Available Questions Page 4 of 14
Standalone Questions
#858
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If a vector makes an angle of $\frac{\pi}{4}$ with the positive directions of both x-axis and y-axis, then the angle which it makes with positive z-axis is :
(A) $\frac{\pi}{4}$
(B) $\frac{3\pi}{4}$
(C) $\frac{\pi}{2}$
(D) 0
Key:
Sol:
Sol:
#857
Mathematics
Vector Algebra
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
13. If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$ then $\vec{a} \cdot \vec{b} \ge 0$ only when:
(A) $0 < \theta < \frac{\pi}{2}$
(B) $0 \le \theta \le \frac{\pi}{2}$
(C) $0 < \theta < \pi$
(D) $0 \le \theta \le \pi$
Key:
Sol:
Sol:
#856
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
A unit vector along the vector $4\hat{i}-3\hat{k}$ is:
(A) $\frac{1}{7}(4\hat{i}-3\hat{k})$
(B) $\frac{1}{5}(4\hat{i}-3\hat{k})$
(C) $\frac{1}{\sqrt{7}}(4\hat{i}-3\hat{k})$
(D) $\frac{1}{\sqrt{5}}(4\hat{i}-3\hat{k})$
Key: B
Sol:
Sol:
#854
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z=18x+9y be the objective function, then :
(A) z is maximum at (2, 72), minimum at (15, 20)
(B) z is maximum at (15, 20), minimum at (40, 15)
(C) z is maximum at (40, 15), minimum at (15, 20)
(D) z is maximum at (40, 15), minimum at (2, 72)
Key:
Sol:
Sol:
#853
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?
(A) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm A$
(B) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm2A$
(C) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm\frac{A}{2}$
(D) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|^{2}=A^{2}$
Key:
Sol:
Sol:
#852
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
5. The value $|\begin{matrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{matrix}|$ is :
(A) 0
(B) 1
(C) $x+y+z$
(D) $2(x+y+z)$
Key:
Sol:
Sol:
#851
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
Let A be a 3\times3 matrix such that | adj A|=64. Then |A| is equal to:
(A) 8 only
(B) \- 8 only
(C) 64
(D) 8 or-8
Key:
Sol:
Sol:
#850
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If |A|=2, where A is a 2\times2 matrix, then |4A^{-1}| equals :
(A) 4
(B) 2
(C) 8
(D) \frac{1}{32}
Key:
Sol:
Sol:
#849
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If |(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0, then the value of a is
(A) 1
(B) 2
(C) 3
(D) 4
Key:
Sol:
Sol:
#848
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
For what value of $x\in[0,\frac{\pi}{2}]$, is $A+A'=\sqrt{3}I$, where $A=\begin{bmatrix}\cos x & \sin x\\ -\sin x & \cos x\end{bmatrix}$ ?
(A) $\frac{\pi}{3}$
(B) $\frac{\pi}{6}$
(C) $0$
(D) $\frac{\pi}{2}$
Key: B
Sol:
Sol:
#847
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
A and B are skew-symmetric matrices of same order. AB is symmetric, if:
(A) $AB=O$
(B) $AB=-BA$
(C) $AB=BA$
(D) $BA=O$
Key:
Sol:
Sol:
#846
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If $A\cdot(\text{adj }A)=\begin{bmatrix}3&0&0\\ 0&3&0\\ 0&0&3\end{bmatrix}$, then the value of $|A|+| ext{adj }A|$ is equal to :
(A) 12
(B) 9
(C) 3
(D) 27
Key:
Sol:
Sol:
#845
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If $A=\begin{bmatrix}1&4&x\\ z&2&y\\ -3&-1&3\end{bmatrix}$ is a symmetric matrix, then the value of $x+y+z$ is :
(A) 10
(B) 6
(C) 8
(D) 0
Key:
Sol:
Sol:
#844
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
4. If a matrix $A=\begin{bmatrix}1 & 2 & 3\end{bmatrix}$, then the matrix $AA'$ (where $A'$ is the transpose of A) is:
(A) 14
(B) $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
(C) $\begin{bmatrix}1 & 2 & 3\\ 2 & 3 & 1\\ 3 & 1 & 2\end{bmatrix}$
(D) $\begin{bmatrix}14\end{bmatrix}$
Key:
Sol:
Sol:
#843
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
3. If A is a square matrix and $A^{2}=A$ then $(I+A)^{2}-3A$ is equal to :
(A) I
(B) A
(C) 2A
(D) 3I
Key:
Sol:
Sol:
#842
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
2. The product $\begin{bmatrix}a & b\\ -b & a\end{bmatrix}\begin{bmatrix}a & -b\\ b & a\end{bmatrix}$ is equal to :
(A) $\begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$
(B) $\begin{bmatrix}(a+b)^{2} & 0\\ (a+b)^{2} & 0\end{bmatrix}$
(C) $\begin{bmatrix}a^{2}+b^{2} & 0\\ a^{2}+b^{2} & 0\end{bmatrix}$
(D) $\begin{bmatrix}a & 0\\ 0 & b\end{bmatrix}$
Key:
Sol:
Sol:
#841
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
1. If $x\begin{bmatrix}1\\ 2\end{bmatrix}+y\begin{bmatrix}2\\ 5\end{bmatrix}=\begin{bmatrix}4\\ 9\end{bmatrix}$, then
(A) $x=1, y=2$
(B) $x=2, y=1$
(C) $x=1, y=-1$
(D) $x=3, y=2$
Key:
Sol:
Sol:
#840
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If A=\begin{bmatrix}0&1\\ -1&0\end{bmatrix} and (3\~I+4\~A)(3\~I-4\~A)=x^{2}I, then the value(s) x is/are:
(A) \pm\sqrt{7}
(B) 0
(C) \pm5
(D) 25
Key:
Sol:
Sol:
#839
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If A=\begin{bmatrix}3&4\\ 5&2\end{bmatrix} and 2A+B is a null matrix, then B is equal to :
(A) \begin{bmatrix}6&8\\ 10&4\end{bmatrix}
(B) \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}
(C) \begin{bmatrix}5&8\\ 10&3\end{bmatrix}
(D) \begin{bmatrix}-5&-8\\ -10&-3\end{bmatrix}
Key:
Sol:
Sol:
#838
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If for a square matrix A, A^{2}-3A+I=O and A^{-1}=xA+yI, then the value of x+y is:
(A) \-2
(B) 2
(C) 3
(D) -3
Key:
Sol:
Sol: