Available Questions 601 found Page 19 of 31
Standalone Questions
#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:
#837
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals
(A) ±1
(B) -1
(C) 1
(D) 2
Key:
Sol:
Sol:
#836
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If for a square matrix A, A² - A + I = O then A⁻¹ equals
(A) A
(B) A+I
(C) I-A
(D) A-I
Key:
Sol:
Sol:
#835
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
Competency
1 Marks
The feasible region of a linear programming problem is shown in the figure below: ... Which of the following are the possible constraints?
(A) $x+2y\ge4, x+y\le3, x\ge0, y\ge0$
(B) $x+2y\le4, x+y\le3, x\ge0, y\ge0$
(C) $x+2y\ge4, x+y\ge3, x\ge0, y\ge0$
(D) $x+2y\ge4, x+y\ge3, x\le0, y\le0$
Key:
Sol:
Sol:
#834
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The number of feasible solutions of the linear programming problem given as Maximize $z=15x+30y$ subject to constraints : $3x+y\le12, x+2y\le10, x\ge0, y\ge0$ is
(A) 1
(B) 2
(C) 3
(D) infinite
Key:
Sol:
Sol:
#833
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
16. Which of the following points satisfies both the inequations $2x+y\le10$ and $x+2y\ge8$?
(A) $(-2,4)$
(B) $(3,2)$
(C) $(-5,6)$
(D) $(4, 2)$
Key:
Sol:
Sol:
#832
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
15. The solution set of the inequation $3x+5y<7$ is:
(A) whole $xy$-plane except the points lying on the line $3x+5y=7$.
(B) whole $xy$-plane along with the points lying on the line $3x+5y=7$.
(C) open half plane containing the origin except the points of line $3x+5y=7$.
(D) open half plane not containing the origin.
Key:
Sol:
Sol:
#831
Mathematics
Probability
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If $P(A\cap B)=\frac{1}{8}$ and $P(\bar{A})=\frac{3}{4}$ then $P(\frac{B}{A})$ is equal to :
(A) $\frac{1}{2}$
(B) $\frac{1}{6}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
Key:
Sol:
Sol:
#830
Mathematics
Probability
MCQ_SINGLE
APPLY
2023
Competency
1 Marks
18. The probability that A speaks the truth is $\frac{4}{5}$ and that of B speaking the truth is $\frac{3}{4}$. The probability that they contradict each other in stating the same fact is :
(A) $\frac{7}{20}$
(B) $\frac{1}{5}$
(C) $\frac{3}{20}$
(D) $\frac{4}{5}$
Key:
Sol:
Sol:
#829
Mathematics
Probability
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If\~P(\frac{A}{B})=0\cdot3, P(A)=0\cdot4 and P(B)=0\cdot8, then P(\frac{B}{A}) is equal to :
(A) 0.6
(B) 0.3
(C) 0.06
(D) 0.4
Key:
Sol:
Sol:
#828
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
(A) 27/32
(B) 5/32
(C) 31/32
(D) 1/32
Key:
Sol:
Sol:
#827
Mathematics
Probability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
If for any two events A and B, P(A)=4/5 and P(A ∩ B)=7/10, then P(B/A) is equal to
(A) 1/10
(B) 1/8
(C) 7/8
(D) 17/20
Key:
Sol:
Sol:
#826
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The value of $\lambda$ for which the angle between the lines $\vec{r}=\hat{i}+\hat{j}+\hat{k}+p(2\hat{i}+\hat{j}+2\hat{k})$ and $\vec{r}=(1+q)\hat{i}+(1+q\lambda)\hat{j}+(1+q)\hat{k}$ is $\frac{\pi}{2}$ :
(A) $-4$
(B) 4
(C) 2
(D) $-2$
Key:
Sol:
Sol:
#825
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If the direction cosines of a line are $(\frac{1}{a}, \frac{1}{a}, \frac{1}{a})$ then:
(A) $0<a<1$
(B) $a>2$
(C) $a>0$
(D) $a=\pm\sqrt{3}$
Key: D
Sol:
Sol:
#824
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
REMEMBER
2023
KNOWLEDGE
1 Marks
14. Distance of the point $(p, q, r)$ from y-axis is :
(A) q
(B) q
(C) $|q|+|r|$
(D) $\sqrt{p^{2}+r^{2}}$
Key:
Sol:
Sol:
#823
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
UNDERSTAND
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Direction cosines of the line $\frac{x-1}{2}=\frac{1-y}{3}=\frac{2z-1}{12}$ are:
(A) $\frac{2}{7},\frac{3}{7},\frac{6}{7}$
(B) $\frac{2}{\sqrt{157}},-\frac{3}{\sqrt{157}},\frac{12}{\sqrt{157}}$
(C) $\frac{2}{7},-\frac{3}{7},-\frac{6}{7}$
(D) $\frac{2}{7},-\frac{3}{7},\frac{6}{7}$
Key:
Sol:
Sol:
#822
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The angle between the lines 2x=3y=-z and 6x=-y=-4z is
(A) 0°
(B) 30°
(C) 45°
(D) 90°
Key:
Sol:
Sol:
#821
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are
(A) 0, -1/√2, 1/√2
(B) -1/√2, 0, 1/√2
(C) 1/√2, 0, -1/√2
(D) 0, 1/√2, 1/√2
Key:
Sol:
Sol: