List of practice Questions

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

Let C be the circle in the complex plane with centre z₀ = $\frac{1}{2}$ (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|² is equal to

In an electrochemical reaction of lead, at standard temperature, if $ E^{\circ}(\text{Pb}^{2+}/\text{Pb}) = m $ volt and $ E^{\circ}(\text{Pb}^{4+}/\text{Pb}^{2+}) = n $ volt, then the value of $ E^{\circ}(\text{Pb}^{4+}/\text{Pb}) $ is given by $ m - xn $. The value of $ x $ is ____

For which of the following aqueous ion, spin only magnetic moment is 3.87 BM?

During the qualitative analysis of $SO _3^2$ using dilute $H _2 SO _4, SO _2$ gas is evolved which turns $K _2 Cr _2 O _7$ solution (acidified with dilute $H _2 SO _4$ ) :

A long solenoid is formed by winding 70 turns/cm. If 2.0 A current flows, then the magnetic field produced inside the solenoid is:

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______

The dissociation constant of acetic acid is $x \times 10^{-5}$ When $25 \,mL$ of $0.2 \,M \,CH _3 COONa$ solution is mixed with $25 \,mL$ of $0.02\, M \,CH _3 COOH$ solution, the $pH$ of the resultant solution is found to be equal to 5. The value of $x$ is ___

In the expansion of $(2^\frac{1}{4}+3^{-\frac{1}{4}})^n$, the ratio of $5^{th}$ term from start and $5^{th}$ term form end is $\sqrt 6 : 1$ , then find $3^{rd}$ term

If $a_1,a_2,.......a_n$ are in arithmetic progression with common difference $d>n$, then find limit $\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})$ is____.

Element not present in Nessler’s reagent is

The pair of lanthanides will exceptionally high 3^rd ionisation enthalpy than neighbouring elements:

$(2x^3-\frac{1}{3}x^8)^5$ → coefficient of $x^4$

The solubility product of BaSO₄ is $1 \times 10^{-10}$ at 298 K. The solubility of BaSO₄ in 0.1 M K₂SO₄(aq) is $x \times 10^{-9}$ g L⁻¹. Calculate the value of $x$.

A radioactive element ${}^{242}_{92}X$ emits two $\alpha$-particles, one electron, and two positrons. The product nucleus is represented by ${}^{234}_{P}Y.$ The value of $P$ is _______.

A parallel plate capacitor with plate area A and plate separation d is filed with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where $x < d$.

Let C₁ and C₂ be the capacitance of the system for $x=\frac{1}{3d}$ and $x=\frac{2d}{3}$, respectively. If $C_1 = 2μF$, the value of C₂ is __________μF.

Let $A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}$,} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where $[x]$ denotes the greatest integer function. Then,

A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres What is the least distance of distinct vision for this person :

An object of mass $8 kg$ is hanging from one end of a uniform rod CD of mass $2 kg$ and length $1 m$ pivoted at its end $C$ on a vertical wall as shown in figure It is supported by a cable $AB$ such that the system is in equilibrium The tension in the cable is : (Take $g =10 m / s ^2$ )

The frequency ($ \nu $) of an oscillating liquid drop may depend upon the radius ($ r $) of the drop, density ($ \rho $) of the liquid, and the surface tension ($ s $) of the liquid as: \[ \nu = k r^a \rho^b s^c \]
The values of $ a $, $ b $, and $ c $ respectively are:

Let $\alpha x+\beta y+y z=1$ be the equation of a plane passing through the point$(3,-2,5)$and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$ Then the value of $\alpha \beta y$is equal to ____

A trisubstituted compound ‘A’, $\text{C}_{10}\text{H}_{12}\text{O}_2$, gives neutral FeCl$_3$ test positive. Treatment of compound ‘A’ with NaOH and CH$_3$Br gives $\text{C}_{11}\text{H}_{14}\text{O}_2$, with hydroiodic acid gives methyl iodide, and with hot conc. NaOH gives a compound ‘B’, $\text{C}_{10}\text{H}_{10}\text{O}_2$. Compound ‘A’ also decolourises alkaline KMnO$_4$. The number of $\pi$-bond/s present in the compound ‘A’ is ______.

The density of a monobasic strong acid (Molar mass $242 \,g$ mol) is $121 \,kg \,L$ The volume of its solution required for the complete neutralization of $25 \,mL$ of $024\, M\, NaOH$ is ___$\times 10^{-2} mL$ (Nearest integer)

Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ Then, the number of ways of choosing $x$ and $y$, such that $x+y$ is divisible by 5 , is ____

The ratio of silica to alumina in cement is: