Series SSJ/1 – Set 4

CBSE Class XII Mathematics Board Paper Term 1 - 2021

Time: 90 minutes

Total Marks: 40

General Instructions:

Read the following instructions very carefully and strictly follow them:

1. This question paper contains 50 questions out of which 40 questions are to be attempted as per instructions. All questions carry equal marks.
2. The Question Paper consists of three sections- Section A, Section B and Section C.
3. Section A contains 20 questions. Attempt any 16 questions from questions no. 1 to 20.
4. Section B also contains 20 questions. Attempt any 16 questions from questions no. 21 to 40.
5. Section C contains 10 questions. Attempt any 8 questions from Q. No. 41 to 50
6. There is only one correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option.
7. There is no negative marking.

SECTION A

In this section, attempt any 16 questions out of questions no. 1 to 20.

1. A relation R is defined on N. Which of the following is the reflexive relation?
2. <math>R = \{(x, y): x > y; x, y \in N\}</math>
3. <math>R = \{(x, y): x + y = 10; x, y \in N\}</math>
4. <math>R = \{(x, y): xy \text{ is the square number; } x, y \in N\}</math>
5. <math>R = \{(x, y): x + 4y = 10; x, y \in N\}</math>
6. The function f: <math>R \rightarrow R</math> defined by <math>f(x) = 4 + 3 \cos x</math> is:
7. bijective
8. one-one but not onto
9. onto but not one-one
10. neither one-one nor onto

3. If <math>y = \cot^{-1} x</math>, <math>x < 0</math>, then:

1. <math>\frac{\pi}{2} < y \le \pi</math>

1. <math>\frac{\pi}{2} < y < \pi</math>

1. <math>-\frac{\pi}{2} < y < 0</math>
2. <math>-\frac{\pi}{2} \leq y < 0</math>

1. The number of functions defined from <math>\{1, 2, 3, 4, 5\} \rightarrow \{a, b\}</math> which are one- one is:
2. 5
3. 3
4. 2
5. 0

5. If <math>A = \begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}</math>, then (A - 2I) (A - 3I) is equal to:

1. A
2. I
3. 5I
4. O

6. If P is a 3 x 3 matrix such that <math>P' = 2P + I</math>, where P' is the transpose of P, then:

1. <math>P = I</math>
2. <math>P = -I</math>
3. <math>P = 2I</math>
4. <math>P = -2I</math>

1. If order of matrix A is 2 x 3, of matrix B is 3 x 2, and of matrix C is 3 x 3, then which one of the following is not defined?
2. <math>C(A + B')</math>
3. <math>C (A + B')'</math>
4. BAC
5. <math>CB + A'</math>

8. If <math>A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}</math> and <math>|A^3| = 27</math>, then the value of <math>\alpha</math> is:

1. <math>\pm 1</math>
2. <math>\pm 2</math>
3. <math>\pm\sqrt{5}</math>
4. <math>\pm\sqrt{7}</math>