List of practice Questions

If the coefficient of $x^{15}$ in the expansion of $\left(a x^3+\frac{1}{b x^{1 / 3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{1 / 3}-\frac{1}{b x^3}\right)^{15}$, where a and $b$ are positive real numbers, then for each such ordered pair $(a, b)$ :

A Spherical ball of radius $1 \,mm$ and density $10.5\, g / cc$ is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $15 \,g / cc$ Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} N$. The value of $x$ is_______ (Given, $g=9.8 \,m / s ^2$ and $\pi=\frac{22}{9}$ )

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

Assume carbon burns according to following equation : $2 C _{( s )}+ O _{2( g )} \rightarrow 2 CO ( g )$ when $12 g$ carbon is burnt in $48 g$ of oxygen, the volume of carbon monoxide produced is___ $\times 10^{-1} L$ at STP [nearest integer] [Given : Assume $CO$ as ideal gas, Mass of $C$ is $12\, g \,mol ^{-1}$, Mass of $O$ is $16 \,g \,mol ^{-1}$ and molar volume of an ideal gas at STP is $22.7\, L\, mol ^{-1}$ ]

The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?

Number of moles of $AgCl$ formed in the following reaction is

Let 9=x1<x2<…<x7 be in an A.P. with common difference d. If the standard deviation of x1,x2 …,x7 is 4 and the mean is xˉ, then xˉ+x6 is equal to :

The temperature of a gas is -50° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?

A particle is thrown vertically upward with initial velocity of 150m/s. Find the ratio of its speed at t=3s and t=5s. (Take g=10 $ms^{-2}$)

R₁ = (15 ± 0.5) Ω
R₂ = (10 ± 0.5) Ω
Find % error in equivalent resistance if resistors R₁ and R₂ are connected in parallel ?

What does Lenz's Law give ?

10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is:

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $|\vec{a}|=\sqrt{31}, 4|\vec{b}|=|\vec{c}|=2$ and $2(\vec{a} \times \vec{b})=3(\vec{c} \times \vec{a})$ If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{2 \pi}{3}$, then $\left(\frac{\vec{a} \times \vec{c}}{\vec{a} \cdot \vec{b}}\right)^2$ is equal to _____

A bullet is fired from a gun at the speed of 280 ms-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is (g = 9.8 ms-2, sin 30° = 0.5)

0.5 gm of an organic compound with 60%. Carbon produce ______ gm of $CO_{2}$ upon complete combustion

For positive integer $n$, define $f(n)=n+\frac{16+5 n-3 n^2}{4 n+3 n^2}+\frac{32+n-3 n^2}{8 n+3 n^2}+\frac{48-3 n-3 n^2}{12 n+3 n^2}+\ldots+\frac{25 n-7 n^2}{7 n^2}$ Then, the value of $\displaystyle\lim _{n \rightarrow \infty} f(n)$ is equal to

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:

The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$ , is_________

The charge flowing in a conductor changes with time as $Q(t)=\alpha t-\beta t ^2+\gamma^3$ Where $\alpha, \beta$ and $\gamma$ are constants Minimum value of current is :

A sample of a metal oxide has formula $M _{0.83} O _{1.00}$ The metal $M$ can exist in two oxidation states $+2$ and $+3$ In the sample of $M _{0.83} O _{1.00}$, the percentage of metal ions existing in $+2$ oxidation state is___$ \%$ (nearest integer)

Given below are two statements:

Statement I

under Clemmensen reduction conditions will give

Statement II

under Wolff-Kishner reduction condition will give

In the light of the above statements, choose the correct answer from the options given below:

Let
Statement 1: (2002)²⁰²³ - (1919)²⁰⁰² is divisible by 8.
Statement 2: 13.13ⁿ - 12n - 13 is divisible by 144 n$ \varepsilon$N, then

The strength of $50$ volume solution of hydrogen peroxide is _____$g / L$ (Nearest integer) Given: Molar mass of $H _2 O _2$ is $34\, g \, mol ^{-1}$ Molar volume of gas at $STP =22.7\, L$

The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______

Let $C$ be the largest circle centred at $(2,0)$ and inscribed in the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$If $(1, a)$ lies on $C$, then $10 \alpha^2$ is equal to

List of practice Questions

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