According to Bohr's model, the highest kinetic energy is associated with the electron in the

In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ and $\mathbf{Y}$ a

In the following reaction sequence, the major product $\mathbf{Q}$ is

The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are

An aqueous solution of hydrazine $\left(\mathrm{N}_2 \mathrm{H}_4\right)$ is electrochemically oxidized by $\mathrm{O}_2

The option(s) with correct sequence of reagents for the conversion of $\mathbf{P}$ to $\mathbf{Q}$ is(are)

The compound(s) having peroxide linkage is(are)

To form a complete monolayer of acetic acid on $1 \mathrm{~g}$ of charcoal, $100 \mathrm{~mL}$ of $0.5 \mathrm{M}$ aceti

Vessel-1 contains $\mathbf{w}_2 \mathrm{~g}$ of a non-volatile solute $\mathbf{X}$ dissolved in $\mathbf{w}_1 \mathrm{~g

For a double strand DNA, one strand is given below: The amount of energy required to split the double strand DNA into t

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into $\math

Among $\left[\mathrm{Co}(\mathrm{CN})_4\right]^{4-},\left[\mathrm{Co}(\mathrm{CO})_3(\mathrm{NO})\right], \mathrm{XeF}_4

An organic compound $\mathbf{P}$ having molecular formula $\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3$ gives ferric chloride

Sum of number of oxygen atoms in $\mathbf{S}$ and $\mathbf{T}$ is _______.

The molecular weight of $\mathbf{U}$ is ______ .

The number of moles of potassium iodide required to produce two moles of $\mathbf{P}$ is _______.

The number of zinc ions present in the molecular formula of $\mathbf{Q}$ is _______.

Considering only the principal values of the inverse trigonometric functions, the value of $$ \tan \left(\sin ^{-1}\lef

Let $S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.$ and $\l

Let $k \in \mathbb{R}$. If $\lim \limits_{x \rightarrow 0+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6$, then the value

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $$ f(x)=\left\{\begin{array}{cc} x^2 \sin \left(\fr

Let $S$ be the set of all $(\alpha, \beta) \in \mathbb{R} \times \mathbb{R}$ such that $$ \lim\limits_{x \rightarrow \i

A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, inter

Let $A_1, B_1, C_1$ be three points in the $x y$-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to t

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbb{R}$, and

A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume tha

Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2

Let $\vec{p}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha, \beta

A normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0,-\alpha)$ to the parabola $x^2=-4 a y$, where $a>0$

Let the function $f:[1, \infty) \rightarrow \mathbb{R}$ be defined by $$ f(t)=\left\{\begin{array}{cc} (-1)^{n+1} 2, &

If $n(X)={ }^m C_6$, then the value of $m$ is _____

If the value of $n(Y)+n(Z)$ is $k^2$, then $|k|$ is _________.

The value of $2 \int\limits_0^{\frac{\pi}{2}} f(x) g(x) d x-\int\limits_0^{\frac{\pi}{2}} g(x) d x$ is ____________.

The value of $\frac{16}{\pi^3} \int\limits_0^{\frac{\pi}{2}} f(x) g(x) d x$ is ______.

A region in the form of an equilateral triangle (in $x-y$ plane) of height $L$ has a uniform magnetic field $\vec{B}$ po

A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M(\gg m)$. The particle is m

A metal target with atomic number $Z=46$ is bombarded with a high energy electron beam. The emission of X-rays from the

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same po

A small electric dipole $\vec{p}_0$, having a moment of inertia $I$ about its center, is kept at a distance $r$ from the

A table tennis ball has radius $(3 / 2) \times 10^{-2} \mathrm{~m}$ and mass $(22 / 7) \times 10^{-3} \mathrm{~kg}$. It

A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}

The dimensions of a cone are measured using a scale with a least count of $2 \mathrm{~mm}$. The diameter of the base and

A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$

A charge is kept at the central point $\mathrm{P}$ of a cylindrical region. The two edges subtend a half-angle $\theta$

Two equilateral-triangular prisms $\mathrm{P}_1$ and $\mathrm{P}_2$ are kept with their sides parallel to each other, in

An infinitely long thin wire, having a uniform charge density per unit length of $5 \mathrm{nC} / \mathrm{m}$, is passin

A spherical soap bubble inside an air chamber at pressure $P_0=10^5 \mathrm{~Pa}$ has a certain radius so that the exces

The $8^{\text {th }}$ bright fringe above the point $\mathrm{O}$ oscillates with time between two extreme positions. The

The maximum speed in $\mu \mathrm{m} / \mathrm{s}$ at which the $8^{\text {th }}$ bright fringe will move is ______.

If the collision occurs at time $t_0=0$, the value of $v_{\mathrm{cm}} /(a \omega)$ will be ______.

If the collision occurs at time $t_0=\pi /(2 \omega)$, then the value of $4 b^2 / a^2$ will be ______.