$$250 \mathrm{~g}$$ solution of $$\mathrm{D}$$-glucose in water contains $$10.8 \%$$ of carbon by weight. The molality o

Given below are two statements. Statement I: $$\mathrm{O}_{2}, \mathrm{Cu}^{2+}$$, and $$\mathrm{Fe}^{3+}$$ are weakly a

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Energ

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Acti

Boiling point of a $$2 \%$$ aqueous solution of a non-volatile solute A is equal to the boiling point of $$8 \%$$ aqueou

The incorrect statement is

Given below are two statements. Statement I : Iron (III) catalyst, acidified $$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}

The total number of $$\mathrm{Mn}=\mathrm{O}$$ bonds in $$\mathrm{Mn}_{2} \mathrm{O}_{7}$$ is __________.

Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R. Assertion A: [6]

In the above reaction product B is :

A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol giv

In Carius method of estimation of halogen, $$0.45 \mathrm{~g}$$ of an organic compound gave $$0.36 \mathrm{~g}$$ of $$\m

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$$20 \mathrm{~mL}$$ of $$0.02 \,\mathrm{M} \,\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$$ solution is used for the ti

$$2 \mathrm{NO}+2 \mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}$$ The above reaction has been st

Amongst the following, the number of oxide(s) which are paramagnetic in nature is $$\mathrm{Na}_{2} \mathrm{O}, \mathrm{

The molar heat capacity for an ideal gas at constant pressure is $$20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1

According to MO theory, number of species/ions from the following having identical bond order is ________. $$\mathrm{CN}

At $$310 \mathrm{~K}$$, the solubility of $$\mathrm{CaF}_{2}$$ in water is $$2.34 \times 10^{-3} \mathrm{~g} / 100 \math

The conductivity of a solution of complex with formula $$\mathrm{CoCl}_{3}\left(\mathrm{NH}_{3}\right)_{4}$$ corresponds

In the titration of $$\mathrm{KMnO}_{4}$$ and oxalic acid in acidic medium, the change in oxidation number of carbon at

Optical activity of an enantiomeric mixture is $$+12.6^{\circ}$$ and the specific rotation of $$(+)$$ isomer is $$+30^{\

In the following reaction The $$\%$$ yield for reaction I is $$60 \%$$ and that of reaction II is $$50 \%$$. The overal

Let $$R_{1}$$ and $$R_{2}$$ be two relations defined on $$\mathbb{R}$$ by $$a \,R_{1} \,b \Leftrightarrow a b \geq 0$$ a

Let $$f, g: \mathbb{N}-\{1\} \rightarrow \mathbb{N}$$ be functions defined by $$f(a)=\alpha$$, where $$\alpha$$ is the m

Let the minimum value $$v_{0}$$ of $$v=|z|^{2}+|z-3|^{2}+|z-6 i|^{2}, z \in \mathbb{C}$$ is attained at $${ }{z}=z_{0}$

Let $$A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$$. Let $$\alpha, \beta \in \mathbb{R}$$ be such that $

The remainder when $$(2021)^{2022}+(2022)^{2021}$$ is divided by 7 is

Suppose $$a_{1}, a_{2}, \ldots, a_{n}$$, .. be an arithmetic progression of natural numbers. If the ratio of the sum of

Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined as $$f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x],

Let $$ I=\int_{\pi / 4}^{\pi / 3}\left(\frac{8 \sin x-\sin 2 x}{x}\right) d x $$. Then

The area of the smaller region enclosed by the curves $$y^{2}=8 x+4$$ and $$x^{2}+y^{2}+4 \sqrt{3} x-4=0$$ is equal to

Let $$y=y_{1}(x)$$ and $$y=y_{2}(x)$$ be two distinct solutions of the differential equation $$\frac{d y}{d x}=x+y$$, wi

Let $$\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}$$ and $$\vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}$$ be two vectors, such

Let $$S$$ be the sample space of all five digit numbers. It $$p$$ is the probability that a randomly selected number fro

Let $$A(1,1), B(-4,3), C(-2,-5)$$ be vertices of a triangle $$A B C, P$$ be a point on side $$B C$$, and $$\Delta_{1}$$

If the circle $$x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$$ passes through the point $$(6,1)$$ and its centre li

Let a function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be defined as : $$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|

For $$k \in \mathbb{R}$$, let the solutions of the equation $$\cos \left(\sin ^{-1}\left(x \cot \left(\tan ^{-1}\left(\c

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 i

An ellipse $$E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ passes through the vertices of the hyperbola $$H: \frac{x^{

Let $$y=y(x)$$ be the solution curve of the differential equation $$\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x

Let $$f(x)=2 x^{2}-x-1$$ and $$\mathrm{S}=\{n \in \mathbb{Z}:|f(n)| \leq 800\}$$. Then, the value of $$\sum\limits_{n \

Let $$S$$ be the set containing all $$3 \times 3$$ matrices with entries from $$\{-1,0,1\}$$. The total number of matric

If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of i

Let $$S=\left\{z \in \mathbb{C}: z^{2}+\bar{z}=0\right\}$$. Then $$\sum\limits_{z \in S}(\operatorname{Re}(z)+\operatorn

A torque meter is calibrated to reference standards of mass, length and time each with $$5 \%$$ accuracy. After calibrat

A bullet is shot vertically downwards with an initial velocity of $$100 \mathrm{~m} / \mathrm{s}$$ from a certain height

Sand is being dropped from a stationary dropper at a rate of $$0.5 \,\mathrm{kgs}^{-1}$$ on a conveyor belt moving with

A bag is gently dropped on a conveyor belt moving at a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The coefficient of frict

Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$, having masses in the ratio $$4: 3$$, are revolving in circular orbits

If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A

Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, th

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is

Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The intern

A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance

A beam of light travelling along $$X$$-axis is described by the electric field $$E_{y}=900 \sin \omega(\mathrm{t}-x / c)

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a li

An electron (mass $$\mathrm{m}$$) with an initial velocity $$\vec{v}=v_{0} \hat{i}\left(v_{0}>0\right)$$ is moving in an

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below. The logi

In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance $$30 \mathr

The one division of main scale of Vernier callipers reads $$1 \mathrm{~mm}$$ and 10 divisions of Vernier scale is equal

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference b

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}

A $$1 \mathrm{~m}$$ long copper wire carries a current of $$1 \mathrm{~A}$$. If the cross section of the wire is $$2.0 \

A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric f

A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When th

A square aluminum (shear modulus is $$25 \times 10^{9}\, \mathrm{Nm}^{-2}$$) slab of side $$60 \mathrm{~cm}$$ and thickn

A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\rig

A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ wi