List of practice Questions

The equation of the circle concentric to the circle $ 2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0 $ and having area double the area of this circle, is

The value of the $ \int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx $ is

Let A be an orthogonal non-singular matrix of order $n$, then the determinant of matrix $AI _{ n }$ ie, $\left| A - I _{ n }\right|$ is equal to

Let $ f(x)=\left\{ \begin{matrix} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \\ \end{matrix} \right. $ the value of a so that $ f(x) $ is continuous at $ x=\frac{\pi }{4} $

A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is

For a party $8$ guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is

If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if

Let $A = \{1,2,3,....., n\}$ and $B = \{a,b,c\}$, then the number of functions from $A$ to $B$ that are onto is

The differential equation of the system of all circles of radius $r$ in the $xy$ plane is

What is the stoichiometric coefficient of $Ca$ in the reaction? $Ca + Al^{3+} \to Ca^{2+} + Al$

If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

Area of the region satisfying $x \leq 2, y \leq|x|, x-$ axis and $x \geq 0$ is:

If average velocity becomes $4$ times then t-hat will be the effect on rms velocity at that Temperature?

Given standard electrode potentials $Fe ^{2}:+2 e ^{-} \longrightarrow Fe E ^{\circ}=-0 \cdot 440 \,V$ $Fe ^{3+}+3 e ^{-} \longrightarrow Fe E ^{\circ}=-0 \cdot 036\, V$ The standard electrode potential $\left(E^{\circ}\right)$ for $Fe ^{3+}+ e ^{-} \longrightarrow Fe ^{2+}$ is :

The displacement of a charge $Q$ in the electric field $E=e_{1} 1+e_{2} j+e_{3} k$ is $r=a i+b j$. The work done is

The minimum value of $2x + 3y,$ when $xy = 6,$ is

The ratio of $Fe _{2} O _{3}$ and $Al$, in thermite is:

Which of the following ketones will not respond to iodoform test?

A solution of sucrose (Molar mass = $342\,g/mol$) is prepared by dissolving $68.4\, g$ of it per litre of solution, what is its osmotic pressure ($R = 0.082 \,L$ atom $K^{-1}$ $mol^{-1}$) at $273\, K$?

$H_2O_2$ used in rocket has the concentration

Setting of plaster of Peris involves

Tautomerism is exhibited by

For all complex numbers $z _{1}, z _{2}$ satisfying $\left| z _{1}\right|=12$ and $\left| z _{2}-(3+4 i )\right|=5$, the minimum value of $\left|z_{1}-z_{2}\right|$ is

Which of the most volatile compounds?