List of practice Questions

A 3.628 kg freight car moving along a horizontal rail road spur track at 7.2 km/hour strikes a bumper whose coil springs experiences a maximum compression of 30 cm in stopping the car. The elastic potential energy of the springs at the instant when they are compressed 15 cm is â

If the equation of transverse wave is \( y = x_0 \cos \left( 2\pi \left( nt - \frac{x}{\lambda} \right) \right) \), the maximum velocity of the particle is twice the wave velocity, if \( k \) is â

Three equal charges (\( q \)) are placed at corners of an equilateral triangle of side \( a \). The force on any charge is â

A uniform electric field and uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
When light is refracted, which of the following does not change?

The given lens is broken into four parts and rearranged as shown. If the initial focal length is \( f \), then after rearrangement the equivalent focal length is â

In Young's double-slit experiment, the 10th-order maximum is obtained at the point of observation in the interference pattern for \( \lambda = 7000 \, \text{Ã} \). If the source is replaced by another one of wavelength 5000 Å, then the order of maximum at the same point will be â

Transfer characteristics (output voltage \( V_o \) vs input voltage \( V_i \)) for a base biased transistor in CE configuration is as shown in the figure. For using transistor as a switch, it is used 



If the extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0, a)$ and the equation of one of the sides is $x = 2a$, then the area of the triangle, in square units, is :
If the integral $\int \frac{cos 8x+1}{cot 2x-tan 2x} dx=A cos 8x+k,$ where $k$ is an arbitrary constant, then $A$ is equal to:
If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8\, cm^2/s$, then the rate of change of its volume is :
If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :
If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t=\sqrt{r^{2b}s^{c}d^{a/2}}.$ It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}.$ The value of $b$ should therefore be :
If the x-intercept of some line $L$ is double as that of the line, $3x+4y = 12$ and the $y$-intercept of $L$, is half as that of the same line, then the slope of $L$ is:
If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of a for which the vectors $\vec{u}=\left(\alpha-2\right)\vec{a}+\vec{b}$ and $\vec{v}=\left(2+3\alpha\right)\vec{a}-3\vec{b}$ are collinear is :
In a face centred cubic lattice, atoms of $A$ form the comer points and atoms of $B$ form the face centred points. If two atoms of $A$ are missing from the comer points, the formula of the ionic compound is :
In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1). If n > > 1$, the frequency of radiation emitted is proportional to
In a metre bridge experiment null point is obtained at $40\, cm$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$, then the new position of the null point from the same end, if one decides to balance a resistance of $3X$ against $Y$, will be close to:
In an experiment, a small steel ball falls through a liquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?
In Goldschmidt aluminothermic process which of the following reducing agents is used:
In nucleophilic substitution reaction, order of halogens as incoming (attacking) nucleophile is: $I^- > \, Br^{-} > \, Cl^-$ The order of halogens as departing nucleophile should be:
In reaction $A + 2B {\rightleftharpoons} 2C + D$, initial concentration of $B$ was $1.5$ times of $[A]$, but at equilibrium the concentrations of $A$ and $B$ became equal. The equilibrium constant for the reaction is :
Let $a_1, a_2, a_3,...$ be an $A.P$, such that $\frac{a_{1}+a_{2}+\ldots+a_{p}}{a_{1}+a_{2}+a_{3}+\ldots+a_{q}} = \frac{p^{3}}{q^{3}} ; p\ne q$ Then $\frac{a_{6}}{a_{21}}$ is equal to:
Let $A (-3,2)$ and $B (-2,1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y+2 = 0$, then the vertex $C$ lies on the line :
Let $a=Im\left(\frac{1+z^{2}}{2iz}\right),$ where $z$ is any non-zero complex number. The set $A=\left\{a:\left|z\right|=1\,and\,z\ne\pm1\right\}$ is equal to: