Combustion of glucose $$(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6)$$ produces $$\mathrm{CO}_2$$ and water. The amount o

Thiosulphate reacts differently with iodine and bromine in the reactions given below: $$\begin{aligned} & 2 \mathrm{~S}_

Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The st

Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. $$\mathrm{Fe}^{3+}$$ oxidises the iod

Which of the following are aromatic?

Among the following halogens $$\mathrm{F}_2, \mathrm{Cl}_2, \mathrm{Br}_2 \text { and } \mathrm{I}_2$$ Which can undergo

Which among the following compounds will undergo fastest SN2 reaction.

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Number of Complexes with even number of electrons in $$\mathrm{t_{2 g}}$$ orbitals is - $$\left[\mathrm{Fe}\left(\mathrm

For the given hypothetical reactions, the equilibrium constants are as follows : $$\begin{aligned} & \mathrm{X} \rightle

An octahedral complex with the formula $$\mathrm{CoCl}_3 \cdot \mathrm{nNH}_3$$ upon reaction with excess of $$\mathrm{A

In the given compound, the number of 2$$^\circ$$ carbon atom/s is ________.

Identify the major products A and B respectively in the following set of reactions.

Identify the product (P) in the following reaction:

Given below are two statements : In the light of the above statements, choose the most appropriate answer from the opti

Given below are two statements: Statement I: $$\mathrm{N}\left(\mathrm{CH}_3\right)_3$$ and $$\mathrm{P}\left(\mathrm{CH

The incorrect statement regarding the given structure is

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If $$279 \mathrm{~g}$$ of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of ani

Consider the following reaction $$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$ The time taken for A to become $$1 / 4^

Major product B of the following reaction has ________ $$\pi$$-bond.

A hypothetical electromagnetic wave is show below. The frequency of the wave is $$\mathrm{x} \times 10^{19} \mathrm{~Hz

Consider the figure provided. $$1 \mathrm{~mol}$$ of an ideal gas is kept in a cylinder, fitted with a piston, at the p

A solution containing $$10 \mathrm{~g}$$ of an electrolyte $$\mathrm{AB}_2$$ in $$100 \mathrm{~g}$$ of water boils at $$

Number of molecules from the following which are exceptions to octet rule is _________. $$\mathrm{CO}_2, \mathrm{NO}_2,

The number of optical isomers in following compound is : __________.

The 'spin only' magnetic moment value of $$\mathrm{MO}_4{ }^{2-}$$ is ________ BM. (Where M is a metal having least meta

Number of amine compounds from the following giving solids which are soluble in $$\mathrm{NaOH}$$ upon reaction with Hin

Let $$A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$$. If $$A^3=4 A^2-A-21 I$$, where

The value of $$k \in \mathbb{N}$$ for which the integral $$I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}$$, sat

Let $$f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10$$. The number of points of local maxima of $$f$$ in interval $$(0,2 \pi)$

The set of all $$\alpha$$, for which the vectors $$\vec{a}=\alpha t \hat{i}+6 \hat{j}-3 \hat{k}$$ and $$\vec{b}=t \hat{i

Let the circles $$C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$$ and $$C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$$ touch eac

Let $$f(x)$$ be a positive function such that the area bounded by $$y=f(x), y=0$$ from $$x=0$$ to $$x=a>0$$ is $$e^{-a}+

Let $$H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1$$ be the hyperbola, whose eccentricity is $$\sqrt{3}$$ and the length of the

The number of critical points of the function $$f(x)=(x-2)^{2 / 3}(2 x+1)$$ is

Let $$y=y(x)$$ be the solution of the differential equation $$(1+y^2) e^{\tan x} d x+\cos ^2 x(1+e^{2 \tan x}) d y=0, y(

Let the sum of two positive integers be 24 . If the probability, that their product is not less than $$\frac{3}{4}$$ tim

For the function $$f(x)=(\cos x)-x+1, x \in \mathbb{R}$$, between the following two statements (S1) $$f(x)=0$$ for only

Let $$P(x, y, z)$$ be a point in the first octant, whose projection in the $$x y$$-plane is the point $$Q$$. Let $$O P=\

Let $$z$$ be a complex number such that $$|z+2|=1$$ and $$\operatorname{lm}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$$. T

The sum of all the solutions of the equation $$(8)^{2 x}-16 \cdot(8)^x+48=0$$ is :

The equations of two sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ of a triangle $$\mathrm{ABC}$$ are $$4 x+y=14$$ and $$3 x

If $$\sin x=-\frac{3}{5}$$, where $$\pi

Let $$[t]$$ be the greatest integer less than or equal to $$t$$. Let $$A$$ be the set of all prime factors of 2310 and $

If the set $$R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}$$ has $$m$$ elements and $$\sum_\limits{n=1}^m\left(1-i^{n !}\r

If the shortest distance between the lines $$\begin{array}{ll} L_1: \vec{r}=(2+\lambda) \hat{i}+(1-3 \lambda) \hat{j}+(3

Let $$I(x)=\int \frac{6}{\sin ^2 x(1-\cot x)^2} d x$$. If $$I(0)=3$$, then $$I\left(\frac{\pi}{12}\right)$$ is equal to

If the orthocentre of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y-1=0$$ and $$a x+b y-1=0$$, is the centroid o

If the range of $$f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}

Let $$\vec{a}=9 \hat{i}-13 \hat{j}+25 \hat{k}, \vec{b}=3 \hat{i}+7 \hat{j}-13 \hat{k}$$ and $$\vec{c}=17 \hat{i}-2 \hat{

Let the positive integers be written in the form : If the $$k^{\text {th }}$$ row contains exactly $$k$$ numbers for ev

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, a

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $$X$$ and $$Y$

Let $$\alpha=\sum_\limits{r=0}^n\left(4 r^2+2 r+1\right){ }^n C_r$$ and $$\beta=\left(\sum_\limits{r=0}^n \frac{{ }^n C_

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$$. If the sum of the diagonal elements of $$A^{13}$$ is

Let the area of the region enclosed by the curve $$y=\min \{\sin x, \cos x\}$$ and the $$x$$ axis between $$x=-\pi$$ to

The value of $$\lim _\limits{x \rightarrow 0} 2\left(\frac{1-\cos x \sqrt{\cos 2 x} \sqrt[3]{\cos 3 x} \ldots \ldots . \

A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of c

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_

Average force exerted on a non-reflecting surface at normal incidence is $$2.4 \times 10^{-4} \mathrm{~N}$$. If $$360 \m

In an expression $$a \times 10^b$$ :

A clock has $$75 \mathrm{~cm}, 60 \mathrm{~cm}$$ long second hand and minute hand respectively. In 30 minutes duration t

The output $$\mathrm{Y}$$ of following circuit for given inputs is :

A player caught a cricket ball of mass $$150 \mathrm{~g}$$ moving at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. If the

Three bodies A, B and C have equal kinetic energies and their masses are $$400 \mathrm{~g}, 1.2 \mathrm{~kg}$$ and $$1.6

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dy

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly toward

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27^{\circ

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved ke

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions o

Critical angle of incidence for a pair of optical media is $$45^{\circ}$$. The refractive indices of first and second me

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume

Correct Bernoulli's equation is (symbols have their usual meaning) :

Binding energy of a certain nucleus is $$18 \times 10^8 \mathrm{~J}$$. How much is the difference between total mass of

In the given circuit, the terminal potential difference of the cell is :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation bet

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\fr

An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the sur

Three vectors $$\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$$ and $$\overrightarrow{\mathrm{OR}}$$ each o

A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly an

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density

A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coord

Resistance of a wire at $$0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$$ and $$t^{\circ} \mathrm{C}$$ is found to be $$1

A parallel beam of monochromatic light of wavelength $$600 \mathrm{~nm}$$ passes through single slit of $$0.4 \mathrm{~m

An electron with kinetic energy $$5 \mathrm{~eV}$$ enters a region of uniform magnetic field of 3 $$\mu \mathrm{T}$$ per

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{