Assuming that the incident radiation is capable of ejecting photoelectrons from all the given metals, the lowest kinetic

If the energies of two light radiations $$E_1$$ and $$E_2$$ are $$25 \mathrm{~eV}$$ and $$100 \mathrm{~eV}$$ respectivel

The electronic configuration of $$\mathrm{Fe}^{3+}$$ is (atomic number of $$\mathrm{Fe}=26$$ )

The element with outer electronic configuration $$(n-1) d^2 n s^2$$, where $$n=4$$, would belong to

Choose the correct option regarding the following statements Statement 1 Nitrogen has lesser electron gain enthalpy than

Among the given configurations, identify the element which does not belong to the same family as the others?

Which compound among the following has the highest dipole moment?

How many among the given species have a bond order of 0.5 ? $$\mathrm{H}_2^{+}, \mathrm{He}_2^{+}, \mathrm{He}_2^{-}, \m

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Among the following the maximum deviation from ideal gas behaviour is expected from

Two flasks $$A$$ and $$B$$ have equal volumes. $$A$$ is maintained at $$300 \mathrm{~K}$$ and $$B$$ at $$600 \mathrm{~K}

If 0.2 moles of sulphuric acid is poured into 250 mL of water, calculate the concentration of the solution.

For the redox reaction $$\mathrm{MnO}_4^{-}+\mathrm{C}_2 \mathrm{O}_4^{2-}+\mathrm{H}^{+} \longrightarrow \mathrm{Mn}^{2

When the temperature of 2 moles of an ideal gas is increased by 20$$^\circ$$C at constant pressure. Find the work involv

Using the data provided, find the value of equilibrium constant for the following reaction at $$298 \mathrm{~K}$$ and $$

Calculate the pOH of 0.10 M HCl solution.

Which among the following pairs is not an acidic buffer?

Assertion (A) The colour of old lead paintings can be restored by washing them with a dilute solution of $$\mathrm{H}_2

In the preparation of baking soda, H$$_2$$O and CO$$_2$$ in ratio ......... is used to react with Na$$_2$$CO$$_3$$.

The structure of diborane B$$_2$$H$$_6$$ is given below. Identify the bond angles of x and y. In diborane, ........... a

The incorrect statement(s) among the following is/are

Which among the following has the highest concentration of PAN?

What is the IUPAC name of $$\mathrm{CH}_3 \mathrm{CH}\left(\mathrm{CH}_2 \mathrm{CH}_3\right) \mathrm{CHO}$$ ?

Among the following, in which type of chromatography, both stationary and mobile phases are in liquid state?

The product formed when a hydrocarbon $$X$$ of molecular formula $$\mathrm{C}_6 \mathrm{H}_{10}$$ is reacted with sodami

The fcc crystal contains how many atoms in each unit cell?

Which condition is not satisfied by an ideal solution?

A solution of urea (molar mass $$60 \mathrm{~g} \mathrm{~mol}^{-1}$$ ) boils at $$100.20^{\circ} \mathrm{C}$$ at the atm

At $$291 \mathrm{~K}$$, saturated solution of $$\mathrm{BaSO}_4$$ was found to have a specific conductivity of $$3.648 \

Find the emf of the following cell reaction. Given, $$E_{\mathrm{Cr}^{3+} / \mathrm{Cr}^{2+}}^{\Upsilon}=-0.72 \mathrm{~

For $$\mathrm{C{r_2}O_7^{2 - } + 14{H^ + } + 6{e^ - }\buildrel {Yields} \over \longrightarrow 2C{r^{3 + }} + 7{H_2}O,{E

The protective power of a lyophilic colloidal sol is expressed in terms of

Due to $$p \pi-p \pi$$ bonding interactions, nitrogen for $$\mathrm{N}_2$$. But phosphorus forms .................. and

Identify the incorrect statements among the following? (i) $$\mathrm{SF}_6$$ does not react with water. (ii) $$\mathrm{S

Which statements among the following are correct about helium? (i) Liquid helium is used to sustain powerful superconduc

The magnetic moment of Fe$$^{2+}$$ is ........ BM.

Which of the following statement is not correct?

Assertion (A) An optically active amino acid can exist in three forms depending on the pH of the solution. Reason (R) Am

The IUPAC name of diacetone alcohol is.

Identify the product of the following reaction.

