ISC Class 12 Maths Sample Paper For Half Yearly Exam 2025

Question No.

1.

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

SECTION – A

i.

ii.

iii.

Iv.

V.

Vi.

Vii.

Viii

Ix.

x.

Xi.

Xii. A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve a problem selected at random from the book ?

Xiii.

Xiv. 

xv. Find the rate of change of the area of a circle with respect to its radius r, when r = 6 cm

2.

3.

4.

Aman owns a Tea stall that serves kachuri , Samosas and juice bottles . On a particular day , 100

items in total were sold . The number of kachuri’s sold was thrice the number of samosas sold . Also ,

the number of samosas sold was10 more than the number of juice bottles sold .

(i) Form a set of simultaneous equationsfor all above information .

(ii) Solve the set of equations formed by matrix method .

(iii) Hence , find the number of items sold in each category .

5.

(i) In an office three employees Ashish , Annu and Prantik process incoming copies of a certain

form . Ashish process 50% of the forms . Annu process 20% and Prantik the remaining 30% of the

forms . Ashish has an error rate of 0.06 . Annu has an error rate of 0.04 and Prantik has an error rate

0.03 .

(a) What is the probability that Annu processed the form and committed an error?

(b) What is the total probability of committing an error in processing the form ?

(c) What is the conditional probability that an error is committed in processing given that Ashish do

not processed the form .

OR

(ii) There are two bags each bag contains 8 red balls , 5 green balls and 7 white balls. Aman takes

one ball from 1st bag and places it in 2nd bag. Then he draws two balls from 2nd bag simultaneously .

(a) What is the probability of Aman selecting a green ball from 1st bag .

(b) After Aman transfers a ball from 1st to 2nd bag , what is the probability of drawing one red ball and

one green ball simultaneously from 2nd bag .

6.

(i) A refrigerator company produces compressor . It has three machines M1, M2 and M3 and which

produce 50% , 25% and 25% respectively of the total daily output of compressor . If it is known that

4% of the compressor produced by each of the machines M1 and M2 are defective . Also , 5% of the compressor produced by machine M3 are defective .

(a) Find the probability of compressor produced by machine M1.

(b) What is the probability of choosing a defective compressor from a day’s production at the company ?

(c) A defective compressor is chosen , what is the probability that it was produced by machine M1 ?

OR

(ii) A wholeseller sales three types of top quality seeds A , B and C from his shop. They are sold as a mixture , the proportions of mixture are 4 : 4 : 2. The germination rates of A , B and C are 45% ,

60% and 35% respectively.

(a) Find the probability that the seed ‘C’ germinate.

(b) Find the probability that top quality seed germinate.

(c) Calculate the probability that the chosen seed is of B, given that a randomly chosen seed does not germinate .

7.

8.

9.

10.

11.

12.

13.

14.

Section B

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

15.

I.

ii.

Iii.If the position vectors of the vertices A , B and C of a ∆ ABC be ( 1,2,3 ), ( -1,0,0 ) and ( 0,1,2 ) respectively then find angle ABC .

Iv. Find the direction cosines of the line segment joining the points A (7,-5,9) and B ( 5,-3,8 )

V. 

16.

Find the equation of the plane passing through the point ( 1,1,-1 ) and perpendicular to the planes x +

2y + 3z = 7 and 2x – 3y + 4z = 0 .

17.

18.

SECTION – C

19.

(i) For the data (1,2 ) , (2,40 , (3,8) , (4,7) , ( 5,10 ) , ( 6 ,5 ) ,( 7 ,14 ) , ( 8 , 16 ) , ( 9,2), ( 10 , 20 ) .Write down the lines of regression of x on y and y on x .Also predict the value of y when x = 6.5 .

OR

(ii) The line of regression of marks in Accountancy (x) and marks in Economics (y) for a class of 50

students is 3y – 5x + 180 = 0 . The average score in Economics is 44 and the variance of marks in Accountancy is ଽ ଵ଺ th of the variance of marks in Economics . Find the average score in Accountancyand also the coefficient of correlation between marks in Accountancy and Economics .

20.

A company owner purchases two types of machines A and B , for his company. The requirements and limitations for the machines are as follows :

He has an area of 9000 sq.m available and 72 skilled man who can operate the machines . How many machines of each type should he buy to maximize the daily out put ?

21.

22.