.What is the shape and magnetic nature of permanganate ion?

Which of the following oxides can act both as an oxidising agent as well as reducing agent?

"The mass and energy both are conserved in an isolated system", is the statement of

Which among the following is correct for electrolysis of brine solution?

The number of pi-bonds present in benzoic acid molecule are

The elevation in boiling point of 0.25 molal aqueous solution of a substance is $\left(K_o=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$

The combining ratios of hydrogen and oxygen in water and hydrogen peroxide are $1: 8$ and $1: 16$. Which law is illustrated in this example?

If a metal crystallises in bcc structure with edge length of unit cell $4.29 \times 10^{-8} \mathrm{~cm}$ the radius of metal atom is

The temperature of $32^{\circ} \mathrm{C}$ is equivalent to

The element which does not belong to group 15 is

The precipitation power of an electrolyte increases with

In leaching of alumina from bauxite by Bayer's process, then ore is treated with

The diagonal relationship in Be and Al is due to

Carbolic acid is oxidised by acidified sodium dichromate to give

The highest oxidation state in plutonium (At. no. $=94$) is

In the electrolysis of aqueous sodium chloride with inert electrodes the products obtained at anode and cathode respectively are

What type of hybridisation is present in carbocation formed during the alkaline hydrolysis of 1 - bromo-1-phenyl ethane?

The integrated rate equation for first order reaction, $A \rightarrow$ product, is

Calculate E.M.F. of following cell at 298 K $\mathrm{Zn}(s)\left|\mathrm{ZnSO}_4(0.01 \mathrm{M})\right|\left|\mathrm{CuSO}_4(1.0 \mathrm{M})\right| \mathrm{Cu}(\mathrm{s})$ if $\mathrm{E}^{\circ}$ cell $=2.0 \mathrm{~V}$

Which mixture is used for respiration by deep sea divers?

Which element among the following is not present in saccharine?

Which among the following statements is true about Schottky defect?

Which among the following salts, solubility decreases with increase in temperature?

Soaps are the sodium or potassium salts of higher fatty acids, containing number of carbon atoms more than,

Oxidation state of nitrogen in nitric oxide is

Which of the following does not give yellow solid on treatment with sodium hypoiodite?

The shape of BrF$_5$ molecule is

The alkane formed on heating sodium butanoate with sodalime is

A gas performs 0.320 kJ work on surrounding and absorbs 120 J of heat from the surrounding. Hence, change in internal energy is

For the elementary reaction, $3 \mathrm{H}_2(g)+\mathrm{N}_2(g) \longrightarrow 2 \mathrm{NH}_3(g)$ identify the correct relation among the following relations:

Natalite is a mixture of

In which among the following compounds, oxidation number of nitrogen is +5 ?

18 gram glucose (Molar mass $=180$ ) is dissolved in 100 ml of water at 300 K . If $R=3$ $0.0821 \mathrm{~L}{-\mathrm{a t m}} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ what is the osmotic pressure of solution?

A flavouring agent found in oil of wintergreen is

Which of the following is not the mineral of iron?

Which of the following metal halide is more covalent?

How many primary amines are possible for molecular formula $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$ ?

The conversion of 2-methylpropan-1-ol to 2-methylpropan-2-ol is

A polymer which becomes soft on heating and hard on cooling, belongs to class of

The effective atomic number of $\operatorname{Iron}(z=26)$ in $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{-3}$ is

Which bond in a molecule of ethyl magnesium bromide is ionic in nature?

Based on first law of thermodynamics which of the following is correct

IUPAC name of the complex Ba[ $\left.\mathrm{CuCl}_4\right]$ is

Hinsberg's reagent is

Which among the following polymer does not show cross linking in it ?

The vitamin that belongs to aromatic series is

Which of the following is not present in DNA?

The SI unit of electrochemical equivalent is

The correct order of boiling points of alkyl halides is

The molar conductivities at infinite dilution for sodium acetate, HCl and NaCl are $91 \mathrm{~S} \mathrm{~cm}{ }^2$ $\mathrm{mol}^{-1}, 425.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and $12.6 .4 \mathrm{~S} \mathrm{~cm}^2$ $\mathrm{mol}^{-1}$ respectively. The molar conductivity of acetic acid at infinite dilution is

The vector equation of the plane $\mathbf{r}=(2 \hat{\mathbf{i}}+\hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}})+\mu(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})$ in scalar product form is $\mathbf{r} \cdot(3 \hat{\mathbf{i}}+2 \hat{\mathbf{k}})=\alpha$, then $\alpha=\ldots$

. Area of the region bounded by $y=\cos x, x=0$, $x=\pi$ and $X$-axis is ... sq. units.

The length of the latusrectum of an ellipse is $\frac{18}{5}$ and eccentricity is $\frac{4}{5}$, then equation of the ellipse is .....

Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b:(p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively......

5. "If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, the inverse of the given statement is

$$\int \log x \cdot[\log (e x)]^{-2} d x=\ldots$$

If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$

If the scalar triple product of the vectors $-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ is 272 then $\lambda=\ldots \ldots$

- The edge of a cube is decreasing at the rate of $0.04 \mathrm{~cm} / \mathrm{sec}$. If the edge of the cube is 10 cms , then rate of decrease of surface area of the cube is...

The joint equation of lines passing through origin and having slopes $(1+\sqrt{2})$ and $\frac{-1}{1+\sqrt{2}}$ is ..........

If $r$ is the radius of spherical balloon at time $t$ and the surface area of balloon changes at a constant rate $K$, then......

$$\int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \cdot \sin ^3 \theta d \theta=$$ ............

If $\omega$ is a complex cube root of unity and $A=\left[\begin{array}{ccc}\omega & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & 1\end{array}\right]$ then $A^{-1}=\ldots$

If $A$ and $B$ are square matrices of order 3 such that $|A|=2,|B|=4$, then $|A(\operatorname{adj} B)|=\ldots$

If $\int \frac{1}{1-\cot x} d x=A x+B \log |\sin x-\cos x|+c$ then $A+B=\ldots \ldots$

The polar co-ordinates of $P$ are $\left(2, \frac{\pi}{6}\right)$. If $Q$ is the image of $P$ about the $X$-axis then the polar co-ordinates of $Q$ are.....̣...

$\mathbf{a}$ and $\mathbf{b}$ are non-collinear vectors. If $\mathbf{c}=(x-2) \mathbf{a}+\mathbf{b}$ and $\mathbf{d}=(2 x+1) \mathbf{a}-\mathbf{b}$ are collinear vectors, then the value of $x=\ldots \ldots$

Let $X$ be the number of successes in ' $n$ ' independent Bernoulli trials with probability of success $p=\frac{3}{4}$. The least value of ' $n$ ' so that $P(X \geq 1) \geq 0.9375$ is ......

The slope of normal to the curve $x=\sqrt{t}$ and $y=t-\frac{1}{\sqrt{t}}$ at $t=4$ is ..........

Which of the following statement pattern is a tautology?

The acute angle between lines $x-3=0$ and $x+y=19$ is.......

In $\triangle A B C$, with the usual notations, if $\left(\tan \frac{A}{2}\right)\left(\tan \frac{B}{2}\right)=\frac{3}{4}$ then $a+b=\ldots \ldots$

If sum of the slopes of the lines given by $x^2-4 p x y+8 y^2=0$ is three times their product then $p=$ ...........

$$\frac{1-2\left[\cos 60^{\circ}-\cos 80^{\circ}\right]}{2 \sin 10^{\circ}}=\ldots \ldots$$

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is......

If $f(x)$ is continuous at $x=3$, where

$$\begin{aligned} f(x) & =a x+1, & \text { for } x \leq 3 \\ & =b x+3 & , \text { for } x>3 \text { then } \end{aligned}$$

The probability that three cards drawn from a pack of 52 cards, all are red is

For any non zero vector, a, b, c $\mathbf{a} \cdot[(\mathbf{b}+\mathbf{c}) \times(\mathbf{a}+\mathbf{b}+\mathbf{c})]=$ ..........

The domain of the real valued function $f(x)=\sqrt{\frac{x-2}{3-x}}$ is......

If $y=\tan ^{-1}\left(\frac{1-\cos 3 x}{\sin 3 x}\right)$, then $\frac{d y}{d x}=$ .......

If $z=a x+b y ; a, b>0$ subject to $x \leq 2, y \leq 2, x+y \geq 3, x \geq 0, y \geq 0$ has minimum value at $(2,1)$ only, then......

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes $x+2 y+3 z=4$ and $4 x+3 y+2 z=1$ are $\ldots \ldots$

$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$

The $P\left(\frac{1}{4}< x<\frac{1}{3}\right)=\ldots$

The eccentricity of the hyperbola $25 x^2-9 y^2=225$ is .......

