List of practice Questions

Let R₁ and R₂ be two relations defined on ℝ by a R₁b ⇔ ab ≥ 0 and aR₂b ⇔ a ≥ b. Then,

Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be

Let
f,g:N = {1} → N be functions defined by
f(a) = α, where α is the maximum of the powers of those primes p such that p^α divides a, and g(a) = a + 1, for all a ∈ N – {1}. Then, the function f + g is

Let the minimum value v₀ of
v = |z|²+|z-3|²+|z-6i|²,z∈C
is attained at z = z₀. Then
\(|2z^2_0-\overline{z}^3_0+3|^2+v^2_0\)
is equal to

In bromination of Propyne, with Bromine 1,1,2,2-tetrabromopropane is obtained in 27% yield. The amount of 1,1,2,2-tetrabromopropane obtained from 1 g of Bromine in this reaction is _______ × 10^–1 g. (Nearest integer)
(Molar Mass : Bromine = 80 g/mol)

Let
\(I = ∫^{\frac{π}{3}}_{\frac{π}{4}}(\frac{8sinx-sin2x}{x})dx\)
Then

A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by \(\frac{π}{2}\). If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?

The area of the smaller region enclosed by the curves y² = 8x + 4 and
x²+y²+4√3x-4=0
is equal to

[Fe(CN)⁶]^3– should be an inner orbital complex. Ignoring the pairing energy, the value of crystal field stabilization energy for this complex is (–) _____ Δ₀. (Nearest integer)

Let R be a relation from the set \(\{1, 2, 3, ….., 60\}\) to itself such that \(R = \{(a, b) : b = pq,\) where \(p, q≥ 3\) are prime numbers\(\}\). Then, the number of elements in R is :

Consider, \(PF_5,BrF_5,PCl_3,SF_6,[ICl_4]^–,ClF_3 and\ IF_5\).
Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having \(sp^3d^2\) hybridisation is _____.

\(\begin{array}{l} \frac{2^3-1^3}{1\times7}+\frac{4^3-3^3+2^2-1^3}{2\times 11}+\frac{6^3-5^3+4^3-3^3+2^3-1^3}{3\times 15}+\cdots+\frac{30^3-29^3+28^3-27^3+\cdots+2^3-1^3}{15\times63}\end{array}\)

is equal to _______.

An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options

A liquid of density 750 kgm^–3 flows smoothly through a horizontal pipe that tapers in
cross-sectional area from A₁ = 1.2 × 10^–2m² to
\(A_2=\frac{A_1}{2}\)
. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is _____ × 10^–3 m³s^–1.