The number of $\sigma$ and $\pi$-bonds in 2-formylbenzoic acid are respectively

The volume of 1 mole of any pure gas at standard temperature and pressure is always equal to

Veronal is used as a/an

Which of the following is also called as nitrogen sesquioxide?

The oxidation number of sulphur in $\mathrm{S}_8$ molecule is

Which among the following is a set of nucleophiles ?

Which of the following acts as oxidising agent in hydrogen-oxygen fuel cell ?

In ozone molecule the formal charge on the central oxygen atom is

According to Werner's theory the geometry of the complex is determined by

How many total constituent particles are present in simple cubic unit cell?

The correct representation of Nernst's equation for half-cell reaction $\mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}^{+}(\mathrm{aq})$ is

Which among the following is a neutral complex?

Identify the equation in which change in enthalpy is equal to change in internal energy

Limestone is used as a flux in the extraction of

How many isomers are possible for an alkane having molecular formula $\mathrm{C}_5 \mathrm{H}_{12}$ ?

Which of following elements does not form amide when reacted with ammonia?

Two moles of an ideal gas is expanded isothermally and reversibly at 300 K from 1 L to 10 L . The enthalpy change in kJ is

$\alpha$-chlorosodium acetate on boiling with aqueous sodium nitrite gives

The bond angle $\mathrm{H}-\mathrm{O}-\mathrm{O}$ in $\mathrm{H}_2 \mathrm{O}_2$ in gaseous phase is

How many metameric ethers are represented by the molecular formula $\mathrm{C_4H_{10}O}$ ?

The activation energy of a reaction is zero. Its rate constant at 280 K is $1.6 \times 10^{-6} \mathrm{~s}^{-1}$, the rate constant at 300 K is

Which of following metals occurs in native state?

Which of the following is not a broad spectrum antibiotics ?

The oxidation state of sulphur in $\mathrm{H}_2 \mathrm{S}_2 \mathrm{O}_7$ is

The reaction in which 2 molecules of chlorobenzene reacts with metallic sodium in presence of dry ether forming diphenyl is an example of,

The percentage of unoccupied volume in simple cubic cell is

Isobutylene on hydroboration followed by oxidation with hydrogen peroxide in presence of base yields

What is the density of water vapour at boiling point of water?

Which of the following molecules form a Zwitter ion?

Which reaction is useful in exchange of halogen in alkyl chloride by iodide?

Propene when treated with cold conc. $\mathrm{H}_2 \mathrm{SO}_4$ forms a compound which on heating with water gives

Identify the amine formed when ethyltrimethyl ammonium iodide is treated with silver hydroxide and further heated strongly

For a chemical reaction rate law is, rate $=k[A]^2[B]$. If $[A]$ is doubled at constant $[B]$, the rate of reaction

Which of the following is a natural polymer?

The monomers used in the preparation of dextron are

When a mixture of manganese dioxide, potassium hydroxide and potassium chlorate is fused, the product obtained is

In which oxidation state, group 15 elements act as Lewis base?

Relationship between van't Hoff's factor (i) and degree of dissociation $(\alpha)$ is

Which of following elements does not react with hot concentrated sulphuric acid?

In the reaction, $\mathrm{H}_2 \mathrm{O}_2(a q) \xrightarrow{\mathrm{I_{(aq)}^-}} \mathrm{H}_2 \mathrm{O}(I)+\frac{1}{2} \mathrm{O}_2(g)$ iodide ion acts as

The ionic charges of manganate and permanganate ion are respectively

How many gram of sodium (atomic mass $23u$) is required to prepare one mole of ethane from methyl chloride by Wurtz reaction?

The enzyme which converts maltose to glucose is

$$\begin{aligned} & \text { If } \mathrm{C}(s)+\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g), \Delta H=-X \\ & \mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g), \Delta H=-Y \end{aligned}$$ Calculate $\Delta_f H$ for $\mathrm{CO}_{(g)}$ formation

What is the atomicity of aluminium phosphate?

Which among the following compounds is obtained when ethane nitrile is acid hydrolysed?

Standard hydrogen electrode (SHE) is a

9 gram anhydrous oxalic acid (mol. $\mathrm{wt} .=90)$ was dissolved in 9.9 moles of water. If vapour pressure of pure water is $p_1^{\circ}$ the vapour pressure of solution is

Which of the following sets of solutions of urea ( mol . mass $60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and sucrose ( mol . mass $342 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is isotonic?