The real valued function $$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+1$$ defined on $$R /\{0\}$$ is

The domain of the function $$f(x)=\frac{1}{[x]-1}$$, where $$[x]$$ is greatest integer function of $$x$$ is

Let $$f: R \rightarrow R$$ be a function defined by $$f(x)=\frac{4^x}{4^x+2}$$, what is the value of $$f\left(\frac{1}{4

For what natural number $$n \in N$$, the inequality $$2^n > n+1$$ is valid?

The value of $$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$ is

Let $$A, B, C, D$$ be square real matrices such that $$C^T=D A B, D^{\mathrm{T}}=A B C$$ and $$S=A B C D$$, then $$S^2$$

$$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$$ and $$B=\left[\begin{arr

Let $$a, b$$ and $$c$$ be such that $$b+c \neq 0$$ and $$\begin{aligned} & \left|\begin{array}{ccc} a & a+1 & a-1 \\ -b

If $$|z-2|=|z-1|$$, where $$z$$ is a complex number, then locus $$z$$ is a straight line

If $${\left( {{{1 + i} \over {1 - i}}} \right)^m} = 1$$, then m cannot be equal to

If $$1+x^2=\sqrt{3} x$$, then $$\sum_{n=1}^{24}\left(x^n-\frac{1}{x^n}\right)^2$$ is equal to

If $$\alpha$$ and $$\beta$$ are the roots of $$11 x^2+12 x-13=0$$, then $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}$$ is equa

The value of $$a$$ for which the equations $$x^3+a x+1=0$$ and $$x^4+a x^2+1=0$$ have a common root is

If $$a$$ is a positive integer such that roots of the equation $$7 x^2-13 x+a=0$$ are rational numbers, then the smalles

Let $$p$$ and $$q$$ be the roots of the equation $$x^2-2 x+A=0$$ and let $$r$$ and $$s$$ be the roots of the equation $$

For $$1 \leq r \leq n, \frac{1}{r+1}\left\{{ }^n P_{r+1}-{ }^{(n-1)} P_{r+1}\right\}$$ is equal to

In how many ways 4 balls can be picked from 6 black and 4 green coloured balls such that at least one black ball is sele

In how many ways can 9 examination papers be arranged so, that the best and the worst papers are never together?

Which of the following is partial fraction of $$\frac{-x^2+6 x+13}{(3 x+5)\left(x^2+4 x+4\right)}$$ is equal to

In a $$\triangle A B C$$, if $$3 \sin A+4 \cos B=6$$ and $$4 \sin B+3 \cos A=1$$, then $$\sin (A+B)$$ is equal to

$$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$$ is equal to

If $$f(x)=\frac{\cot x}{1+\cot x}$$ and $$\alpha+\beta=\frac{5 \pi}{4}$$, then the value of $$f(\alpha) f(\beta)$$ is eq

If $$\theta \in[0,2 \pi]$$ and $$\cos 2 \theta=\cos \theta+\sin \theta$$, then the sum of all values of $$\theta$$ satis

For how many distinct values of $$x$$, the following $$\sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0

In $$\triangle A B C$$, suppose the radius of the circle opposite to an angle $$A$$ is denoted by $$r_1$$, similarly $$r

In $$\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$$, then $$\tan \frac{C}{8}$$ is equal to

Which of the following vector is equally inclined with the coordinate axes?

If $$\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$, a

$$X$$ intercept of the plane containing the line of intersection of the planes $$x-2 y+z+2=0$$ and $$3 x-y-z+1=0$$ and a

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf

Let $$L_1$$ (resp, $$L_2$$ ) be the line passing through $$2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$$ (resp. $$2 \hat{\mathbf

Let $$\mathbf{a}, \mathbf{b}$$ and $$\mathbf{c}$$ be three-unit vectors and $$\mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cd

Let $$x$$ and $$y$$ are real numbers. If $$\mathbf{a}=(\sin x) \hat{\mathbf{i}}+(\sin y) \hat{\mathbf{j}}$$ and $$\mathb

The mean and variance of $$n$$ observations $$x_1, x_2, x_3, \ldots . . x_n$$ are 5 and 0 respectively. If $$\sum_{i=1}^

Mean of the values $$\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$$ is

P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stati

If $$A$$ and $$B$$ are two events with $$P(A \cap B)=\frac{1}{3}, P(A \cup B)=\frac{5}{6}$$ and $$P\left(A^C\right)=\fra

A coin is tossed 2020 times. The probability of getting head on 1947th toss is

A discrete random variable X takes values 10, 20, 30 and 40. with probability 0.3, 0.3, 0.2 and 0.2 respectively. Then t

Let $$X$$ be a random variable which takes values $$1,2,3,4$$ such that $$P(X=r)=K r^3$$ where $$r=1,2,3,4$$ then

Given, two fixed points $$A(-2,1)$$ and $$B(3,0)$$. Find the locus of a point $$P$$ which moves such that the angle $$\a

When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new syste

If $$A(4,7), B(-7,8)$$ and $$C(1,2)$$ are the vertices of $$\triangle A B C$$, then the equation of perpendicular bisect

The ratio in which the straight line $$3 x+4 y=6$$ divides the join of the points $$(2,-1)$$ and $$(1,1)$$ is

Find the equation of a line passing through the point $$(4,3)$$, which cuts a triangle of minimum area from the first qu

If the orthocenter of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y+1=0$$ and $$a x+b y-1=0$$ lies at origin, th

The equation $$8 x^2-24 x y+18 y^2-6 x+9 y-5=0$$ represents a

Find the angle between the pair of lines represented by the equation $$x^2+4 x y+y^2=0$$.

If the acute angle between lines $$a x^2+2 h x y+b y^2=0$$ is $$\frac{\pi}{4}$$, then $$4 h^2$$ is equal to

The angle between the lines represented by $$\cos \theta(\cos \theta+1) x^2-\left(2 \cos \theta+\sin ^2 \theta\right) x

The equations of the tangents to the circle $$x^2+y^2=4$$ drawn from the point $$(4,0)$$ are

If $$P(-9,-1)$$ is a point on the circle $$x^2+y^2+4 x+8 y-38=0$$, then find equation of the tangent drawn at the other

Find the equation of a circle whose radius is 5 units and passes through two points on the $$X$$-axis, which are at a di

If a foot of the normal from the point $$(4,3)$$ to a circle is $$(2,1)$$ and $$2 x-y-2=0$$, is a diameter of the circle

The length of the tangent from any point on the circle $$(x-3)^2+(y+2)^2=5 r^2$$ to the circle $$(x-3)^2+(y+2)^2=r^2$$ i

The equation of the circle, which cuts orthogonally each of the three circles $$\begin{aligned} & x^2+y^2-2 x+3 y-7=0, \

Find the equation of the parabola which passes through (6, $$-$$2), has its vertex at the origin and its axis along the

In an ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentr

If the points (2, 4, $$-$$1), (3, 6, $$-$$1) and (4, 5, $$-$$1) are three consecutive vertices of a parallelogram, then

$$A(-1,2-3), B(5,0,-6)$$ and $$C(0,4,-1)$$ are the vertices of a $$\triangle A B C$$. The direction cosines of internal

If the projections of the line segment AB on xy, yz and zx planes are $$\sqrt{15},\sqrt{46},7$$ respectively, then the p

Find the equation of the plane passing through the point $$(2,1,3)$$ and perpendicular to the planes $$x-2 y+2 z+3=0$$ a

If $$f(x)=\left\{\begin{array}{cc}\frac{e^{\alpha x}-e^x-x}{x^2}, & x \neq 0 \\ \frac{3}{2}, & x=0\end{array}\right.$$

The value of $$k(k > 0)$$, for which the function $$f(x)=\frac{\left(e^x-1\right)^4}{\sin \left(\frac{x^2}{k^2}\right) \

If $$\log \left(\sqrt{1+x^2}-x\right)=y\left(\sqrt{1+x^2}\right)$$, then $$\left(1+x^2\right) \frac{d y}{d x}+x y$$ is e

If $$f^{\prime \prime}(x)$$ is continuous at $$x=0$$ and $$f^{\prime \prime}(0)=4$$, then find the following value. $$\l

If $$y=e^{x^2+e^{x^2+e^{x^2+\cdots \infty}}}$$, then $$\frac{d y}{d x}$$ is equal to

$$\frac{d}{d x}\left[\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)\right]$$ is equal to

The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is

Given, $$f(x)=x^3-4x$$, if x changes from 2 to 1.99, then the approximate change in the value of $$f(x)$$ is

If the curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect at right angles, then $$a^2$$ is equal to

Let $$x$$ and $$y$$ be the sides of two squares such that, $$y=x-x^2$$. The rate of change of area of the second square

