List of practice Questions

Let C be the circle in the complex plane with centre z₀ =\(\frac{1}{2}\) (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|₂ is equal to

Let $a _{ n }=\int\limits_{-1}^{ n }\left(1+\frac{ x }{2}+\frac{ x ^2}{2}+\frac{ x ^3}{3}+\ldots \ldots +\frac{ x ^{ n -1}}{ n }\right) dx$ for $n \in N$ Then the sum of all the elements of the set $\left\{ n \in N : a _{ n } \in(2,30)\right\}$ is ______

Consider a system of large number of particles that can be in three energy states with energies 0 meV, 1 meV, and 2 meV. At temperature T = 300 K, the mean energy of the system (in meV) is closest to
Given: Boltzmann constant k_B = 0.086 meVK^-1

Let 𝑋1, 𝑋2 be a random sample from a distribution having a probability density function
\(f(x) =\begin{cases} \frac{1}{θ}e^{\frac{y}{θ}} & \quad \text{if }x >0,\\ 0, & \quad Otherwise \end{cases}\)\(𝜃\)
where 𝜃∈(0, ∞) is an unknown parameter. For testing the null hypothesis 𝐻₀ : 𝜃=1 against 𝐻1∶ 𝜃≠1, consider a test that rejects 𝐻₀ for small observed values of the statistic \(𝑊 = \frac{𝑋_1+𝑋_2}{ 2}\) . If the observed values of 𝑋₁and 𝑋₂ are 0.25 and 0.75, respectively, then the 𝑝-value equals___(round off to two decimal places)

If sin^-1x = 2 tan^-1x , then number of integral values of x is equal to:

Calculate mass of Tollen’s Reagent Required?

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

If the circles $x^2+y^2+6 x+8 y+16=0$ and $x^2+y^2+2(3-\sqrt{3}) x+x+2(4-\sqrt{6}) y$ $= k +6 \sqrt{3}+8 \sqrt{6}, k >0$ touch internally at the point $P(\alpha, \beta)$, then $(\alpha+\sqrt{3})^2+(\beta+\sqrt{6})^2$ is equal to _______

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$ If the curve passes through the point $(1,2)$ and $(8,1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to

The sum $1^2-2 \cdot 3^2+3 \cdot 5^2-4 \cdot 7^2+5 \cdot 9^2-\ldots+15 \cdot 29^2$ is_____

Let the area of the region $\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}$ be $A$ Then $(6 A +11)^2$ is equal to ____

$\displaystyle\lim _{n \rightarrow \infty} \frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\ldots +\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

If \(\frac{dy}{dx}\) = y+7 and y(0) = 0, then the value of y(1) is?

Let $A$ be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a If $P(A)=\frac{11}{36}$, then a is equal to _____

The remainder when $(11)^{1011}+(1011)^{11}$ is divided by $9$ is

In a given data set mean of 40 observations is 50 and standard deviation is 12. Two readings which were 20 and 25, were mistakenly taken as 40 and 45. Find correct variance of data set

It is observed that characteristic $X$-ray spectra of elements show regularity When frequency to the power " $n$ " ie $v^n$ of $X$-rays emitted is plotted against atomic number " $Z$ ", following graph is obtained

Conversion of compound (X) to product (Y)

In the above conversion of compound $( X )$ to product $( Y )$, the sequence of reagents to be used will be:

Match List I with List II.

List-I		List-II
A	Sulphate	I	Pesticide
B	Fluoride	II	Bending of bones
C	Nicotine	III	Laxative effect
D	Sodium arsinite	IV	Herbicide

Choose the correct answer from the options given below:

Which of the following has maximum number of l.p. at central atom?

What is the chemical formula of freon gas?

How many meaningful words can be formed using the first, the third, the fifth and the sixth letters of the word TRADEMARK using each letter only once in each word?

Arrange the soils of India in descending order of their percentage share in total area of the country.
A. Alfisols
B. Vertisols
C. Entisols
D. Inceptisols
Choose the correct answer from the options given below:

Which one of the following theories does not explain the origin of tides?

If the position of a particle is changing with time as r=t²-2t (m). Find the velocity at t=2s.