List of practice Questions

In the given figure, $a =15\, m / s ^{2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R =2.5\, m$ at a given instant of time. The speed of the particle is -

A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $(E_{\text{sphere}} / E_{\text{cylinder}})$ Will be

A $100\, \Omega$ resistance and a capacitor of $100\, \Omega$ reactance are connected in series across a $220\, V$ source. When the capacitor is $50\%$ charged, the peak value of the displacement current is

Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperature. Which one will conduct most heat ?

If $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is

Derivative of $log \left(sec\,\theta +tan \,\theta\right) $ with respect to $sec\, \theta$ at $\theta = \pi/4$ is

A solution contains 4 g of NaOH and 16.2 g of water. The mole fraction solute and solvent are respectively

A compound 'A'with molecular formula \({C_5H_{10}O}\)gives a positive \({2,4-DNP}\) test but a negative Tollen's test. On treatment with sodium hypochlorite, it gives \({CHCl_3}\) and compound 'B'. Compound 'B' is

Sphagnum is slowly carbonised, compressed and fossilised over thousands of years to produce a dark spongy mass called peat. Peat helps to keep soil porous and it also improves water holding capacity of the soil.

The number of surjective functions from $A$ to $B$ where $A = \{1, 2, 3, 4 \}$ and $B = \{a, b\}$ is

If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is

If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}| $ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)

The value of $ (1 + \omega - \omega^2)^7$ is

The equation of one of the common tangents to the parabola $y^2 = 8x$ and $x^2 + y^2 - 12x + 4 = 0$ is

What is the area of a loop of the curve $r = a \sin^3 \theta$ ?

A tetrahedron has vertices at $O (0, 0, 0), A (1, 2, 1) B (2, 1, 3) $ and $C (-1, 1, 2)$. Then the angle between the faces $OAB$ and $ABC$ will be

If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ is

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.

If $e^x = y + \sqrt{ 1 + y^2}$ , then the value of y is

$CO$ is a stronger ligand than $Cl^-$ because

The sulphur compound in which the sulphur atom has octet configuration in its valence shell among the following is

All the words that can be formed using alphabets $A, H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

Block $A$ of mass $m$ and block $B$ of mass $2 m$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both the sides. If the coefficient of friction between the block $A$ and the wedge is $2 / 3$ and that between the block $B$ and the wedge is $1 / 3$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ I. $f(x)$ is increasing in $[-1,1]$ II. $f(x)$ has no root in $(-1,1)$. Which of the statements given above is/are correct?

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :