List of practice Questions

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.

List I		List II
(P)	XeF2	(1)	Trigonal bipyramidal and two lone pair of electrons
(Q)	XeF4	(2)	Tetrahedral and one lone pair of electrons
(R)	XeO3	(3)	Octahedral and two lone pair of electrons
(S)	XeO3F2	(4)	Trigonal bipyramidal and no lone pair of electrons
		(5)	Trigonal bipyramidal and three lone pair of electrons

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

List I		List II
(P)		(1)
(Q)		(2)
(R)		(3)
(S)		(4)
		(5)

List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

List I		List II
(P)		(1)
(Q)		(2)
(R)		(3)
(S)		(4)
		(5)

Let \(a=3\sqrt2\) and \(b=\frac{1}{5^{1/6}\sqrt5}\). If x, y ∈ R are such that
\(3x+2y=\log_a(18)^{\frac{5}{4}}\) and
\(2x-y=\log_b(\sqrt{1080})\), 
then 4x + 5y is equal to _______.

Let f(x) = x⁴ + ax³ + bx² + c be a polynomial with real coefficients such that f(1) = -9. Suppose that \(i\sqrt3\) is a root of the equation 4x³ + 3ax² + 2bx = 0, where\(i=\sqrt{-1}\) . If a₁, a₂, a₃ and a₄ are all the roots of the equation f(x) = 0, then |a₁|² + |a₂|² + |a₃|² + |a₄|² is equal to ______.

Let \(S=\left\{\begin{pmatrix} 0 & 1 & c \\ 1 & a & d\\ 1 & b & e \end{pmatrix}:a,b,c,d,e\in\left\{0,1\right\}\ \text{and} |A|\in \left\{-1,1\right\}\right\}\), where |A| denotes the determinant of A. Then the number of elements in S is _______.

A group of 9 students, s₁, s₂,…., s₉, is to be divided to form three teams X, Y and Z of sizes 2, 3, and 4, respectively. Suppose that s₁ cannot be selected for the team X and s₂ cannot be selected for the team Y. Then the number of ways to form such teams, is _______.

Let \(\overrightarrow{OP}=\frac{\alpha-1}{\alpha}\hat{i}+\hat{j}+\hat{k},\overrightarrow{OQ}=\hat{i}+\frac{\beta-1}{\beta}\hat{j}+\hat{k}\) and \(\overrightarrow{OR}=\hat{i}+\hat{j}+\frac{1}{2}\hat{k}\) be three vector where α, β ∈ R - {0} and 0 denotes the origin. If \((\overrightarrow{OP}\times\overrightarrow{OQ}).\overrightarrow{OR}=0\) and the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.

Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy -plane, and P(X = x) = 0 for all x ∈ R - {0,1,2,3,4}. If the mean of X is \(\frac{5}{2}\) , and the variance of X is α, then the value of 24α is ______.

The specific heat capacity of a substance is temperature dependent and is given by the formula C = kT, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from −73 ° C to 27 ° C is nk, the value of n is ___[Given: 0 K = −273 °C.]

A disc of mass \(M\) and radius \(R\) is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass \(M\) and radius \(R/2\) is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \(\omega\). If the angular speed at which the large disc rotates is \(\omega/n\), then the value of \(n\) is _____

A point source \(S\) emits unpolarized light uniformly in all directions. At two points A and B, the ratio \(r = I_A/I_B\) of the intensities of light is \(2\). If a set of two polaroids having 45° angle between their pass-axes is placed just before point B, then the new value of r will be ____

A source (S) of sound has frequency\( 240 Hz\). When the observer (O) and the source move towards each other at a speed \(v\) with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be \(288 Hz\). However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be \(n\) Hz. The value of \(n\) is _____.

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height ℎ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If \(H = ( \frac{16}{ 9} ) ℎ\), then the ratio t1/t2 is ___

Consider the following volume−temperature (V−T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, C_V,_m = 12 J K⁻¹mol⁻¹ and gas constant, R=8.3 JK⁻¹ mol⁻¹]

Consider the following reaction,
\(2H_2(g) + 2NO(g) \rightarrow N_2(g) + 2H_2O(g)\)
which follows the mechanism given below:
\(2NO(g)\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} N_2O_2(g)\) (fast equilibrium)
\(N_2O_2(g)+H_2(g) \xrightarrow[]{K_2}N_2O(g)+H_2O\)  (slow reaction)
\(N_2O(g)+H_2(g) \xrightarrow[]{K_3}N_2(g)+H_2O\)  (fast reaction)
The order of the reaction is________

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens' test, whereas Q on acidification gives positive Tollens' test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of p-toluenesulfonic acid (PTSA) gives product R.
Sum of the number of methylene groups (-CH2-) and oxygen atoms in R is _______

Among V(CO)₆, Cr(CO)₅, Cu(CO)₃, Mn(CO)₅, Fe(CO)₅, [Co(CO)₃]^3-, [Cr(CO)₄]^4-, and Ir(CO)₃, the total number of species isoelectronic with Ni(CO)₄ is _________.
[Given, atomic number: V = 23, Cr=24, Mn 25, Fe 26, Co 27, Ni 28, Cu = 29, Ir = 77]

In the following reaction sequence, the major product P is formed.

Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl₂ yields Ca-soap R, quantitatively. Starting with one mole of Q, the amount of R produced in gram is ______.
[Given, atomic weight: H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35, Ca = 40]

Among the following complexes, the total number of diamagnetic species is ______.
[Mn(NH₃)₆]³⁺, [MnCl₆]³⁻, [FeF₆]³⁻, [CoF₆]³⁻, [Fe(NH₃)₆]³⁺, and [Co(en)₃]³⁺
[Given, atomic number: Mn = 25, Fe = 26, Co = 27;
en = H₂NCH₂CH₂NH₂]

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.

Zitkala-Sa says, “Eating by formula wasn’t the hardest trial in that first day.” What does she mean by ‘Eating by formula’? (Memories of Childhood)

Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$. The distance of the point $$ \left( \frac{11}{3}, \frac{11}{3}, \frac{19}{3} \right) $$ from the line $L$ along the line $$ \frac{3x - 11}{2} = \frac{3y - 11}{1} = \frac{3z - 19}{2} $$ is equal to: 

Two long insulated straight wires carrying currents of \( 3A \) and \( 5A \) are arranged in the XY plane as shown in the figure. Find the magnitude and direction of the net magnetic fields at points \( P_1(2m, 2m) \) and \( P_2(-1m, 1m) \). 

Why does Derry not like being with people? (On The Face Of It)