Basic Mathematics
127 Questions
Start Allen Test
Q101
Allen
9. CROSS PRODUCT
MCQ
Which of the following vector identities is false?
A.
$\vec{P} + \vec{Q} = \vec{Q} + \vec{P}$
B.
$\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$
C.
$\vec{P}. \vec{Q} = \vec{Q}. \vec{P}$
D.
$\vec{P} \times \vec{Q} = -(\vec{Q} \times \vec{P})$
Q102
Allen
9. CROSS PRODUCT
MCQ
What is the value of $\left(\vec{\mathrm{A}} +\vec{\mathrm{B}}\right)\times \left(\vec{\mathrm{A}} -\vec{\mathrm{B}}\right)$ ?
A.
$-2(\vec{\mathrm{A}}\times \vec{\mathrm{B}})$
B.
$2(\vec{\mathrm{B}}\times \vec{\mathrm{A}})$
C.
$\vec{0}$
D.
both 1 and 2
Q103
Allen
9. CROSS PRODUCT
MCQ
The angle between vectors $(\vec{A} \times \vec{B})$ and $-(\vec{B} \times \vec{A})$ is:
A.
$\pi$ rad
B.
$\frac{\pi}{2}$ rad
C.
$\frac{\pi}{4}$ rad
D.
zero
Q104
Allen
9. CROSS PRODUCT
MCQ
A vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards south. The vector product $\vec{A} \times \vec{B}$ is
A.
zero
B.
along west
C.
along east
D.
vertically downward
Q105
Allen
9. CROSS PRODUCT
MCQ
If $\frac{3}{4}|\vec{A}\times\vec{B}|=|\vec{A}.\vec{B}|$ , then the angle between $\vec{A}$ and $\vec{B}$ will be:
A.
$30^{\circ}$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$53^{\circ}$
Q106
Allen
9. CROSS PRODUCT
MCQ
If $\vec{A} = 3\hat{\mathrm{i}} +4\hat{\mathrm{j}}$ and $\vec{B} = 6\hat{\mathrm{i}} +8\hat{\mathrm{j}}$ and A and B are the magnitudes of $\vec{A}$ and $\vec{B}$ , then which of the following is true?
A.
$\vec{A}\times \vec{B} = \vec{0}$
B.
$\frac{A}{B} = 2$
C.
$\vec{A}.\vec{B} = 48$
D.
$A = 10$
Q107
Allen
9. CROSS PRODUCT
MCQ
Two non zero vectors $\vec{A}$ and $\vec{B}$ are such that $\left|\vec{A}+\vec{B}\right|=\left|\vec{A}-\vec{B}\right|$ . Then select correct alternative
A.
$\vec{A}.\vec{B}=0$
B.
$\vec{A}\times\vec{B}=\vec{0}$
C.
$\vec{A}=\vec{0}$
D.
$\vec{B}=\vec{0}$
Q108
Allen
9. CROSS PRODUCT
MCQ
A vector $\vec{\mathrm{F}}_1$ is along the positive Y-axis. If its vector product with another vector $\vec{\mathrm{F}}_2$ is zero then $\vec{\mathrm{F}}_2$ may be :-
A.
$4\hat{\mathrm{j}}$
B.
$-(i + \hat{j})$
C.
$(i + \hat{k})$
D.
$-4\hat{i}$
Q109
Allen
9. CROSS PRODUCT
MCQ
If $\vec{A} \times \vec{B} = \vec{0}$ and $\vec{B} \times \vec{C} = \vec{0}$ , then the angle between $\vec{A}$ and $\vec{C}$ may be:
A.
$\pi$
B.
$\frac{\pi}{4}$
C.
$\frac{\pi}{2}$
D.
None
Q110
Allen
9. CROSS PRODUCT
MCQ
The vector $\vec{B}=6\hat{i}+2\hat{j}+S\hat{k}$ is parallel to the vector $\vec{A}=3\hat{i}+\hat{j}+2\hat{k}$ if S=
A.
1
B.
4
C.
6
D.
