A school offers students the choice of three modes for attending classes:
• Mode A: Offline (in-person) – 40% of students
• Mode B: Online (live virtual classes) – 35% of students
• Mode C: Recorded lectures – 25% of students
After a feedback survey:
• 20% of students from Mode A reported the class as “Excellent”
• 30% from Mode B rated it as “Excellent”
• 50% from Mode C rated it as “Excellent”
A student is selected at random from the entire group, and it is found that they rated
the class as “Excellent.”
(a) Represent the data in terms of probability. Define the events clearly.
(b) Using Bayes’ Theorem, find the probability that the student attended the
Recorded lectures (Mode C), given that they rated the class as “Excellent.”
(c) Interpret your result. Which mode has the highest likelihood of being chosen
if a student says “Excellent”?
----------------------------------------------------------------------------------------------------------------------
ISC (CLASS XII) SPECIMEN QUESTION PAPER 2026

Evaluate: ∫ ( log x ) dx
 x -3 0 
symmetric matrix? Question 9

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
If A =   , then A is: (iv) ∫ 2 dx is equal to:
0 0  0 x +1

Write the smallest equivalence relation from the set
cos x
A to A, where A = {1, 2, 3}. (i) Evaluate: ∫ dx
3cos x - 5
 0 1 -2 
 OR

For what value of x, is A =  -1 0 3  a skew

2] 5 10 2  2 x +1 3x 
Statement 1: If ‘A’ is an invertible matrix, then (A2)-1
of the differential equation (1 + x2) dy + (1 + y2)
= (A-1)2
dx = 0
Statement 2: If ‘A’ is an invertible matrix, then |A-1|

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
Which of the following is a homogenous differential -2
equation? (c) (d) 0
(a) (4x2 + 6y + 5) dy - (3y2 + 2x + 4) dx = 0