Kerala Plus One Question Paper 2024 Maths Commerce

Kerala Board

Question Paper
2024

Reg. No. : ......................................
FY-451 Name : ...........................................

FIRST YEAR HIGHER SECONDARY EXAMINATION, MARCH 2024

Time : 2 Hours
Part – III Cool-off time : 15 Minutes
MATHEMATICS (COMMERCE)
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-451 1 P.T.O.

Answer any 6 questions from 1 to 8. Each carries 3 scores. (6  3 = 18)

1. (i) A  A' = _________. 1

(a) A (b) A'

(c) U (d) 

(ii) If A = {2, 4, 6, 8} and B = {2, 3, 5, 7} then find (A B) and (A  B). 2

2. (i) Is the relation R = {(2, 4), (2, 8), (3, 6), (5, 10)} be a function ? Justify your
answer. 2

(ii) The range of the constant function f(x) = k is _______. 1

2 x  1 3x  1
3. Solve  . Represent the solution on number line.
3 2

4. What is the total number of words formed using all the letters of the word ‘VIRAT’ in
which all vowels come together ?

5. Find the centre and radius of the circle x2 + y2 – 4x + 4y + 7 = 0.

6. (i) lim x3 + x2 + x + 1 = _______. 1
x 1

x100 – 1
(ii) Find lim 50 . 2
x 1 x – 1

FY-451 2

1  8    6  .

3  . (6  3 = 18)

1. (i) A  A' = _________. 1

(a) A (b) A'

(c) U (d) 

(ii) A = {2, 4, 6, 8}  B = {2, 3, 5, 7}   (A B)  (A  B) 

. 2

2. (i) R = {(2, 4), (2, 8), (3, 6), (5, 10)}      ?

  . 2

(ii) f(x) = k      _______ . 1

2 x  1 3x  1
3.       .
3 2

4. ‘VIRAT’        

      ?

5. x2 + y2 – 4x + 4y + 7 = 0   ,  .

6. (i) lim x3 + x2 + x + 1 = _______. 1
x 1

x100 – 1
(ii) lim 50   . 2
x 1 x – 1

FY-451 3 P.T.O.

d
7. (i) (tan x) = 1
dx

d
(ii) (sin x  cos x) = 2
dx

8. Consider the following data :

4, 7, 8, 9, 11, 13, 17, 19.

Find mean deviation about 11 of the given data.

Answer any 6 questions from 9 to 16. Each carries 4 scores. (6  4 = 24)

9. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be universal set

A = {1, 2, 5, 7, 9}, B = {1, 3, 8, 7}

Find the following :

(i) A' and B' 1

(ii) A–B 1

(iii) Verify that (A  B)' = A'B' 2

10. (i) Draw the graph of the function f(x) = | x | + 1. 2

(ii) Write domain and range of above function. 2

FY-451 4

d
7. (i) (tan x) = 1
dx

d
(ii) (sin x  cos x) = 2
dx

8.     :

4, 7, 8, 9, 11, 13, 17, 19.

  11     .

9  16    6  .

4  . (6  4 = 24)

9. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}  

A = {1, 2, 5, 7, 9}, B = {1, 3, 8, 7}

   :

(i) A'  B'  1

(ii) A–B 1

(iii) (A  B)' = A'B'   . 2

10. (i) f(x) = | x | + 1    . 2

(ii)       . 2

FY-451 5 P.T.O.


11. (i) Write the value of tan . 1
4

(ii) Which among the following is equal to sin (135°) ? 1

1 2
(a) (b)
2 2

3 4
(c) (d)
2 2

sin 8 x  sin 6 x
(iii) = tan x. 2
cos 8 x  cos 6 x

12. Let z = (–2 + 3i) + (4 – 5i), then

(i) Express z in a + ib form and then write conjugate of z. 2

1
(ii) Find and write in a + ib form. 2
z

13. (i) The value of nC0 is _______. 1

(a) 0 (b) 1

(c) n (d) –1

(ii) A team of 3 students is to be formed from a group of 2 boys and 3 girls of a
school. In how many ways this can be done ? In how many of these committees
consists of one boy and 2 girls ? 3

14. (i) Number of terms in the expansion of (1 – x)n is _________. 1

(ii) The sum of the indices of a and b in each term of the binomial expansion of
(a + b)n is ________. 1

4
2 x
(iii) Expand    using Binomial theorem. 2
 x 2

FY-451 6


11. (i) tan   . 1
4
(ii)   sin (135°)    ? 1

1 2
(a) (b)
2 2
3 4
(c) (d)
2 2

sin 8 x  sin 6 x
(iii) = tan x  . 2
cos 8 x  cos 6 x

12. z = (–2 + 3i) + (4 – 5i) 

(i) z  a + ib   , z   . 2

1
(ii)   a + ib  . 2
z

13. (i) nC   _______ . 1
0

(a) 0 (b) 1
(c) n (d) –1
(ii)  2  3      3
   .   
   ?    
 2      ? 3

14. (i) (1 – x)n      _________ . 1

(ii) (a + b)n     a  b  
  ________ . 1

4
2 x
(iii)         . 2
 x 2
FY-451 7 P.T.O.

