List of practice Questions

Which one of the following is not an autoimmune disease?

The strongest Lewis acid among boron halides is

Let $A = \{ 0,1,2 \}$, $B =\{ 4,2,0 \}$ and $ f,g $ : $ A \rightarrow B $ be the functions defined by $ f(x) = x^2-x $ and $ g(x) = 2|x-\frac{1}{2}|-1 $ Then,

Let $f = \{ (1,1),(2,4),(0,- 2),(-1,- 5) \}$ be a linear function from $ Z $ into $ Z $ . Then, $ f (x) $ is

The ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, - 8)$ is divided by xy-plane is

The value of $\lambda$ for which the lines $\frac{1-x}{3}=\frac{y-2}{2\lambda}=\frac{z-3}{2}$ and $ \frac{x-1}{3\lambda}=\frac{y-1}{1}=\frac{6-z}{7}$

If $ A $ is a square matrix such that $ A^2 $ = $ A $ , then $ (I-A)^3+A $ is equal to

A fair coin is tossed $ n $ number of times. If the probability of having at least one head is more than 90%, then $ n $ is greater than or equal to

The co-ordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1, - 1, 0)$ are

Which one of the following is not associated with the total internal reflection?

The following figure represents

A block of mass $m$ is placed on a smooth sphere of radius $R$. It slides when pushed slightly. At what distance $h$, from the top, will it leave the sphere?

Choose the incorrect statement out of the following.

If $E, M, L$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then the quantity $\left(E^{2} L^{2} / M^{5} G^{2}\right)$ has the dimensions of

A body $A$ is thrown up vertically from the ground with a velocity $v_{0}$ and another body $B$ is simultaneously dropped from a height $H$. They meet at a height $\frac{H}{2}$ if $v_{0}$ is equal to

An AC voltage source of variable angular frequency to and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When to is increased

A ray $OP$ of monochromatic light is incident on the face $AB$ of prism $ABCD$ near vertex $B$ at an incident angle of $60^{\circ}$ (see figure). If the refractive index of the material of the prism is $\sqrt3$, which of the following is (are) correct?

One mole of an ideal gas in initial state A undergoes a cyclic process ABC A, as shown in the figure. Its pressure at A is p$_0$. Choose the correct option(s) from the following.

A biconvex lens of focal length $15\, cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10\,cm$. A small object is kept at a distance of $30\,cm$ from the lens. The final image is

The value of $ \lambda $ for which the lines $ \frac{1-x}{3} = \frac{y-2}{2\lambda}=\frac {z-3}{2} = \frac{x-1}{3\lambda} =\frac{y-1}{1} =\frac {6-z}{7} $ are perpendicular to each other is

The complex showing a spin only magnetic moment of $2.82\, BM$ is

Which of the following have been arranged in decreasing order of oxidation number of sulphur?

The most adsorbed gas on activated charcoal is

$A$ block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and tan $\theta >\mu.$ The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_{1}=mg$ $\left(sin\,\theta-\mu\,cos\,\theta\right)$ to $P_{2}=mg$ $\left(sin\theta+\mu cos\theta\right)$, the frictional force $f$ versus $P$ graph will look like

Which of the following is a disaccharide?