In a bionomial distribution, mean is 18 and variance is 12 then $p=$ ...........

If lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\lambda}{2}=\frac{z}{1}$ intersect each other, then $\lambda=\ldots \ldots$

The particular solution of the differential equation $\log \left(\frac{d y}{d x}\right)=x$, when $x=0, y=1$ is ..............

The p.d.f of a random variable $x$ is given by

$$\begin{aligned} & f(x)=\frac{1}{4 a}, \quad 00) \\ & =0 \text {, otherwise } \end{aligned}$$

and $P\left(x<\frac{3 a}{2}\right)=k P\left(x>\frac{5 a}{2}\right)$ then $k=$ ..............

If the function $f(x)=\frac{\left(e^{k x}-1\right) \tan k x}{4 x^2}, x \neq 0$

$$\qquad \qquad=16 \qquad x=0$$

is continuous at $x=0$, then $k=\ldots \ldots$

The solution of the differential equation $y d x-x d y=x y d x$ is ......

The maximum value of $z=6 x+8 y$ subject to $x-y \geq 0, x+3 y \leq 12, x \geq 0, y \geq 0$ is $\ldots \ldots$.

If $\sum_{r=1}^n(2 r+1)=440$, then $n=$ ...............

If $p$ and $q$ are true and $r$ and $s$ are false statements, then which of the following is true?

If the standard deviation of the random variable $X$ is $\sqrt{3 p q}$ and mean is $3 p$ then $E\left(x^2\right)=\ldots \ldots$

If $f(x)=[x]$, where $[x]$ is the greatest integer not greater than $x$, then $f^{\prime}\left(1^{+}\right)=$ ...........

If lines represented by $$\left(1+\sin ^2 \theta\right) x^2+2 h x y+2 \sin \theta y^2=0, \theta \in[0,2 \pi]$$ are perpendicular to each other then $\theta=$ ...........

If $A=\{x \mid x \in N, x$ is a prime number less than $12\}$ and $B=\{x \mid x \in N, x$ is a factor of 10$\}$, then $A \cap B=$ .............

If $R$ is the circum radius of $\triangle A B C$, then $A(\triangle A B C)=\ldots \ldots$

If $A, B, C$ and $D$ are $(3,7,4),(5,-2,-3),(-4,5,6)$ and $(1,2,3)$ respectively, then the volume of the parallelopiped with $A B, A C$ and $A D$ as the co-terminus edges, is .......... cubic units.

If $(-\sqrt{2}, \sqrt{2})$ are cartesian co-ordinates of the point, then its polar co-ordinates are .........

If $$\int \frac{\cos x-\sin x}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c,$$ then $p=$ .............

If $A$ is non-singular matrix and $(A+I)(A-I)=0$ then $A+A^{-1}=$ .............

Equations of planes parallel to the plane $x-2 y+2 z+4=0$ which are at a distance of one unit from the point $(1,2,3)$ are ............

The $y$-intercept of the line passing through $A(6,1)$ and perpendicular to the line $x-2 y=4$ is ...........

If function

$$\begin{aligned} f(x) & =x-\frac{|x|}{x}, x<0 \\ & =x+\frac{|x|}{x}, x>0 \\ & =1, \quad x=0, \text { then } \end{aligned}$$

In $\triangle A B C$, if $\tan A+\tan B+\tan C=6$ and $\tan A \cdot \tan B=2$ then $\tan C=$ ...........

If $P(6,10,10), Q(1,0,-5), R(6,-10, \lambda)$ are vertices of a triangle right angled at $Q$, then value of $\lambda$ is ............

For L.P.P, maximize $z=4 x_1+2 x_2$ subject to $3 x_1+2 x_2 \geq 9, x_1-x_2 \leq 3, x_1 \geq 0, x_2 \geq 0$ has

The function $f(x)=x^3-3 x$ is ............

If $x=\sin \theta, y=\sin ^3 \theta$ then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{2}$ is ............

The area of the region enclosed between pair of the lines $x y=0$ and the lines $x y+5 x-4 y-20=0$, is .............

If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is

If $f(x)=3 x+6, g(x)=4 x+k$ and $f \circ g(x)=g \circ f(x)$ then $k=$

If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is ..........

The negation of " $\forall, n \in N, n+7>6$ " is .............

