List of practice Questions

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

In the given circuit, the current (I) through the battery will be

Height of the receiving and transmitting antenna in communication of a signal are 245 m and 180 m respectively. Find the maximum distance between the two antennas for proper communication.

The position vector of a particle related to time t is given by $\vec{r}=(10t\hat{i}+15t^2\hat{j}+7\hat{k})m$
The direction of net force experienced by the particle is :

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21% ?

The speed of a wave produced in water is given by v=$λ^ag^bρ^c$. Where λ,g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are:

A vector in x-y plane makes an angle of 30º with y-axis. The magnitude of y-component of vector is $2\sqrt3$. The magnitude of x -component of the vector will be :

A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by 'l'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the entre (O) of shell can be graphically represented as –

A thermodynamic system is taken through cyclic process. The total work done in the process is:

A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is:
(Given: Atomic Weight of Ar = 39.9)

In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given below:

A capacitor of capacitance 900 μF is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of the uncharged capacitor is connected to the positive plate and another plate of the uncharged capacitor is connected to the negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}$ J. The value of $x$ is:

Let for x∈R, S₀(x)=x,Sk(x)=Ckx+k$∫^x_0S_{k−1}$(t)dt, where C₀=1,C_k≡1−$∫^1_0S_{k−1}$(x)dx,k==1,2,3,..... Then s₂(3)+6c₃ is equal to___.

Let the image of the point $\left(\frac{5}{3},\frac{5}{3},\frac{8}{3}\right)$ in the plane x - 2y + z - 2 = 0 be P. If the distance of the point Q(6,-2,α), α > 0, from P is 13, then α is equal to___.

In the figure given below, a block of mass $M=490 g$ placed on a frictionless table is connected with two springs having same spring constant $\left( K =2 N m ^{-1}\right)$ If the block is horizontally displaced through ' $X$ ' $m$ then the number of complete oscillations it will make in $14 \pi$ seconds will be

The speed of a swimmer is $4 km h ^{-1}$ in still water If the swimmer makes his strokes normal to the flow of river of width $1 km$, he reaches a point $750 m$ down the stream on the opposite bank.The speed of the river water is ___ $km h ^{-1}$

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 \Omega$ The internal resistance of each cell will be__ $\Omega$

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increase is

A thin rod having a length of $1 m$ and area of cross-section $3 \times 10^{-6} m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ} C$ to $160^{\circ} C$ After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} N m ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is ____ $kg$. (Take $g =10 \ m s ^{-2}$)

An inductor of $0.5 mH$, a capacitor of $20 \mu F$ and resistance of $20 \Omega$ are connected in series with a $220 V$ ac source If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}$ A The value of $x$ is -

Compound A reacts with $NH _4 Cl$ and forms a compound B Compound B reacts with $H _2 O$ and excess of $CO _2$ to form compound $C$ which on passing through or reaction with saturated $NaCl$ solution forms sodium hydrogen carbonate Compound $A , B$ and $C$, are respectively

Let $\overrightarrow{a}=3\^i+\^j −\^k$ and $\overrightarrow{c}=2\^i+3\^j −3\^k$ if $\overrightarrow{b}$ is a vector such that $\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}$ and $|\overrightarrow{b}|=50$ , then $|72|\overrightarrow{b}+\overrightarrow{c}|^2|$| | is equal to _______.

Which of the following statements is incorrect for antibiotics?

If S={ x ∈ R : sin⁻¹$( \frac{x + 1}{ √ x^ 2 + 2 x + 2} ) $−-sin⁻¹$(\frac{x}{√x ^2+1 }) = \frac{π}{ 4} $}
then $∑_{x∈R }(sin( (x^2+x+5)\frac{π}{2})−cos( ( x^2+x+5)π ) ) $is equal to ____.