CBSE Class 12 Mathematics Compartment Question Paper 2024 with Answer Key (Set 1 - 65/S/1)

Question 1:

If X, Y and XY are matrices of order 2 × 3, m × n, and 2 × 5 respectively, then the number of elements in matrix Y is:

• (A) 6
• (B) 10
• (C) 15
• (D) 35

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Question 2:

For the function f(x) = x³, x = 0 is a point of:

• (A) local maxima
• (B) local minima
• (C) non-differentiability
• (D) inflexion

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Question 3:

The greatest integer function defined by f(x) = [x], 1 < x < 3 is not differentiable at x =:

• (A) 0
• (B) 1
• (C) 2
• (D) 3/2

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Question 4:

If the radius of a circle is increasing at the rate of 0.5 cm/s, then the rate of increase of its circumference is:

• (A) 2π/3 cm/s
• (B) π cm/s
• (C) 4π/3 cm/s
• (D) 2π cm/s

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Question 5:

The area (in sq. units) of the region bounded by the curve y = x, x-axis, x = 0 and x = 2 is:

• (A) 3/2
• (B) log 2 / 2
• (C) 2
• (D) 4

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Question 6:

The number of arbitrary constants in the general solution of the differential equation dy/dx + y = 0 is:

• (A) 0
• (B) 1
• (C) 2
• (D) 3

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Question 7:

Given that f(x) = log x / x, find the point of local maximum of f(x).

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Question 8:

Find the general solution of the differential equation y dx – x dy + (x log x) dx = 0.

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Question 9:

It is known that 20% of the students in a school have above 90% attendance and 80% of the students are irregular. Past year results show that 80% of students who have above 90% attendance and 20% of irregular students get ‘A’ grade in their annual examination. At the end of a year, a student is chosen at random from the school and is found to have an ‘A’ grade. What is the probability that the student is irregular?

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Question 10:

Using integration, evaluate the area of the region bounded by the curve y = x^2, the lines y = 1 and y = 3, and the y-axis.

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