If the vectors $x \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+y \hat{\mathbf{j}}-z \hat{\mathbf{k}}$ are collinear then the value of $\frac{x y^2}{z}$ is equal

$$\begin{aligned} & \text { If } \int \tan (x-\alpha) \tan (x+\alpha) \cdot \tan 2 x d x \\ & =p \log |\sec 2 x|+q \log |\sec (x+\alpha)| \\ & +r \log |\sec (x-\alpha)|+c \text { then } p+q+r=\ldots \ldots \ldots \end{aligned}$$

Using differentiation, approximate value of $f(x)=x^2-2 x+1$ at $x=2.99$ is ............

A particle moves so that $x=2+27 t-t^3$. The direction of motion reverses after moving a distance of ....... units.

Which of the following is not equal to $\mathbf{w} \cdot(\mathbf{u} \times \mathbf{v})$ ?

The value of $\sin 18^{\circ}$ is $\qquad$

If the foot of the perpendicular drawn from the point $(0,0,0)$ to the plane is $(4,-2,-5)$ then the equation of the plane is .............

$$\int \frac{x^2+1}{x^4-x^2+1} d x=\ldots \ldots$$

If $x^y=e^{x-y}$, then $\frac{d y}{d x}$ at $x=1$ is ...........

If $A=\left[\begin{array}{cc}1+2 i & i \\ -i & 1-2 i\end{array}\right]$, where $i=\sqrt{-1}$, then $A(\operatorname{adj} A)=\ldots$

Which of the following statements is contingency?

$$\int_\limits a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x=\ldots \ldots$$

The intercept on the line $y=x$ by the circle $x^2+y^2-2 x=0$ is $A B$. The equation of the circle with $A B$ as a diameter is .............

The equation of the circle concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $Y$-axis is ............

$$\int_0^1 x(1-x)^5 d x=\ldots \ldots$$

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$ then $x=$ ............

If $\int_0^a \sqrt{\frac{a-x}{x}} d x=\frac{K}{2}$, then $K=\ldots .$.

In $\triangle A B C$; with usual notations, $$\frac{b \sin B-c \sin C}{\sin (B-C)}=\ldots \ldots$$

The solution of the differential equation $\frac{d \theta}{d t}=-k\left(\theta-\theta_0\right)$ where $k$ is constant, is .............

A metal surface is illuminated by light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one fourth of its original value then the maximum KE of the emitted photoelectrons would be

Torque acting on a rectangular coil carrying current ' $l$ ' situated parallel to magnetic field of induction ' $B$ ', having number of turns ' $n$ ' and area ' $A$ ' is

A force $(F)=-5 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ acting on a particle causes a displacement $(s)=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ in its own direction. If the work done is 14 J , then the value of ' $a$ ' is

When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the

Light of wavelength ' $\lambda$ ' is incident on a single slit of width ' $a$ ' and the distance between slit and screen is ' $D$ '. In diffraction pattern, if slit width is equal to the width of the central maximum then ' $D$ ' is equal to

In U.C.M., when time interval $\delta t \rightarrow 0$, the angle between change in velocity ( $\delta \mathbf{v}$ ) and linear velocity $(\boldsymbol{v})$ will be

A stretched string fixed at both ends has ' $m$ ' nodes, then the length of the string will be

A particle is performing a linear simple harmonic motion of amplitude ' $A$ '. When it is midway between its mean and extreme position, the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?

Three identical rods each of mass ' $M$ ' and length ' $L$ ' are joined to form a symbol ' $H$. The moment of inertia of the system about one of the sides of ' $H$ ' is

The luminous border that surrounds the profile of a mountain just before sun rises behind it, is an example of

A block of mass ' $m$ ' moving on a frictionless surface at speed ' $v$ ' collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle ' $\theta$ ' with its initial direction and has speed ' $v_1$ '. The speed of the second block after collision is

Three point masses each of mass ' $m$ ' are kept at the corners of an equilateral triangle of side. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to $\left(\cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)$

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is

When light enters glass from vacuum, then the wavelength of light

Which one of the following statement is correct?

What is the minimum energy required to launch a satellite of mass ' $m$ ' from the surface of the earth of mass ' $M$ ' and radius ' $R$ ' at an altitude $2 R$ ?

