List of practice Questions

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 lift of mass $M =500 kg$ is descending with speed of $2 ms ^{-1}$ Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2 ms ^{-2}$ The kinetic energy of the lift at the end of fall through to a distance of $6 m$ will be ___ $kJ$

The radius of the $2^{\text {nd }}$ orbit of $Li ^{2+}$ is $x$. The expected radius of the $3^{\text {rd }}$ orbit of $Be ^{3+}$ is

Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : $\frac{y^2}{25} − \frac{x^2}{16 }$= 1. If Q is the point from which the tangents drawn to H have slopes |m₁| and |m₂| and they make positive intercepts α and β on the x-axis, then $\frac{( P Q ) ^2}{ α β}$ α β is equal to _____.

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

Coagulating value of the electrolytes AlCl₃ and NaCl for As₂S₃ are 0.09 and 50.04 respectively. The coagulating power of AlCl₃ is x times the coagulating power of NaCl. The value of x 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.

If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio 2:1 and their enthalpy of vaporizations are in the ratio 1:2, then the boiling point elevation constant of X is m times the boiling point elevation constant of Y. The value of m is ______ (nearest integer).

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

The number of species from the following carrying a single lone pair on central atom Xenon is ______ .
XeF₅⁺, XeO₃, XeO₂F₂, XeF₅^-, XeO₃F₂, XeOF₄, XeF₄

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

The drift velocity of electrons for a conductor connected in an electrical circuit is $V _{ d }$ The conductor in now replaced by another conductor with same material and same length but double the area of cross section The applied voltage remains same The new drift velocity of electrons will be

The negation of the statement $((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A$ is

Match List l with List ll.

List I Natural amino acid	List II One letter code
(I) Glutamic acid	(a) Q
(II) Glutamine	(b) W
(III) Tyrosine	(c) E
(IV) Tryptophan	(d) Y

Choose the correct answer from the options given below:

A rod with circular cross-section area $2\, cm ^2$ and length $40 cm$ is wound uniformly with $400$ turns of an insulated wire If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6}\, Wb$ The relative permeability of the rod is(Given : Permeability of vacuum $\mu_0=4 \pi \times 10^{-7}\, NA ^{-2}$ )

Let O be the origin and the position vector of the point P be $\hat i-2\hat j+3\hat k$. If the position vectors of the points A, B and C are $-2\hat i+\hat j-3\hat k,2\hat i+4\hat j-2\hat k$ and $-4\hat i+2\hat j-\hat k$ respectively then the projection of the vector $\overrightarrow{OP}$ on a vector perpendicular to the vectors $\overrightarrow{ AB}$ and $\overrightarrow {AC}$ is