The number of protons, neutrons and electrons in $$_6^{13}$$C respectively are

The masses of an electron, a proton and a neutron respectively will be n the ratio

Match the following species with the correct number of electrons present in them. .tg {border-collapse:collapse;border

The correct order of electronegativity of carbon in various hybridisation states is

Which of the following is not arranged in the correct sequence?

Which of the following statement is incorrect?

Bond order is an inverse measure of

Which of the following molecule has the maximum dipole moment?

Which compound among the following will have a permanent dipole moment?

Which among the following statements is/are incorrect regarding real gases? (i) Their compressibility factor is never eq

Which among the following species does not show disproportionation reaction?

An alloy of metals X and Y weighs 12 g and contains atoms X and Y in the ratio of 2 : 5. The percentage of metal X in th

For the reaction, $$\mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})$$ at $$T=100^{\circ}

At $$60^{\circ} \mathrm{C}$$, dinitrogen tetroxide is dissociated. Find it's standard free energy change at this tempera

The solubility of $$\operatorname{AgBr}(s)$$, having solubility product $$5 \times 10^{-10}$$ in $$0.2 \mathrm{~M} \math

Le-Chatelier's principle is not applicable to

Which of the following does not form double salts?

$$\mathrm{AlF}_3$$ is soluble in HF only in the presence of KF due to formation of

What would be the product of following reaction? $$\mathrm{SiCl}_4 \stackrel{\text { Excess of } \mathrm{H}_2 \mathrm{O}

Which among the following is not a greenhouse gas?

An organic compound of molecular formula $$\mathrm{C_6H_6Br_2}$$ has six carbon atoms in a ring system, two non-conjugat

Using Kjeldahl’s method over 1g of a soil sample, the ammonia evolved could neutralise 25 mL of 1 M H$$_2$$SO$$_4$$. The

Which compound among the following is most reactive towards electrophilic reagents?

Which of the following is not explained by hyperconjugation?

In the face centered unit cell, the lattice points are present at

If the $$K_{\mathrm{H}}$$ values for $$\operatorname{Ar}(g), \mathrm{CO}_2(g), \mathrm{HCHO}(g)$$ and $$\mathrm{CH}_4(\m

If 500 mL of CaCl$$_2$$ solution contains 3.01 $$\times$$ 10$$^{22}$$ chloride ions, molarity of the solution will be

Which statement among the following is incorrect?

For zero order reaction, a plot of $$t_{1 / 2}$$ versus $$[A]_0$$ will be

If hydrogen electrons dipped in two solutions of pH = 3 and pH = 6 are connected by a salt bridge, the emf of the result

In an adsorption experiment, a graph between $$\log (x / m)$$ versus $$\log p$$ was found to be linear with a slope of $

The correct order of sulphur-oxygen bond in $$\mathrm{SO}_3, \mathrm{~S}_2 \mathrm{O}_3^{2-}$$ and $$\mathrm{SO}_4^{2-}$

Potassium cyanide is made alkaline with NaOH and boiled with thiosulphate ions. The solution is cooled and acidified wit

Which among the following is coloured?

Which of the following complexes formed by nickel is tetrahedral and paramagnetic?

Vitamin-B$$_1$$ is

Identify the product of the following reaction.

The correct order of acidic strength among the following is

Identify (Z) in the following reaction. $$\mathrm{C{H_3}COOH\buildrel {LiAl{H_4}} \over \longrightarrow (X)\mathrel{\ma

Identify the major product of the following reaction.

$$f(x)=\sin x+\cos x \cdot g(x)=x^2-1$$, then $$g(f(x))$$ is invertible if

If $$f: z \rightarrow z$$ is defined by $$f(x)=x^9-11 x^8-2 x^7+22 x^6+x^4 -12 x^3+11 x^2+x-3, \forall x \in z$$, then $

Let $$f(x)=x^3$$ and $$g(x)=3^x$$, then the quadratic equation whose roots are solutions of the equation $$(f \circ g)(x

The trace of the matrix $$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$ is

If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z

If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta

If $$z_1=2+3 i$$ and $$z_2=3+2 i$$, where $$i=\sqrt{-1}$$, then $$\left[\begin{array}{cc}z_1 & z_2 \\ -\bar{z}_2 & \bar{

What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ?

The radius of the circle represented by $$(1+i)(1+3i)(1+7i)=x+iy$$ is $$(i=\sqrt{-1})$$.

If $$1, \alpha_1, \alpha_2, \alpha_3$$ and $$\alpha_4$$ are the roots of $$z^5-1=0$$ and $$\omega$$ is a cube root of un

If $$a > 0$$ and $$z=x+i y$$, then $$\log _{\cos ^2 \theta}|z-a|>\log _{\cos ^2 \theta}|z-a i|,(\theta \in R)$$ implies

If one root of the equation $$i x^2-2(i+1) x+(2-i)=0$$ is $$(2-i)$$, then the other root is

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\

If $$2, 1$$ and $$1$$ are roots of the equation $$x^3-4 x^2+5 x-2=0$$, then the roots of $$\left(x+\frac{1}{3}\right)^3-

If $$f(x)=2x^3+mx^2-13x+n$$ and 2, 3 are the roots of the equation $$f(x)=0$$, then the values of m and n are

The value of $${ }^6 P_4+4 \cdot{ }^6 P_3$$ is

The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is

In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?

Given, $$\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}$$, then $$4 A+2 B+4 C$$ is equal to

What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ?

If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third qu

If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1

If $$\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$$, then $$\theta$$ is equal

If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$

In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B

In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum

The position vectors of the points $$A$$ and $$B$$ with respect to $$O$$ are $$2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\ha

Let $$\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j

If the lines, $$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$ and $$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$ are

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$

Let $$\mathbf{a}=\hat{\mathbf{i}}$$ and $$\mathbf{b}=\hat{\mathbf{j}}$$, the point of intersection of the lines $$\mathb

The mean deviation from the mean of the set of observation $$-1,0,4$$ is

Let an angle of a triangle is 60$$^\circ$$. If the variance of the angles of the triangle is 1014$$^\circ$$, then the ot

One card is selected at random from 27 cards numbered form 1 to 27. What is the probability that the number on the card

Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white

The probabilities that $$A$$ and $$B$$ speak truth are $$\frac{4}{5}$$ and $$\frac{3}{4}$$ respectively. The probability

The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater tha

For the random variable X with probability distribution is given by the table .tg {border-collapse:collapse;border-spa

The locus of a point, which is at a distance of 4 units from $$(3,-2)$$ in $$x y$$-plane is

When the axes are rotated through an angle 45$$^\circ$$, the new coordinates of a point P are (1, $$-$$1). The coordinat

Find the equation of a straight line passing through $$(-5,6)$$ and cutting off equal intercepts on the coordinate axes.

Line has slope $$m$$ and $$y$$-intercept 4 . The distance between the origin and the line is equal to

The equation of the base of an equilateral triangle is $$x+y=2$$ and one vertex is $$(2,-1)$$, then the length of the si

The equation of a straight line which passes through the point $$\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$$ and p

The acute angle between lines $$6 x^2+11 x y-10 y^2=0$$ is

If the lines, joining the origin to the points of intersection of the curve $$2 x^2-2 x y+3 y^2+2 x-y-1=0$$ and the line

The equation of bisector of the angle between the lines represented by $$3 x^2-5 x y+4 y^2=0$$ is

If the bisectors of the pair of lines $$x^2-2 m x y-y^2=0$$ is represented by $$x^2-2 n x y-y^2=0$$, then

Find the equation of the circle which passes through origin and cuts off the intercepts $$-$$2 and 3 over the $$X$$ and

The angle between the pair of tangents drawn from $$(1,1)$$ to the circle $$x^2+y^2+4 x+4 y-1=0$$ is

If the circle $$x^2+y^2-4 x-8 y-5=0$$ intersects the line $$3 x-4 y-m=0$$ in two distinct points, then the number of int

Let $$C$$ be the circle center $$(0,0)$$ and radius 3 units. The equation of the locus of the mid-points of the chords o

The length of the common chord of the circles $$x^2+y^2+3x+5y+4=0$$ and $$x^2+y^2+5x+3y+4=0$$ is __________ units.

Find the equation of the circle which passes through the point $$(1,2)$$ and the points of intersection of the circles $

The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a para

If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one

If one focus of a hyperbola is $$(3,0)$$, the equation of its directrix is $$4 x-3 y-3=0$$ and its eccentricity $$e=5 /

If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthoc

A(2, 3, 4), B(4, 5, 7), C(2, $$-$$6, 3) and D(4, $$-$$4, k) are four points. If the line AB is parallel to CD, then k is

If the direction cosines of two lines are $$\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)$$ and $$\left( {{5 \ove

$$\mathop {\lim }\limits_{n \to \infty } {{n{{(2n + 1)}^2}} \over {(n + 2)({n^2} + 3n - 1)}}$$ is equal to

If the function $$f(x)$$, defined below, is continuous on the interval $$[0,8]$$, then $$f(x)=\left\{\begin{array}{cc}x^

If $$f(x)$$, defined below, is continuous at $$x=4$$, then $$f(x) = \left\{ {\matrix{ {{{x - 4} \over {|x - 4|}} + a}

If $$f(x)=2x^2+3x-5$$, then the value of $$f'(0)+3f'(-1)$$ is equal to

If $$y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)$$

$$\frac{d}{d x}\left\{\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\right\}$$ is equal to

If $$y=\tan ^{-1}\left\{\frac{a x-b}{b x+a}\right\}$$, then $$y^{\prime}$$ is equal to

If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are

Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are t

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating i

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively.

$$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to

If $$\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C$$, then $$k$$ is equal to

If $$\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.$$ then $$f(x) \cdot g(x)$$ i

If $$\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R$$, then $$\frac{P}{Q}$$ is equal to

If $$\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}} $$, then the value of a is equal to

$$\int_1^2 {{{{x^3} - 1} \over {{x^2}}}} $$ is equal to

The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of

The displacement of a particle starting from rest at $$t=0$$ is given by $$s=9 t^2-2 t^3$$. The time in seconds at which

The range of a projectile is 100 m. Its kinetic energy will be maximum after covering a distance of

Two cars A and B are moving with a velocity of 30 km/h in the same direction. They are separated by 10 km. The speed of

A book is lying on a table. What is the angle between the normal reaction acting on the book on the table and the weight

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $$(f_a )$$ cannot

When a force F = 17 $$-$$ 2x + 6x$$^2$$N acts on a body of mass 2 kg and displaces it from x = 0 m to x = 8 m, the work

A rifle bullet loses $$\left(\frac{1}{25}\right)$$th of its velocity in passing through a plank. The least number of suc

A uniform chain has a mass m and length $$l$$. It is held on a frictionless table with one-sixth of its length hanging o

A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cove

Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a

If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of ine

A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscilla

The gravitational potential energy is maximum at

A geostationary satellite is taken to a new orbit, such that its distance from centre of the earth is doubled. Then, fin

A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 $$\times$$ 10$$^7$$ Nm$$^{-2}$$.

A glass flask weighting 390 g, having internal volume 500 cc just floats when half of it is filled with water. Specific

Water does not wet an oily glass because

Boiling water is changing into steam. The specific heat of boiling water is

If the volume of a block of metal changes by $$0.12 \%$$ when heated through $$20^{\circ} \mathrm{C}$$, then find its co

Isothermal process is the graph between

For a monoatomic ideal gas is following the cyclic process ABCA shown in the U versus p plot, identify the incorrect opt

The pressure of a gas is proportional to

A string fixed at both ends vibrate in 5 loops as shown in the figure. The total number of nodes and anti-nodes respecti

The position of the direct image obtained at O, when a monochromatic beam of light is passed through a plane transmissio

What is the electric flux for Gaussian surface $$A$$ that encloses the charged particles in free space? [Given, $$q_1=-1

Two charges 8 $$\mu$$C each are placed at the corners A and B of an equilateral triangle of side 0.2 m in air. The elect

A 60 $$\mu$$F parallel plate capacitor whose plates are separated by 6 mm is charged to 250 V, and then the charging sou

Five current carrying conductors meet at a point P. What is the magnitude and direction of the current in the fifth cond

A wire of length $$L$$ metre carrying a current $$I$$ ampere is bent in the form of a circle. Magnitude of its magnetic

What is the net force on the square coil?

A paramagnetic sample showing a net magnetisation of $$0.8 \mathrm{~A} \mathrm{~m}^{-1}$$, when placed in an external ma

The induced emf cannot be produced by

Assertion (A) When plane of coil is perpendicular to magnetic field, magnetic flux linked with the coil is minimum, but

A 20 V AC is applied to a circuit consisting of a resistor and a coil with negligible resistance. If the voltage across

The electric and the magnetic fields associated with an electromagnetic wave propagating along the $$z$$-axis, can be re

The graph between the maximum speed $$(v_{max})$$ of a photoelectron and frequency $$(\nu)$$ of the incident radiation,

The angular momentum of the orbital electron is integral multiple of

Which of the following values is the correct order of nuclear density?

The truth table given below corresponds to logic gate.