If $$f^{\prime \prime}(x)$$ is a positive function for all $$x \in R, f^{\prime}(3)=0$$ and $$g(x)=f\left(\tan ^2(x)-2 \

$$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$$ is equal to

$$\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x$$ is equal to

$$\int \sqrt{e^{4 x}+e^{2 x}} d x$$ is equal to

If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to

If $$\int_0^{\pi / 2} \tan ^n(x) d x=k \int_0^{\pi / 2} \cot ^n(x) d x$$, then

$$\int_0^2 x e^x d x$$ is equal to

If $$x^2+y^2=1$$, then

The speed of ripples $$(v)$$ on water surface depends on surface tension $$(\sigma)$$, density $$(\rho)$$ and wavelength

An object travelling at a speed of 36 km/h comes to rest in a distance of 200 m after the brakes were applied. The retar

A ball is projected upwards. Its acceleration at the highest point is

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/h. The centripetal force acting on the car is

A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of

Two blocks $$A$$ and $$B$$ of masses $$4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ are as shown in the figure. A horizontal

What is the shape of the graph between speed and kinetic energy of a body?

A quarter horse power motor runs at a speed of 600 rpm. Assuming 60% efficiency, the work done by the motor in one rotat

A particle of mass m is projected with a velocity u making an angle $$\theta$$ with the horizontal. The magnitude of ang

A sphere of mass m is attached to a spring of spring constant k and is held in unstretched position over an inclined pla

A girl of mass M stands on the rim of a frictionless merry-go-round of radius R and rotational inertia I, that is not mo

A block of mass $$\mathrm{l} \mathrm{kg}$$ is fastened to a spring of spring constant of $$100 ~\mathrm{Nm}^{-1}$$. The

The scale of a spring balance which can measure from 0 to $$15 \mathrm{~kg}$$ is $$0.25 \mathrm{~m}$$ long. If a body su

The distance through which one has to dig the Earth from its surface, so as to reach the point where the acceleration du

Infinite number of masses each of 3kg are placed along a straight line at the distances of 1 m, 2m, 4m, 8m, ...... from

Young's modulus of a wire is $$2 \times 10^{11} \mathrm{Nm}^{-2}$$. If an external stretching force of $$2 \times 10^{11

Identify the incorrect statement regarding Reynold's number $$\left(R_e\right)$$.

Expansion during heating

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Which of the following is not a reversible process?

Which one of the graphs below best illustrates the relationship between internal energy U of an ideal gas and temperatur

A refrigerator with coefficient of performance 0.25 releases 250 J of heat to a hot reservoir. The work done on the work

A vessel has 6 g of oxygen at pressure p and temperature 400 K. A small hole is made in it, so that oxygen leaks out. Ho

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Light of wavelength $$300 \mathrm{~nm}$$ in medium $$A$$ enters into medium $$B$$ through a plane surface. If the freque

In Young’s double slit experiment, the separation between the slits is halved and the distance between the screen is dou

Gauss's law helps in

Charge on the outer sphere is $$q$$ and the inner sphere is grounded. The charge on the inner sphere is $$q^{\prime}$$,

Four capacitors with capacitances $$C_1=l \propto \mathrm{F}, C_2=1.5 \propto \mathrm{F}, C_3=2.5 \propto \mathrm{F}$$ a

In a potentiometer of 10 wires, the balance point is obtained on the 6th wire. To shift the balance point to 8th wire, w

In a co-axial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions

The magnetic field, of a given length of wire for single turn coil, at its centre is B, then its value for two turns coi

A solenoid of length $$60 \mathrm{~cm}$$ with 15 turns per $$\mathrm{cm}$$ and area of cross-section $$4 \times 10^{-3}

A bulb of resistance $$280 \Omega$$ is supplied with a 200 V AC supply. What is the peak current?

The magnetic field of a plane electromagnetic wave is given by $$B=(400 \propto \mathrm{T})\sin \left[\left(4.0 \times 1

The de-Broglie wavelength associated with a proton under the influence of an electric potential of 100 V is

The ionisation potential of hydrogen atom is 13.6 V. How much energy need to be supplied to ionise the hydrogen atom in

Which of the following statement is correct?

The length of germanium rod is $$0.925 \mathrm{~cm}$$ and its area of cross-section is $$1 \mathrm{~mm}^2$$. If for germ

In an amplitude modulated signal, the maximum amplitude is $$15 \mathrm{~V}$$ and minimum amplitude is $$5 \mathrm{~V}$$