List of practice Questions

In Young's double slit experiment, the central point on the screen is
Two thin lenses are in contact and the focal length of the combination is $80\, cm$. If the focal length of one lens is $20 \,cm$, then the power of the other lens will be
A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is $0.5\, m/s$ at an angle of $120^?$ with the direction of flow of water. The speed of water is
The Young?? modulus of a perfectly rigid body is
An electric dipole is kept in a uniform electric field. It experiences
A mass of $0.5\, kg$ moving with a speed of $1.5\, m/ s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50\, N/m$. The maximum compression of the spring would be
If the differential equation for a simple harmonic motion is $\frac{d^{2}y}{dt^{2}}+2y=0,$ the time-period of the motion is
The magnetic field at a distance r from a long wire carrying current i is 0.4 tesla. The magnetic field at a distance 2r is
A rain drop of radius $0.3\, mm$ has a terminal velocity in air is $1\, m/s$. The viscosity of air is $8 \times 10^{-5}$ poise. The viscous force on it is
A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_H$ and $\tau_S$ respectively, then
A circle has radius 3 and its centre lies on the line $y = x -1$ . The equation of the circle, if it passes through $(7, 3)$, is
If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to
The system of linear equations : $x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0$ has :
The area under the curve $y = | cos\, x - sin \,x |, 0 \le x\le\frac{\pi}{2}$, and above x-axis is :
The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :
If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to
Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is
Which of the following is the tallest perennial grass?
A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)
A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass $M$ and radius $R$ attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis $OO'$, passing through the centre of $D_1$, as shown in the figure, will be :
A rectangular solid box of length $0.3\, m$ is held horizontally, with one of its sides on the edge of a platform of height $5\,m$. When released, it slips off the table in a very short time $\tau = 0.01\,s$, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :
A string is wound around a hollow cylinder of mass $5\, kg$ and radius $0.5\, m$. If the string is now pulled with a horizontal force of $40\, N$, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :
Chlorine on reaction with hot and concentrated sodium hydroxide gives :
Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $'\theta_2'$ and $' \theta_1'$ respectively, $(\theta_2 > \theta_1)$. The temperature at the interface is :-
A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency $512\, Hz$ produces first resonance when the tube is filled with water to a mark $11\, cm$ below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency $256\, Hz$ which produces first resonance when water reaches a mark $27\, cm$ below the reference mark. The velocity of sound in air, obtained in the experiment, is close to: