List of practice Questions

A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field B_H = 3 × 10^-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms^-2 )

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g=10ms^-2).

Let $\alpha \in(0,1)$ and $\beta=\log _e(1-\alpha)$ Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int\limits_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to

Match List I with List II :

List-I (molecule)		List-II (hybridization; shape)
A	XeO3	i	sp3d ; linear
B	XeF2	ii	sp3; pyramidal
C	XeOF4	iii	sp3d3; distorted octahedral
D	XeF6	iv	sp3d2 ;square pyramidal

Choose the correct answer from the options given below:

Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d(b-c)=b c(a-d)$ Then $R$ is

Let R=$\begin{pmatrix}a&3&b\\c&2&d\\0&5&0\end{pmatrix}$: a,b,c,d ∈ {0,3,5,7,11,13,17,19}. Then the number of invertible matrices in R is

The derivative $\frac{dy}{dx} $ of the function y = sin(cos(log(x))) is,

Let f : (-2, 2) → IR be defined by $f(x) = \begin{cases} x[x] & \quad -2<x<0\\ (x-1)[x], & \quad 0\leq x<2 \end{cases}$
Where [x] denotes the greatest integer function. If m and n respectively are the number of points in (-2, 2) at which y = |f(x)| is not continuous and not differentiable, then m + n is equal to ______.

जल का पर्यायवाची शब्द?

For the following logic circuit, the truth table is:

Which of the following refractive errors is associated with the image given below?
$refractive errors is associated with the image$

The Jacobian matrix for transforming from (x, y) to another orthogonal coordinates system (u, v) as shown in the figure is

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A): Range of a horizontal projectile is maximum when angle of projection is $θ = 45°$.
Reason (R): Range is maximum when $sin\ (2θ)=1$.
In the light of the above statements, choose the correct answer from the options given below

The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?

We ___ touch the antique pieces.

If A is a square matrix of order 3 and $|A| = 6$, then the value of $|\text{adj} A|$ is:

If ABCD is a parallelogram and AC and BD are its diagonals, then $\overrightarrow{AC} + \overrightarrow{BD}$ is:

Function f is defined as: \[ f(x) = \begin{cases} 2x + 2, & x<2 \\ k, & x = 2 \\ 3x, & x>2. \end{cases} \text{Find the value of } k \text{ for which } f \text{ is continuous at } x = 2. \]

Let $x = 2$ be a root of the equation $x^2 + px + q = 0$ and $f(x)=\begin{cases}\frac{1-cos(x^2-4px+q^2+8q+16)}{(x-2p)^4} & x≠2p\\0 & x=2p\end{cases}$.
Then $lim_{x \rightarrow 2p}[f(x)]$, where [·] denotes greatest integer function, is

Enthalpies of formation of $CCl _4( g ), H _2 O ( g ), CO _2( g )$ and $HCl ( g )$ are $-105,-242,-394$ and $-92\, kJ$ mol $^{-1}$ respectively The magnitude of enthalpy of the reaction given below is ___$kJ \, mol ^{-1}$ (nearest integer) $CCl _4( g )+2 H _2 O ( g ) \rightarrow CO _2( g )+4 HCl ( g )$

Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt[x]-x}$ where [x] denotes the smallest integer greater than or equal to x . Then among the statements
(S1) : A ∩ B = (1, ∞) – N and
(S2) : A ∪ B = (1, ∞)

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is:

The equivalent resistance between the points A and B in the following circuit is

The mean deviation about the median for the data $3,5,9,3,8,10,7$ is ?

Carbohydrates are the major components of all living organisms. Sugars are carbohydrates. The major types of sugars include monosaccharides and disaccharides. The main difference between monosaccharides, disaccharides and polysaccharides is that monosaccharides are monomer of sugars and disaccharides are composed of two monomers, whereas polysaccharides are composed of a large number of monomers. Monosaccharides are single sugar molecules which act as the building blocks of disaccharides and polysaccharides. Disaccharides are also simple sugars. Disaccharides are classified into two groups according to their reducing strength: Reducing and Non-reducing sugars. When a polymer is formed from a monomer, a condensation reaction occurs that forms a glycosidic bond and water molecule is lost. Starch, glycogen and cellulose are examples of polysaccharides. Starch is found in many parts of plant cell and consists of amylose and amylopectin. Glycogen is the major carbohydrate storage product found in humans. It is present in liver, muscles and brain.

Cellulose is the most abundant organic molecule on Earth. It makes up around 50% of all organic carbon.