List of practice Questions

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.

If z ≠ 0 be a complex number such that$|z-\frac{1}{z}|=2$, then the maximum value of |z| is

If $z = 2 + 3i$, then $z^5 + (\overline{z})^5$ is equal to:

The reaction of zinc with excess of aqueous alkali, evolves hydrogen gas and gives:

Let A and B be two $3 × 3$ non-zero real matrices such that AB is a zero matrix. Then

Lithium nitrate and sodium nitrate, when heated separately, respectively, give :

A ball is released from a height h. If t₁ and t₂ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t₁ and t_2..

The integral $\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx$ is equal to

As shown in the figure, a potentiometer wire of resistance 20 Ω and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance ‘R‘ of resistance box introduced into the circuit, the null point for a cell of 20 mV is found to be 60 cm. The value of ‘R ‘ is Ω.

If $\frac{1}{(20-a)(40-a)} + \frac{1}{(40-a)(60-a)} + \ldots + \frac{1}{(180-a)(200-a)} = \frac{1}{256}$, then the maximum value of a is :

A 1.84 mg sample of polyhydric alcoholic compound ‘X’ of molar mass 92.0 g/mol gave 1.344 mL of H₂ gas at STP. The number of alcoholic hydrogens present in compound ‘X’ is____.

Let
$f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}$
Then, the value of ∑_n∈S f(n) is equal to ________.

If momentum of a body is increased by 20%, then its kinetic energy increases by

If the system of equations
$ x + y + z = 6 $,
$ 2x + 5y + \alpha z = \beta $,
$ x + 2y + 3z = 14 $
has infinitely many solutions, then $ \alpha + \beta $ is equal to:

For the curve
$\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}$

$\begin{array}{l}\text{the value of}\ 3y’ – y^3y”, \text{at the point}\end{array}$

$(α, α), α > 0$, on C is equal to ________.

In following pairs, the one in which both transition metal ions are colourless is :

Two electric dipoles of dipole moments 1.2 × 10^–30 C-m and 2.4 × 10^–30 C-m are placed in two different uniform electric fields of strength 5 × 10⁴ NC^–1 and 15 × 10⁴NC^–1 respectively. The ratio of maximum torque experienced by the electric dipoles will be 1:x. The value of x is _______

For a cell, $Cu(s)|Cu^{2+}(0.001M)||Ag^+(0.01M)|Ag(s)$
the cell potential is found to be $0.43 V$ at $298 K$. The magnitude of standard electrode potential for $Cu^{2+}/{Cu}$ is ____ $× 10^{–2}$ V.
[Given: $E_{Ag^+/Ag^⊖}=0.80$ V and $\frac {2.303RT}{F}=0.06 V$]

Let
$\begin{array}{l}f\left(x\right) = min \{\left[x – 1\right], \left[x – 2\right], …., \left[x – 10\right]\}\end{array}$
where [t] denotes the greatest integer ≤t. Then
$\begin{array}{l} \displaystyle\int\limits_{0}^{10}f\left(x\right)dx+\displaystyle\int\limits_{0}^{10}\left(f\left(x\right)\right)^2dx+\displaystyle\int\limits_{0}^{10}\left|f\left(x\right)\right|dx\end{array}$
is equal to ________.

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^TA is 6 is ________.

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m^–3at the rate of 0.35 cms^–1. The coefficient of viscosity of the solution is _______ poise (in nearest integer). (The density of air is negligible).