8
Q111
Allen
9. CROSS PRODUCT
MCQ
If three vectors satisfy the relation $\vec{A}.\vec{B}=0$ and $\vec{A}.\vec{C}=0$ , then $\vec{A}$ can be parallel to
A.
$\vec{C}$
B.
$\vec{B}$
C.
$\vec{B}\times\vec{C}$
D.
$\vec{B}.\vec{C}$
Q112
Allen
9. CROSS PRODUCT
MCQ
For a body, angular velocity $\vec{\omega} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$ and radius vector $\vec{r} = \hat{\mathrm{i}} + \hat{\mathrm{j}} + \hat{\mathrm{k}}$ , then its velocity $(\vec{v} = \vec{\omega} \times \vec{r})$ is:
A.
$-5\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$
B.
$-5\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$
C.
$-2\hat{\mathrm{i}} + 2\hat{\mathrm{k}}$
D.
$-5\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - 3\hat{\mathrm{k}}$
Q113
Allen
9. CROSS PRODUCT
MCQ
Find unit vector perpendicular to the plane of $\vec{a} = 2\hat{i} - 2\hat{j} +\hat{k}$ and $\vec{b} = \hat{i} +2\hat{j} +2\hat{k}$
A.
$\frac{2}{3}\hat{\mathrm{i}} +\frac{1}{3}\hat{\mathrm{j}} +\frac{2}{3}\hat{\mathrm{k}}$
B.
$-\frac{2}{3}\hat{\mathrm{i}} -\frac{1}{3}\hat{\mathrm{j}} -\frac{2}{3}\hat{\mathrm{k}}$
C.
$-\frac{2}{3}\hat{\mathrm{i}} -\frac{1}{3}\hat{\mathrm{j}} +\frac{2}{3}\hat{\mathrm{k}}$
D.
$\frac{2}{3}\hat{\mathrm{i}} +\frac{2}{3}\hat{\mathrm{j}} -\frac{1}{3}\hat{\mathrm{k}}$
Q114
Allen
10. PYQ
MCQ
If vectors $\vec{A} = \cos \omega t\hat{i} +\sin \omega t\hat{j}$ and $\vec{B} = \cos \frac{\omega t}{2}\hat{i} +\sin \frac{\omega t}{2}\hat{j}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is:
A.
$t = 0$
B.
$t = \frac{\pi}{4\omega}$
C.
$t = \frac{\pi}{2\omega}$
D.
$t = \frac{\pi}{\omega}$
Q115
Allen
10. PYQ
MCQ
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :-
A.
$0^{\circ}$
B.
$90^{\circ}$
C.
$45^{\circ}$
D.
$180^{\circ}$
Q116
Allen
10. PYQ
MCQ
A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:
A.
increase
B.
decrease
C.
remain constant
D.
change according to the smallest force $\overrightarrow{QR}$
Q117
Allen
10. PYQ
MCQ
If $\vec{\mathrm{F}} = 2\hat{\mathrm{i}} +\hat{\mathrm{j}} -\hat{\mathrm{k}}$ and $\vec{\mathrm{r}} = 3\hat{\mathrm{i}} +2\hat{\mathrm{j}} -2\hat{\mathrm{k}}$ , then the scalar and vector products of $\vec{\mathrm{F}}$ and $\vec{\mathrm{r}}$ have the magnitudes respectively as:
A.
$5,\sqrt{3}$
B.
$4,\sqrt{5}$
C.
$10,\sqrt{2}$
D.
$10,2$
Q118
Allen
11. ANALYTICAL QUESTIONS
MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Current has magnitude as well as direction but still not considered as vector.
Reason (R): Current do not follow vector algebra.
In the light of the above statements,
choose the most appropriate answer from the options given below:
Assertion (A): Current has magnitude as well as direction but still not considered as vector.
Reason (R): Current do not follow vector algebra.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q119
Allen
11. ANALYTICAL QUESTIONS
MCQ
Two vectors $\vec{A} \& \vec{B}$ have equal magnitude equal to $Z$ . If angle between $\vec{A} \& \vec{B}$ is $60^{\circ}$ then match the following: Match the Column-I with Column-II
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
A.
