List of practice Questions

$tan^{-1}(\frac {1+\sqrt 3}{3+\sqrt 3})+sec^{-1}(\sqrt {\frac {8+4\sqrt 3}{3+3\sqrt 3})}$ is equal to:

Let a tangent to the curve $y^2=24 x$ meet the curve $x y=2$ at the points $A$ and $B$ Then the mid points of such line segments $A B$ lie on a parabola with the

The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is

Ratio of molar heat capacity at constant pressure and at constant volume for monoatomic and diatomic gas is?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
S-1 $\rightarrow$ Steel is used in construction of a bridge and house.
S–2 $\rightarrow$ Modulus of elasticity of steel is high.
In the light of the above statements, choose the correct answer from the options given below

Statement-I : If we move upward and downward from the surface of earth surface acceleration due to gravity decreases in both upward and downward direction.
Statement-II : Acceleration due to gravity changes by same amount when we go up to height h and depth d when h = d.
Choose the correct options based on above statements.

If frequency can be represented as f = (radius)a (density)b (surface tension)c. Find a, b, c?

When a parallel beam of white light incident on convex lens split into different colours the phenomenon is called.

In an electromagnetic wave electric field and magnetic field is given by
E = E₀ sin (kx – ωt + ϕ)
B = B₀ sin (kx – ωt + ϕ)
Find correct relation.

$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be:

Match List I with List II:

List I		List II
A	Microwaves	i	Radioactive decay of the nucleus
B	Gamma waves	ii	Rapid acceleration and deceleration of electrons in aerials
C	Radio waves	iii	Inner shell electrons
D	X - rays	iv	Klystron valve

Choose the correct answer from the options given below:

Given below are two statements : One is labelled as Assertion $A$ and the other is labelled as Reason R
Assertion A : Two metallic spheres are charged to the same potential One of them is hollow and another is solid, and both have the same radii Solid sphere will have lower charge than the hollow one.
Reason R : Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
A. By changing the magnitude of the magnetic field within the coil
B. By changing the area of coil within the magnetic field
C. By changing the angle between the direction of magnetic field and the plane of the coil
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below :

In an amplitude modulation, a modulating signal having amplitude of $X V$ is superimposed with a carrier signal of amplitude $Y V$ in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude $2 YV$. The ratio of modulation index in the two cases respectively will be :

Choose the correct statement about Zener diode :

As shown in the figure, a long straight conductor with semi-circular are of radius $\frac{\pi}{10} m$ is carrying current $I =3 A$. The magnitude of the magnetic field at the center $O$ of the arc is :(The permeability of the vacuum $=4 \pi \times 10^{-7} NA ^{-2}$ )

For three low density gases $A , B , C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ' $K$ ' is :

If the vectors $\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}$, $\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}$ are coplanar and the projection of $\overrightarrow{a}$ on the vector $\overrightarrow{b}$ is $\sqrt{54}$ units, then the sum of all possible values of $\lambda + \mu$ is equal to

Let [x] denote the greatest integer ≤ x. Consider the function $f(x)=max \{x^2,1+[x] \}$. Then the value of the integral $∫_0^2 f(x)dx$ is

$\displaystyle\lim _{t \rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots+n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

Let the tangents at the points A(4, –11) and B(8, –5) on the circle $x^2+y^2-3x+10y-15=0$, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

If a radioactive element with a half-life of 30 min undergoes beta decay. The fraction of the radioactive element that remains undecayed after 90 min is:

A block of mass m slides down the plane inclined at angle $30\degree$ with an acceleration $\frac{g}{4}$. The value of the coefficient of kinetic friction will be:

The surface tension of a soap bubble is $2 \times 10^{-2} \, \text{N/m}$. Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be: