List of practice Questions

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

Consider the following salts: $NaCl,\, HgCl_2,\, Hg_2Cl_2,\, CuCl_2,\, CuCl$ and $AgCl$. Identify the correct set of insoluble salts in water

In a mixture, two enantiomers are found to be present in $85\%$ and $15\%$ respectively. The enantiomeric excess $(e, e)$ is

A simple pendulum of length $L$ swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed $v$ is ($g$ is the gravitational acceleration

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

Match each disease with its correct type of vaccine.

Which of the following diseases is caused by a protozoan?

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

A potentiometer wire has length 4 m and resistance $8\, \Omega.$ The resistance that must be connected in series with the wire and an accumulator of e.m.f. 2 V, so as to get a potential gradient 1 mV per cm on the wire is

If potential (in volts) in a region is expressed as $V(x, y , z)$ = $6xy - y + 2yz$, the electric field $(in\, N/C)$ at point $(1, 1, 0)$ is

A stretched string is vibrating in the second overtone, then the number of nodes and anti nodes between the ends of the string are respectively

The terga, sterna and pleura of cockroach body are joined by

A straight conductor $0.1\, m$ long moves in a uniform magnetic field $0.1\, T$. The velocity of the conductor is $15\, m / s$ and is directed perpendicular to the field. The emf induced between the two ends of the conductor is

Two particles, $A$ and $B$, having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii $R_{1}$ and $R_{2}$, respectively. The ratio of the masses of $A$ and $B$ is

Two particles $A$ and $B$ are moving as shown in the figure. Their total angular momentum about the point $O$ is

A fall in glomerular filtration rate activates

BOD refers to

Hibernating animals have tissues containing mitochondria with a membrane protein that accelerates electron transport while blocking the synthesis of ATP. What is the consequence of this?

Which one of the following monomers form biodegradable polymer?

A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are

$0.06\%\, (w/v)$ aqueous solution of urea is isotonic with

A coil of area $5 \, cm^2$ having $20$ turns is placed in a uniform magnetic field of $10^3$ gauss. The normal to the plane of coil makes an angle $30^{\circ}$ with the magnetic field. The flux through the coil is