List of practice Questions

A car moves from $A$ to $B$ with a speed of $30 \,kmph$ and from $B$ to $A$ with a speed of $20\,kmph$. What is the average speed of the car ?

Coefficient of $ x^{11}$ in the expansion of $(1 + x^2)^4 (1 + x^3)^7 (1 + x^4)^{12} $

If $ x, y $ and $ z $ are all different and $ \begin{vmatrix}x&x^{2}&1+x^{3}\\ y&y^{2}&1+y^{3}\\ z&z^{2}&1+z^{3}\end{vmatrix}=0 $ then

Let the straight line $ x = b $ divide the area enclosed by $ y = (1 - x)^2 $ , $ y = 0 $ and $ x = 0 $ into two parts $ R_1(0 \le x \le b) $ and $ R_2(b \le x \le 1) $ such that $ R_1-R_2 = \frac {1}{4}. $ Then, $b$ equals

If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2 + px + q = 0\), then the values of \(\alpha^{3}, \beta^{3}\) and \(\alpha^{4}+\alpha^{2}\beta^{3}+\beta^{4}\) are respectively

Which of these is an excitatory neurotransmitter in brain?

The component of bacteria that retains the crystal violet stain during Gram-staining is

Which of the following organs does not produce any digestive enzymes?

How many ATP are produced when one molecule of $FADH_2$ is oxidized to $FAD$ through Electron Transport System?

If $ \alpha,\beta $ are the roots of the equation $ ax^2+bx+c = 0 $ and $ S_n = \alpha^n + \beta^n, $ then a $ S_{n+1} + bS_{n} + cS_{n-1} $ is equal to

Widal test is done to confirm

Let, $\vec {a} = - \hat {i} - \hat {k}, \vec {b} = - \hat {i} +\hat {j} $ and $\vec {c} = \hat {i}+2\hat {j}+3\hat {k} $ be three given vectors. If $\vec {r} $ is a vector such that $ \vec {r} \times \vec {b} = \vec {c} \times \vec{b} $ and $\vec {r} \cdot \vec{a} = 0 $ , then the value of $\vec {r} \cdot \vec {b} $ is

If $ \int_{0}^{\frac{\pi}{3}}\frac{cos x}{3 + 4 sin x}dx = k\, log \left(\frac{3+2\sqrt{3}}{3}\right) $ then $k$ is

Dettol contains

The susceptibility of a magnetism at $300\, K$ is $1 .2 � 10^{-5}$. The temperature at which the susceptibility increases to $ 1 .8 � 10^{-5}$ is

Negatively charged particles are called

$45\, g$ of ethylene glycol $\left(C_{2} H_{6} O_{2}\right)$ is mixed with $600\, g$ of water, what is the depression of freezing point?

What is added to the blood during haemodialysis to prevent blood clotting?

Hydrogen peroxide in its reaction with $ KIO_4 $ and $ NH_2OH $ respectively, is acting as a

A rod of length $L$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is

$10\, g$ of a mixture of $BaO$ and $ CaO$ requires $100 \, cm^3$ of $2.5\, M\, HCl$ to react completely. The percentage of calcium oxide in the mixture is approximately (Given : molar mass of $BaO \,= \,153$)

Internal energy of a gas remains unchanged in (I) an isothermal process (II) an adiabatic process (III) a reversible process (IV) a cyclic process Which of the these are true?

Function of zinc in plants is

A body starts from rest and moves with constant acceleration for $t \,s$. It travels a distance $x_1$ in first half of time and $x_2$ in next half of time, then