List of practice Questions

If the function \[ f(x) = \begin{cases} [ tan (\frac {\pi}{4}+x)]^{1/x} & \quad for\, x \neq 0\\ K \,\,\,\,\,\,\,\,\,\text{if } x =0 \end{cases} \] is continuous at $x = 0$, then $K = ?$

The area of the region bounded by the lines $y = 2x + 1, y = 3x + 1$ and $x = 4$ is

Two spherical black bodies have radii $?r_1?$ and $'r_2'$ . Their surface temperatures are $'T_1'$ and $'T_2'$. If they radiate same power then $\frac{r_2}{r_1}$ is

A disc of moment of inertia $'I_1'$ is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane w ith constant angular speed $?\omega_1'$. Another disc of moment of inertia $?I_2? $ having zero angular speed is placed coaxially on a rotating disc. Now both the. discs are rotating with constant angular speed $?\Omega_2 ?$. The energy lost by the initial rotating disc is

A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6 m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring = 36 N/m).

Which of the following does not contain Plane of symmetry?

Which of the following options gives the correct sequence of events during mitosis ?

If $\theta_1$ and $\theta_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by :

Consider the reactions :- Identify $A, X, Y$ and $Z$

Artificial selection to obtain cows yielding higher milk output represents :

DNA replication in bacteria occurs:

Which one is the most acidic compound ?

A particle executes linear simple harmonic motion with an amplitude of $3 \,cm$. When the particle is at $2\,cm$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is :

Good vision depends on adequate intake of carotene rich food : Select the best option from the following statements : (a) Vitamin A derivatives are formed from carotene (b) The photopigments are embedded in the membrane discs of the inner segment (c) Retinal is a derivative of Vitamin A (d) Retinal is a light absorbing part of all the visual photopigments

Which of the following reactions is appropriate for converting acetamide to methanamine ?

If $\theta_1$ and $\theta_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by :

The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is

If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is

The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point

Which one is the correct order of acidity ?

The given electrical network is equivalent to :

In a common emitter transistor amplifier the audio signal voltage across the collector is $3\,V$. The resistance of collector is $3\, k\Omega$. If current gain is $100$ and the base resistance is $2\, k\Omega$, the voltage and power gain of the amplifier is :

The resistance of a wire is $'R'$ ohm. If it is melted and stretched to $'n'$ times its original length, its new resistance will be :

A long solenoid of diameter $0.1\, m$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid, a coil of $100$ turns and radius $0.01\, m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0\,A$ from $4\, A$ in $0.05 \,s$. If the resistance of the coil is $10\pi^2 \Omega$ . the total charge flowing through the coil during this time is :

Young's double slit experment is first performed in air and then in a medium other than air. It is found that $8th$ bright fringe in the medium lies where $5th$ dark fringe lies in air. The refractive index of the medium is nearly :