A wire of length ' $L$ ' and area of cross section ' $A$ ' is made of material of Young's modulus ' $r$. It is stretched by an amount ' $x$ '. The work done in stretching the wire is

In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2 . If the initial capacity of the capacitor is $4 \mu \mathrm{~F}$. then its new capacity is

An aircraft is moving with uniform velocity $150 \mathrm{~m} / \mathrm{s}$ in the space. If all the forces acting on it are balanced, then it will

In case of $p$-n junction diode, the width of depletion region is

In the study of transistor as an amplifier, the ratio of collector current to emitter current is 0.98 then the ratio of collector current to base current will be

A stretched wire of length 260 cm is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2: 3: 4$. Their lengths must be

The force ' $F$ ' acting on a body of density ' $d$ ' are related by the relation $F=\frac{y}{\sqrt{d}}$. The dimensions of ' $y$ ' are

The magnetization of bar magnet of length 5 cm , cross sectional area $2 \mathrm{~cm}^2$ and net magnetic moment $1 \mathrm{Am}^2$ is

The dimensions of self or mutual inductance are given as

Which of the following molecules is a polar molecule?

Magnetic susceptibility of a paramagnetic substance is

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A . The magnitude of the magnetic field at the centre of coil is $\left[\mu_0=12.56 \times 10^{-7} \mathrm{SI}\right.$ Unit]

A simple harmonic progressive wave is represented as $y=0.03 \sin \pi(2 t-0.01 x) \mathrm{m}$. At a given instant of time, the phase difference between two particles 25 m apart is

The equation of state for 2 g of oxygen at a pressure ' $P$ ' and temperature ' $T$, when occupying a volume ' $V$ ' will be

The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of ' $X$ ' in SI units. If the distance between the point and the magnet is halved then the magnitude of dipole moment will be

The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of

If ' $x$ ', $v$ ' and ' $a$ ' denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time $h$ then which one of the following does not change with time?

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in $\mathrm{m} / \mathrm{s}^2$ is

Find the wrong statement from the following about the equation of stationary wave given by $Y=0.04 \cos (\pi x) \sin (50 \pi t) \mathrm{m}$ where $t$ is in second. Then for the stationary wave.

A convex lens of focal length ' $f$ ' is placed in contact with a concave lens of the same focal length. The equivalent focal length of the combination is

Two light balls are suspended as shown in figure. When a stream of air passes through the space between them, the distance between the balls will

The range of an ammeter of resistance ' $G$ can be increased from ' $I$ ' to ' $nI$ ' by connecting

The critical angle for light going from medium ' $x^{\prime}$ to medium ' $y$ ' is ' $\theta$ '. The speed of light in medium ' $x$ ' is ' $v_x$ '. The speed of light in medium ' $y$ ' is

When a 12000 joule of work is done on a flywheel, its frequency of rotation increases from 10 Hz to 20 Hz . The moment of inertia of flywheel about its axis of rotation is $\left(\pi^2=10\right)$

A rigid body is rotating with angular velocity ' $\omega$ ' about an axis of rotation. Let $v$ ' be the linear velocity of particle which is at perpendicular distance ' $r$ ' from the axis of rotation. Then the relation $v=r \omega$ ' implies that

In the given electrical circuit, which one of the following equations is a correct equation?

In the given electrical circuit, which one of the following equations is a correct equation?

The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$, Wien's constant, $b=2898 \mu \mathrm{mK}$ )

A lift is tied with thick iron ropes having mass ' $M$ '. The maximum acceleration of the lift is ' $a$ ' $\mathrm{m} / \mathrm{s}^2$ and maximum safe stress is ' S ' $\mathrm{N} / \mathrm{m}^2$. The minimum diameter of the rope is

In Balmer series, wavelength of first line is ' $\lambda_1$ ' and in Brackett series wavelength of first line is ' $\lambda_2$ ' then $\frac{\lambda_1}{\lambda_2}$ is

An alternating voltage is given by $E=100 \sin \left(\omega+\frac{\pi}{6}\right) \mathrm{V}$. The voltage will be maximum for the first time when is [ $T=$ periodic time)

In frequency modulated wave

With a resistance of ' $X$ ' in the left gap and resistance of $9 \Omega$ in the right gap of a meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance $3 \Omega$ resistance be connected to obtain the balance at 50 cm from the left end?

The excess of pressure, due to surface tension, on a spherical liquid drop of radius ' $R$ ' is proportional to

$\mathbf{P}$ and $\mathbf{Q}$ are two non-zero vectors inclined to each other at an angle ' $\theta$ '. ' $p$ ' and ' $q$ ' are unit vectors along $\mathbf{P}$ and $\mathbf{Q}$ respectively. The component of $\mathbf{Q}$ in the direction of $\mathbf{Q}$ will be