15. Find co-ordinates of foci, the vertices, length of latus rectum, length of major axis of
x 2 y2
the ellipse  = 1.
9 4

16. (i) Which of the following points lies on XY-plane ? 1

(a) (0, 1, 1) (b) (1, 0, 1)

(c) (1, –1, 0) (d) (1, 0, –1)

(ii) Let P(–2, 3, 5), Q(1, 2, 3), R(7, 0, –1) are three points in space

(a) Find PQ, QP and PR. 2

(b) Check whether the points are collinear. 1

Answer any 3 questions from 17 to 20. Each carries 6 scores. (3  6 = 18)

n(n  1)
17. (i) The nth term of a sequence is an = . Write 6th term. 1
n2

(ii) Find 10th term of the G.P. 1, 3, 9, …….. 1

(iii) Find sum of the sequence 6, 66, 666, ..... to n terms. 4

18. (i) y = 3 is a line parallel to _________. 1

(a) x=y (b) x=0

(c) x=3 (d) y=0

(ii) A line l1 through the points (–2, 6) and (4, 8) is perpendicular to the line l2

through the points (8, 12) and (x, 24). Find the values of x. 3

(iii) Find the distance of the point (3, –3) from the line 3x – 4y – 26 = 0. 2

FY-451 8

x 2 y2
15.  = 1   , ,  
9 4
,     .

16. (i)   XY-plane     ? 1

(a) (0, 1, 1) (b) (1, 0, 1)

(c) (1, –1, 0) (d) (1, 0, –1)

(ii) P(–2, 3, 5), Q(1, 2, 3), R(7, 0, –1)   .

(a) PQ, QP, PR   2

(b)    . 1

17  20    3 
. 6  . (3  6 = 18)

n(n  1)
17. (i)   n-  an =  6-  . 1
n2

(ii) 1, 3, 9, ……..   10-  . 1

(iii) 6, 66, 666, .....   n   . 4

18. (i) y = 3   _________  . 1

(a) x=y (b) x=0

(c) x=3 (d) y=0

(ii) (–2, 6), (4, 8)       l1 (8, 12),

(x, 24)       l2  .

 x   . 3

(iii) (3, –3)   3x – 4y – 26 = 0     
 . 2

FY-451 9 P.T.O.

19. Calculate mean, variance and standard deviation of the following data :

Class 0-10 10-20 20-30 30-40 40-50

Frequency 3 9 18 15 5

20. (i) If E and F are two events associated with the same random experiment such that
2 3 1
P(E) = , P(F) = , P(E  F) =
7 7 7

Find (a) P(E or F) 2

(b) P(not E and not F). 2

(ii) A committee of 3 persons is selected from a group of 3 men and 3 women. What
is the probability of that the committee will have 3 men ? 2

_____________

FY-451 10

19.     , 
  .

 0-10 10-20 20-30 30-40 40-50

 3 9 18 15 5

20. (i) E  F        .

2 3 1
P(E) = , P(F) = , P(E  F) =   .
7 7 7

(a) P(E or F) 2

(b) P(not E and not F). 2

(ii) 3  3      3   

. 3    
  ? 2

_____________

FY-451 11 P.T.O.

FY-451 12

QUESTION PAPERS
GET PREVIOUS YEAR QUESTION PAPERS FOR ALL CLASSES FOR CBSE, ISCSE, ISC AND ALL ALL
STATE BOARDS HERE AT

Andhra Pradesh Board Question Papers
BOARD
WISE Assam Board Question Papers
Bihar Board Question Papers
Chhattisgarh Board Question Papers
Goa Board Question Papers
Gujarat Board Question Papers
Haryana Board Question Papers
Himachal Pradesh Board Question Papers
J&K State Board Question Papers
Jharkhand Board Question Papers
Karnataka Board Question Papers
Kerala Board Question Papers
Madhya Pradesh Board Question Papers
Maharashtra State Board Question Papers
Manipur Board Question Papers
Meghalaya Board Question Papers
Mizoram Board Question Papers
Nagaland Board Question Papers
Orissa Board Question Papers
Punjab Board Question Papers
Rajasthan Board Question Papers
Tamil Nadu Board Question Papers
Telangana State Board Question Papers
Tripura Board Question Papers
Uttarakhand Board Question Papers
Uttar Pradesh (UP) Board Question Papers
West Bengal (WB) Board Question Papers