If $f(x)=x+\frac{1}{x}, x \neq 0$, then local maximum and minimum values of function $f$ are respectively.......

Derivative of $\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right)$ is

A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amount is

In $\triangle A B C$, with the usual notations, if $\sin B \sin C=\frac{b c}{a^2}$, then the triangle is. ...........

If $A=\left\{x \in R / x^2+5|x|+6=0\right\}$ then $n(A)=\ldots \ldots$

$$\int \frac{d x}{(\sin x+\cos x)(2 \cos x+\sin x)}=$$

The solution of differential equation $\left(x^2+1\right) \frac{d y}{d x}+\left(y^2+1\right)=0$ is $\ldots$

$\sin \left[3 \sin ^{-1}(0.4)\right]=\ldots \ldots$

If line $\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$ and $\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{1}$ are perpendicular to each other then $\lambda=$ ............

For a sequence $\left(t_n\right)$, if $S_n=5\left(2^n-1\right)$ then $t_n=$ .........

$$\begin{aligned} & \text { If } f(x)=\left[\tan \left(\frac{\pi}{4}+x\right)\right]^{\frac{1}{x}}, \quad x \neq 0 \\ & =k \text {, } \qquad x=0 \text { is continuous }\\ & x=0 \end{aligned}$$ Then $k=$

Which of the following function has period 2?

Which of the following can not be the direction cosines of a line?

If $A, B, C$ are $p^{\text {th }}, q^{\text {th }}$ and $r^{\text {th }}$ terms of a GP respectively then $A^{q-r} \cdot B^{r-p} \cdot C^{p-q}=\ldots \ldots$

$$\int_{\frac{\pi}{18}}^{\frac{4 \pi}{9}} \frac{2 \sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x=\ldots \ldots$$

The maximum value of $Z=5 x+4 y$, Subject to $y \leq 2 x, x \leq 2 y, x+y \leq 3, x \geq 0, y \geq 0$ is ........

In amplitude modulation, the amplitude of carrier wave is $A_c$ and that of the modulating signal is $A_m$. In practice, the ratio of $A_m$ to $A_c$ is kept less than or equal to one, to avoid

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{\text {th }}$ overtone is

Glass has refractive index $\mu$ with respect to air and the critical angle for a ray of light going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, corresponding angle of refraction is

Maximum kinetic energy gained by the charged particle in the cyclotron is independent of

A molecule of water on the surface experiences a net

The magnifying power of a telescope is nine. When it is adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm . The focal length of objective and eyepiece are respectively

The SI unit and dimensions of Stefan's constant $\sigma$ in case of Stefan's law of radiation is

In a hydrogen atom, an electron of charge $e$ revolves in a orbit of radius $r$ with speed $v$. Then, magnetic moment associated with electron is

$V-I$ characterstics of LED is shown correctly by graph

The stopping potential of the photoelectrons, from a photo cell is

The refractive index of the material of crystal is 1.68 and that of castor oil is 1.2. When a ray of light passes from oil to glass, its velocity will change by a factor

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote radius and mass of the earth. If $\omega$ is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be $\left(\cos 0^{\circ}=1\right)$

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1=+10 \mathrm{~A}, I_2=-13 \mathrm{~A}, I_3=+10$ $\mathrm{A}, I_4=+7 \mathrm{~A}, I_5=-12 \mathrm{~A}$ and $I_6=+18 \mathrm{~A}$. The magnetic induction at a perpendicular distance of 10 cm from the cable is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{A}-\mathrm{m}\right)$

The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by $69 \%$, keeping the length constant. The frequency of the wire is

A potentiometer wire has length $L$ For given cell of emf $E$, the balancing length is $\frac{L}{3}$ from the positive end of the wire. If the length of potentiometer wire is increased by $50 \%$, then for the same cell, the balance point is obtained at length

For homogeneous isotropic material, which one of the following cannot be the value of Poisson's ratio?

A mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now halved keeping the angular momentum same, the linear velocity is

A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is

In Young's double slit experiment fifth dark fringe is formed opposite to one of the slit. IID is the distance between the slits and the screen and $d$ is the separation between the slits, then the wavelength of light used is

Figure show the circular coil carrying current $I$ kept very close but not touching at a point $A$ on a straight conductor carrying the same current $I$. The magnitude of magnetic induction at the centre of the circular coil will be

A 220 V input is supplied to a transformer. The output circuit draws a current of 2.0 A at 440 V . If the ratio of output to input power is 0.8 , then the current drawn by primary winding is

A sonometer wire is in unison with a tuning fork, when it is stretched by weight $w$ and the corresponding resonating length is $L_4$. If the weight is reduced to $\left(\frac{w}{4}\right)$, the corresponding resonating length becomes $L_2$. The ratio $\left(\frac{L_1}{L_2}\right)$ is

If the speed of an electron of hydrogen atom in the ground state is $2.2 \times 10^6 \mathrm{~m} / \mathrm{s}$, then its speed in the third excited state will be

A rod $l \mathrm{~m}$ long is acted upon by a couple as shown in the figure. The moment of couple is $\tau \mathrm{~Nm}$. If the force at each end of the rod, then magnitude of each force is

$$\left(\sin 30^{\circ}=\cos 60^{\circ}=0.5\right)$$

The vectors $(\mathbf{A}+\mathbf{B})$ and $(\mathbf{A}-\mathbf{B})$ are at right. angles to each other. This is possible under the condition

A coil has inductance 2 H . The ratio of its reactance, when it is connected first to an $A C$ source and then to DC source, is

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$, the time period of the pendulum will be

A charged conductor produces an electric field of intensity $10^3 \mathrm{~V} / \mathrm{m}$ just outside its surface in vacuum. Then, it produces the electric field of intensity E just outside its surface, when it is placed in a medium of dielectric constant 4. The value of $E$ will be

In damped SHM, the SI unit of damping constant is

A wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$, the increase in length is $I$. If another wire of the same material but double the length and radius is stretched with a force $2 F$, then increase in length is

When certain metal surface is illuminated with a light of wavelength $\lambda$, the stopping potential is $V$, When the same surface is illuminated by light of wavelength $2 \lambda$, the stopping potential is $\left(\frac{V}{3}\right)$. The threshold wavelength for the surface is

Which of the following regions of a transistors are, respectively, heavily dopped and lightly dopped?

A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, it weigh at the bottom of the hole?

Eight identical drops of water falling through air with uniform velocity of $10 \mathrm{~cm} / \mathrm{s}$ combine to form a single drop of big size, then terminal velocity of the big drop will be

A solid sphere rolls down from top of inclined plane, 7 m high, without slipping. Its linear speed at the foot of plane is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

A body of mass $m$ is performing a UCM in a circle of radius $r$ with speed $v$. The work done by the centripetal force in moving it through $\left(\frac{2}{3}\right) \mathrm{rd}$ of the circular path is

Which of the following is the dimensional formula for electric polarisation?

The phenomenon of interference is based on

A vector $P$ has $X$ and $Y$ components of magnitude 2 units and 4 units respectively. A vector $Q$ along negative $X$-axis has magnitude 6 units. The vector $(\mathbf{Q}-\mathbf{P})$ will be

A magnetizing field of $5000 \mathrm{~A} / \mathrm{m}$ produces a magnetic flux of $4 \times 10^{-5} \mathrm{~Wb}$ in an iron rod of cross-sectional area $0.4 \mathrm{~cm}^2$. The permeabilit of the rod in Wb/A-m, is

When a large bubble rises from bottom of a water lake to its surface, then its radius doubles. If the atmospheric pressure is equal to the pressure of height $H$ of a certain water column, then the depth of lake will be

A block of mass $M$ is pulled along a smooth horizontal surface with a rope of mass $m$ by force $F$. The acceleration of the block will be

In the network shown cell E has internal resistance $r$ and the galvanometer shows zero deflection. If the cell is replaced by a new cell of emf $2 E$ and internal resistance $3 r$ keeping everything else identical, then

In hydrogen emission spectrum, for any series, the principal quantum number is $n$. Corresponding maximum wavelength $\lambda$ is ( $R=$ Rydberg's constant)

$\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-2}\right]$ are the dimensions of

For formation of beats, two sound notes must have

If the radius of the circular path and frequency of revolution of a particle of mass $m$ are doubled, then the change in its kinetic energy will be $\left(E_i\right.$ and $E_1$ are the initial and final kinetic energies of the particle respectively,)

The total energy of a simple harmonic oscillaior is proportional to

The rms speed of oxygen molecule in a gas is $u$, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be