ISC Class 11 Maths Half Yearly Sample Paper 2025: Download Free PDF

Questions

Section A (65 Marks)

1

[2]

2

In sub- parts (i) to (x) choose the correct options and in Sub-parts (xi) to (xv) answer the questions as instructed                   [ 1x15]

(i) In this question there are two statements . Statement I and Statement II . Choose which one of

the following options is correct ?

(a) Statement I is false but Statement II is true

(b) Both the statements are true and statement II is the correct explanation of statement I .

(c) Both the statements are true and statement II is not the correct explanation of statement I .

(d) Statement I is true but Statement II is false

(ii) 

(iii) 

(iv) If there are 10 persons in a party , and if each two of them shakes hands with each other , how many hand shakes happen in the party .

(v) 

(vi) 

Choose the correct answer ?

(a) Statement 1 is correct but statement 2 is incorrect .

(b) Statement 1 is incorrect but statement 2 is correct .

(c) Both statement 1 and statement 2 are correct.

(d) Both statement 1 and statement 2 are incorrect .

(vii) In the question , a statement of Assertion (A) is followed by a statement of Reason (R).

Choose the correct answer .

(a) Both A and R are true but R is not the correct explanation of A

(b) A is true but R is false

(c) Both A and R are true and R is the correct explanation of A

(d) A is false but R is true .

Assertion (A) : If a licence plate contains three letters of english alphabet followed by any three digits , then the total number of different car licence plates is (26)3 x 900 ( if repetitions are allowed)

Reason (R) : The number of permutations of n different things taken r at a time when each

things may be repeated any number of times is nr.

(viii)

(ix) Find the equation of the circle which touches the x-axis at the origin and whose radius is 5.

(x) 

(xi)

(xii)

(xiii)

(xiv)

(xv)

3

4

(i) Find the value of Cos6x in terms of Cosx .

OR

(ii) Prove that : 1 + Cos2x + Cos4x + Cos6x = 4 Cosx . Cos2x . Cos3x .

5

6

7

(i) A student has to answer 10 questions , choosing at least 4 from each of parts A and B . If there are 6 questions in Part A and 7 questions in Part B in how many ways can the student choose 10 questions ?

OR

(ii) How many words , can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together ?

8

(i) Find the value of Cos6x in terms of Cosx .         [2]

OR

9

(i) Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the

point ( 2,3 ).

OR

(ii) Find the equation of line passing through the point of intersection of lines 2x – 5y + 3 = 0 and 4x- 3y – 1 = 0 and making an angle of 45 degree with positive direction of x-axis.

10

11

(i) Solve the equation : |z + 1| = z + 2 ( 1 + i )

OR

(ii) Find the cube root of – 27 and show that the sum of the cube roots is zero.

12

OR

In how many ways can the letters of the word PERMUTATIONS be arranged if there are always 4 letters between P and S ?

11

Calculate the mean , mean deviation about mean and standard deviation (By step deviation method ) of the following data :

SECTION B (15 Marks)

15

16

(6) 

17

In sub-parts(i) and (ii) choose the correct options and in sub-part (iii) to (v), answer the questions as instructed .                         [1x5]

(i) In this question , a statement of Assertion (A) is followed by a statement of Reason (R) . Choose the correct answer of the following choices .

(a) (A) is false but (R) is true .

(b) Both (A) and (R) are true but (R) is not the correct explanation of (A) .

(c) Both (A) and (R) are true and (R) is the correct explanation of (A) .

(d) (A) is true but (R) is false .

Let the centre of an ellipse is at (0,0)

(ii)

Section C (15 Marks)

18

(i) Calculate Spearman’s rank correlation for the following data :

X : 15 18 21 24 27 30 36 39 42 48

Y : 25 25 27 27 31 33 35 41 41 45

(ii) Taking 2015 as the base year with an index number 100 ,calculate an index number for 2020, based on weighted average of price relative from the table:

19

Calculate the 3 yearly moving average and draw the moving average graph.                                   [6]

Year : 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Variable: 1.5 1.8 1.9 2.2 2.6 3.7 2.2 6.4 3.6 5.4

20

In Sub-parts (i) and (ii) choose the correct options and in subparts (iii) to(v) answer the questions as instructed.

(i) This question consists of two statements . Statement 1 and Statement 2. Read the statements

carefully and choose the correct answer from the four options.

(a) Statement 1 is true , Statement 2 is false .

(b) Both the statements are true and statement 2 is the correct explanation of statement 1 .

(c) Statement 1 is false , Statement 2 is true .

(d) Both the statements are true and statement 2 is not the correct explanation of statement 1 .

(ii) If the median of the numbers 6 , 14 , 15 , 17 , x – 1 , x + 2 , 29 , 32 , 35 , 45 written in ascending

order is 21.5 , then the value of x is

(a) 20 (b) 21 (c) 22 (d) 21.5

CHECK: ISC Class 11 Half Yearly Maths Sample Paper 2025; Download Free PDF