List of practice Questions

A capacitor of capacitance 900 μF is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of the uncharged capacitor is connected to the positive plate and another plate of the uncharged capacitor is connected to the negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}$ J. The value of $x$ is:

Let for x∈R, S₀(x)=x,Sk(x)=Ckx+k$∫^x_0S_{k−1}$(t)dt, where C₀=1,C_k≡1−$∫^1_0S_{k−1}$(x)dx,k==1,2,3,..... Then s₂(3)+6c₃ is equal to___.

Let the image of the point $\left(\frac{5}{3},\frac{5}{3},\frac{8}{3}\right)$ in the plane x - 2y + z - 2 = 0 be P. If the distance of the point Q(6,-2,α), α > 0, from P is 13, then α is equal to___.

The speed of a swimmer is $4 km h ^{-1}$ in still water If the swimmer makes his strokes normal to the flow of river of width $1 km$, he reaches a point $750 m$ down the stream on the opposite bank.The speed of the river water is ___ $km h ^{-1}$

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 \Omega$ The internal resistance of each cell will be__ $\Omega$

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increase is

A thin rod having a length of $1 m$ and area of cross-section $3 \times 10^{-6} m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ} C$ to $160^{\circ} C$ After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} N m ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is ____ $kg$. (Take $g =10 \ m s ^{-2}$)

Let $\overrightarrow{a}=3\^i+\^j −\^k$ and $\overrightarrow{c}=2\^i+3\^j −3\^k$ if $\overrightarrow{b}$ is a vector such that $\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}$ and $|\overrightarrow{b}|=50$ , then $|72|\overrightarrow{b}+\overrightarrow{c}|^2|$| | is equal to _______.

Which of the following statements is incorrect for antibiotics?

If S={ x ∈ R : sin⁻¹$( \frac{x + 1}{ √ x^ 2 + 2 x + 2} ) $−-sin⁻¹$(\frac{x}{√x ^2+1 }) = \frac{π}{ 4} $}
then $∑_{x∈R }(sin( (x^2+x+5)\frac{π}{2})−cos( ( x^2+x+5)π ) ) $is equal to ____.

Kinetic energy of electron, proton and a particle is given as K, 2K and 4K respectively, then which of the following gives the correct order of De-Broglie wavelengths of electron, proton and a particle

A solid sphere of mass $1 \,kg$ rolls without slipping on a plane surface Its kinetic energy is $7 \times 10^{-3} J$. The speed of the centre of mass of the sphere is ___$cm s ^{-1}$.

The correct sequence of reagents for the preparation of Q and R is:

Find area bounded by the curves $y$ = $max\{sin x, cos x\}$ and $x-axis$ between $x = - \pi $and $x = \pi$

A cubic solid is made up of two elements $X$ and $Y$ Atoms of $X$ are present on every alternate corner and one at the enter of cube $Y$ is at $\frac{1}{3} td$ of the total faces The empirical formula of the compound is

Let α be the constant term in the binomial expansion of $ (√x−\frac{6}{x^{\frac{3}{2}}} )^n ,n≤15.$ If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of x^-n is λα, then λ is equal to _______.

The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph

For hydrogen atom, $\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$ The value of $x$ is

Find out the oxidation number of the central metal atom of fe(CO)₅ , VO₂⁺, and WO₃. Then calculate the sum of their oxidation state.

The number of seven-digit positive integers formed using the digits 1, 2, 3, and 4 only, and whose sum of the digits is 12, is

The number of incorrect statements from the following is _____
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. E°_cell is dependent on the pressure.
C. dE^θ cell/dT = Δ_rS^θ/nF
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

100 balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t s$ The total force exerted by the balls on the wall is

Let ω = z$\bar{z}$ + k₁z + k₂iz + λ(1+i), k₁ , k₂ ∈ $\mathbb{R}$. Let Re(ω) = 0 be the circle C of radius 1 in the first quadrant touching the line y =1 and the y-axis. If the curve Im (ω) = 0 intersects C at A and B, then 30 (AB)² is equal to _____

For complete combustion of ethene,
$C_2H_4(g) + 3O_2(g) \longrightarrow 2CO_2(g) + 2H_2O (l)$
the amount of heat produced as measured in bomb calorimeter is 1406 kJ mol^-1 at 300K. The minimum value of $T\Delta S$ needed to reach equilibrium is (-) _____ . kJ.(Nearest integer)
Given: R = 8.3 J K^-1 mol^-1

Given below are two statements:
Statement I: In redox titration, the indicators used are sensitive to change in pH of the solution.
Statement II: In acid-base titration, the indicators used are sensitive to change in oxidation potential.
In the light of the above statements, choose the most appropriate answer from the options given below