The current in a circuit is defined as $I=\frac{dq}{dt}$. The charge (q) flowing through a circuit, as a function of time (t), is given by $q=5t^2-20t+3$. The minimum charge flows through the circuit at:

The current in a circuit is defined as $I=\frac{dq}{dt}$. If the charge (q) flowing through a circuit is given by $q=(t^2-3t+4),$ current flowing through the circuit is equal to zero at:

Work done by a force (F) in displacing a body by dx is given by W=$\int F\left(x\right).dx$. If the force is given as a function of displacement (x) by $F\left(x\right)=(x^2-2x+1)N$, then work done by the force from x=0 to x=3 m is:

The impulse due to a force on a body is given by I=$\int \mathrm{Fdt}$. If the force applied on a body is given as a function of time (t) as $\mathrm{F}=(3{\mathrm{t}}^2+2\mathrm{t}+5)\mathrm{N}$, then impulse on the body between t=3 sec to t = 5 sec is:

Which of the following option is not true, if $\overrightarrow{\mathrm{A}} = 3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}} = 6\hat{\mathrm{i}} + 8\hat{\mathrm{j}}$, where A and B are the magnitudes of $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$?

The angle made by the vector $\overrightarrow{\mathrm{A}} = \sqrt{3}\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$ with y-axis is:

In the space, if the sum of vectors of unequal magnitude is zero, then the minimum number of vectors are

If $\overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}}$ is perpendicular to $\overrightarrow{\mathrm{A}} - \overrightarrow{\mathrm{B}}$  , then which of the following statement is correct?

The angle between the two vectors $\left(-2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \hat{\mathrm{k}}\right)$ and $\left(\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - 4\hat{\mathrm{k}}\right)$ is:

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} = \overrightarrow{0}$; then which of the following statements is incorrect?

When a force of magnitude F acts on a body of mass m the acceleration produced in the body is
a. If three coplanar forces of equal magnitude F act on the same body as shown in the figure, then acceleration produced is

1.  0

2.  $\left(\sqrt{3} +\hspace{0.17em}1\right)\mathrm{a}$

3.  $\left(\sqrt{3} -\hspace{0.17em}1\right)\mathrm{a}$

4.  $\sqrt{3}\mathrm{a}$>

Three forces each of magnitude 1 N act along with the sides AB, BC, and CD of a regular hexagon. The magnitude of their resultant is:

If a unit vector $\hat{j}$ is rotated through an angle of 45° anticlockwise, then the new vector will be:

If $\overrightarrow{\mathrm{a}} = 2\hat{\mathrm{i}} + \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{b}} = 3\hat{\mathrm{i}} + 2\hat{\mathrm{j}}$, then $\left|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\right|=?$ 

$\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are two vectors given by $\overrightarrow{\mathrm{A} }= 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + \hat{\mathrm{j}}$. The component of $\stackrel{\to \; }{\mathrm{A}}$parallel to $\overrightarrow{\mathrm{B}}$ is:

If a vector is inclined at angles, $\mathrm{\alpha }, \mathrm{\beta }, \mathrm{and} \mathrm{\gamma }$ with x, y, and z-axis respectively, then the value of ${\sin }^2 \mathrm{\alpha } + {\sin }^2 \mathrm{\beta }+ {\sin }^2 \mathrm{\gamma }$ is equal to

If $\hat{\mathrm{p}}$ is the unit vector in the direction $\overrightarrow{\mathrm{B}}$, then:

Which of the following sets of forces cannot give zero resultant?

The minimum number of non-coplanar vectors whose vector sum can be zero is:

The resultant vector of $\overrightarrow{\mathrm{P}} \mathrm{and} \overrightarrow{\mathrm{Q}}$ makes angle ${\mathrm{\theta }}_1$ with $\overrightarrow{\mathrm{P}}$ and ${\mathrm{\theta }}_2$ with $\overrightarrow{\mathrm{Q}}$.Then-

A vector $\overrightarrow{\mathrm{A}}$, which has magnitude 8.0 is added to a vector $\overrightarrow{\mathrm{B}}$ which lies on the x-axis. The sum of these two vectors lies on the y-axis and has a magnitude twice the magnitude of $\overrightarrow{\mathrm{B}}$. The magnitude of the vector $\overrightarrow{\mathrm{B}}$

If $\overrightarrow{\mathrm{A}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{B}} = 3\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - \hat{\mathrm{k}}$, then the unit vector in the direction of $\overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}}$ is

The forces ${\mathrm{F}}_1 \mathrm{and} {\mathrm{F}}_2$ are acting perpendicular to each other at a point and have resultant R. If force ${\mathrm{F}}_2$ is replaced by $\frac{{\mathrm{R}}^2 - {\mathrm{F}}_1^2}{{\mathrm{F}}_2}$ acting in the direction opposite to that of ${\mathrm{F}}_2$, the magnitude of resultant

A force of 20 N acts on a particle along a direction, making an angle of 60° with the vertical. The component of the force along the vertical direction will be

If $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are two vectors inclined to each other at an angle $\theta$, then the component of $\overrightarrow{\mathrm{A}}$ perpendicular to $\overrightarrow{\mathrm{B}}$ and lying in the plane containing $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ will be:

If $\left|\overrightarrow{\mathrm{A}}\right| \ne \left|\overrightarrow{\mathrm{B}}\right|$ and $\left|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}\right|$ = $\left|\overrightarrow{\mathrm{A}} · \overrightarrow{\mathrm{B}}\right|$, then 

If $\overrightarrow{\mathrm{R}}$ is the resultant of two vectors $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{R}}$' is the difference in them, and $\left|\overrightarrow{\mathrm{R}}\right| = \left|\overrightarrow{\mathrm{R}}\text{'}\right|$, then:

Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:

Given are two vectors,  $\overrightarrow{\mathrm{A}}= (2\hat{\mathrm{i}} - 5\hat{\mathrm{j}} + 2\hat{\mathrm{k}})$ and $\overrightarrow{\mathrm{B}} = (4\hat{\mathrm{i}} - 10\hat{\mathrm{j}} + \mathrm{c}\hat{\mathrm{k}})$. What should be the value of c so that vector $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ would become parallel to each other?

In the following questions, a statement of assertion (A) is followed by a statement of the reason (R).

A: A vector must have, magnitude and direction.

R: A physical quantity cannot be called a vector if its magnitude is zero.