A-R, B-S, C-Q, D-P
B.
A-R, B-Q, C-S, D-P
C.
A-P, B-Q, C-R, D-S
D.
A-Q, B-P, C-S, D-P
Q120
Allen
11. ANALYTICAL QUESTIONS
MCQ
Match the following
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
A.
(A)-(S), (B)-(R), (C)-(P), (D)-(Q)
B.
(A)-(R), (B)-(S), (C)-(Q), (D)-(P)
C.
(A)-(P), (B)-(Q), (C)-(R), (D)-(S)
D.
(A)-(S), (B)-(R), (C)-(Q), (D)-(P)
Q121
Allen
11. ANALYTICAL QUESTIONS
MCQ
Given below are two statements:
Statement I : Resultant of 2 forces of magnitude 4N and 5N can be 2N in magnitude.
Statement II: $\left|\vec{a}\right|-\left|\vec{b}\right|\leq\left|\vec{a}+\vec{b}\right|\leq\left|\vec{a}\right|+\left|\vec{b}\right|$
In the light of the above statements,
choose the most appropriate answer from the options given below :
A.
Both statement I and statement II are correct.
B.
Statement I is correct and statement II is incorrect.
C.
Statement I is incorrect and statement II is correct.
D.
Both statements I and statements II are incorrect.
Q122
Allen
11. ANALYTICAL QUESTIONS
MCQ
Given below are two statements :
Statement I : Two null vector have same direction.
Statement II: $\vec{A} \times \vec{B}$ lies in the plane of $\vec{A} + \vec{B}$ .
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both statement I and statement II are correct.
B.
Statement I is correct and statement II is incorrect.
C.
Statement I is incorrect and statement II is correct.
D.
Both statements I and statements II are incorrect.
Q123
Allen
11. ANALYTICAL QUESTIONS
MCQ
Which of the following is correct :
(i) $\vec{A} \cdot \vec{B}$ is a vector quantity
(ii) $\vec{A} \times \vec{B}$ is perpendicular to plane of $\vec{A} + \vec{B}$
(iii) For two orthogonal vectors $\vec{A} \cdot \vec{B} = 0$
(iv) If vectors are parallel or antiparallel, then $\vec{A} \times \vec{B} = \vec{0}$
(i) $\vec{A} \cdot \vec{B}$ is a vector quantity
(ii) $\vec{A} \times \vec{B}$ is perpendicular to plane of $\vec{A} + \vec{B}$
(iii) For two orthogonal vectors $\vec{A} \cdot \vec{B} = 0$
(iv) If vectors are parallel or antiparallel, then $\vec{A} \times \vec{B} = \vec{0}$
A.
(i) only
B.
(i) & (ii)
C.
(iii) & (iv) only
D.
(ii), (iii) & (iv)
Q124
Allen
11. ANALYTICAL QUESTIONS
MCQ
Given below are two statements:
Statement-I : For every small angle $\theta$ , we may use approximation $\sin\theta \approx \theta \approx \tan\theta$ .
Statement-II : For very small angle $\theta$ , the hypotenuse and the base become approximately of the same length.
A.
Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I.
B.
Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I.
C.
Statement-I is true, Statement-II is false.
D.
Statement-I is false, Statement-II is true.
Q125
Allen
11. ANALYTICAL QUESTIONS
MCQ
Refer the given figure and identify correct statement(s)
(A) Distance of A from x-axis is $5\sqrt{3}$ cm.
(B) Distance of B from x-axis is 6 cm.
(C) Distance of A from y-axis is 5 cm.
(D) Distance of B from y-axis is 8 cm.
(A) Distance of A from x-axis is $5\sqrt{3}$ cm.
(B) Distance of B from x-axis is 6 cm.
(C) Distance of A from y-axis is 5 cm.
(D) Distance of B from y-axis is 8 cm.
A.
A, C
B.
A, D
C.
A, B, C
D.
A, B, C, D