CBSE Class 12 Maths Answer Key 2024: On March 9, 2024, the CBSE Class 12 Mathematics Paper was administered. Generally speaking, students may feel anxious about the number of questions they answered correctly after taking the exam. The right answers to every question on the test are included in the CBSE Class 12 Maths answer key 2024. The solution key is available for students to use in estimating their likely scores.
Following the exam, all sets of the class 12 Mathematics answer key 2024 were made available on this page by our highly qualified teachers. However, students need to remember that the solution key cannot always be accurate and to double-check with the sources.CBSE Class 12 Maths Question Paper PDF
1. If the sum of all the elements of a 3 x 3 scalar matrix is 9, then the product of all its elements is:
(A) 0 (B) 9 (C) 27 (D) 729Answer: (C) 27
2. Let f: R+ [5, ∞) be defined as f(x) = 9×2 + 6x – 5, where R, is the set of all non-negative real numbers. Then, f is:
(A) one-one (B) onto (c) bijective (D) neither one-one nor ontoAnswer: (A) one-one
5. The function f(x) = x³-3x² + 12x – 18 is:
(A) strictly decreasing on R (B) strictly increasing on R (C) neither strictly increasing nor strictly decreasing on R (D) strictly decreasing on (-∞, 0)Answer:(B) strictly increasing on R
7. The differential equation dy dx differential equation, if F(x, y) is: = F(x, y) will not be a homogeneous
(A) cos x – sin (y/x) (B) y/x (C) (x²+y²)/xy (D) cos²(x/y)Answer:(A) cos x – sin (y/x)
9. The coordinates of the foot of the perpendicular drawn from the point (0, 1, 2) on the x-axis are given by:
(A) (1, 0, 0) (B) (2, 0, 0) (C) (√5, 0, 0) (D) (0, 0, 0)Answer:(C) (√5, 0, 0)
10. The common region determined by all the constraints of a linear programming problem is called:
(A) an unbounded region (B) an optimal region (C) a bounded region (D) a feasible regionAnswer:(D) a feasible region
11. Let E be an event of a sample space S of an experiment, then P(S|E) =
(A) P(S∩E) (B) P(E) (C) 1 (D) 0Answer:(C) 1
12. If A = [ajj] be a 3 x 3 matrix, where ajj = i – 3j, then which of the following is false?
(A) a11 < 0 (B) a12 + a21= – 6 (C) a13 > a31 (D) a31= 0Answer:(C) a13 > a31
13. The derivative of tan-1 (x2) w.r.t. x is:
(A) x/1+x4 (B) 2x/1+x4 (C) – 2x/1+x4 (D) 1/4 1+x4Answer:(B) 2x/1+x4
14. The degree of the differential equation (y”)2 + (y’)³ = x sin (y’) is:
(A) 1 (B) 2 (C) 3 (D) not defined.Answer:(D) not defined
18. If a line makes an angle of 30° with the positive direction of x-axis, 120° with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is:
(A) 90° (C) 60° (B) 120° (D) 0°Answer: (A) 90°
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.19. Assertion (A): For any symmetric matrix A, B’AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P’ = – P.Answer: (D) Assertion (A) is false, but Reason (R) is true.
1 (C) ±2
2 (C) (5/e)x log 5
3 (D) [0, 6]
4 (C) π/2
5 (C) x + 2y ≥ 76, 2x + y ≤ 104, x,y ≥ 0
6 (A) [ 1/2 0 0]
[ 0 1/3 0] [ 0 0 1/5]7 (C) a skew symmetric matrix
8 (C) [1, ∞)
9 (A) 2a
10 (D) continuous everywhere
11 (C) f'(x) = 0 and f'(x) does not change its sign from left to right of that point.
12 (A) 0
13 (C) first order linear differential equation.
14 (C) perpendicular vectors
15 (D) cos α + cos β + cos γ = 1
16 (B) constraints
17 (D) 0
18 (D) aij = {0, if i ≠ j
= {1, if i = j19 (D) Assertion (A) is false, but Reason (R) is true.
20 (C) Assertion (A) is true, but Reason (R) is false.
1 (D) -1/(e-2x – 1)1/2
2 (D) 2, 2
3 (B) j
4 (D) 2, -1, 3
5 (A) 0
6 (D) 90°
7 (C) 27
8 (A) one-one
9 (D) 4
10 (B) 1
11 (A) strictly decreasing on R
12 (B) -cosx + sinx
13 (B) y/x
14 (C) a · b ≤ | a | | b |
15 (C) (√5, 0, 0)
16 (D) a feasible region
17 (C) 1
18 (D) a13 > a31
19 (D) Assertion (A) is false, but Reason (R) is true
20 (D) Assertion (A) is false, but Reason (R) is true.
CBSE Class 12 Maths Marking Scheme 2024 |
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Section | No of Questions | Total Marks | Type of Questions |
Section- A | 18 | 1 x 18 = 18 | MCQs |
Section- B | 5 | 2 x 5 = 10 | Very Short Answer Questions |
Section- C | 6 | 3 x 6 = 18 | Short Answer Questions |
Section- D | 4 | 5 x 4 = 20 | Long Answer Questions |
Section- E | 3 | 4 x 3 = 12 | Short Answer Questions |
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