tan 2 15º
17. (i) = ________. (1)
1  tan 2 15º
1 3
(a) (b)
3 2
(c) 2 (d) 3
sin 3x – sin x
(ii) = 2 sin x  . (2)
cos2 x – sin 2 x
1 1 
(iii) tan  = , tan  =   +  =  . (3)
2 3 4

18. (i) 2, 8, 32, ......  G.P.    32768 ? (2)
(ii)  G.P.      14   
  112   ,  ,  n
   . (4)

1
19. (i)    f(x) =   
x
. (3)
d  x 2  1 
(ii) . (3)
dx  x 2  1 
 

20. (i)       
.
4, 7, 8, 9, 10, 12, 13, 17. (2)
(ii)     . (4)
Class 4–8 8 – 12 12 – 16 16 – 20
Frequency 3 6 4 7
______________

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