Which of the following statements is NOT correct regarding order of reaction?

Identify cross linked polymer from following.

Which of the following forces is involved in dinitrogen?

Which among the following is dicarboxylic acid?

Calculate the edge length of unit cell if metal having atomic radius 170 pm forms simple cubic unit cell.

Calculate the frequency in Hz of orange colour light having wavelength 600 nm .

$$ \left[\mathrm{C}=3 \times 10^8 \mathrm{~ms}^{-1}\right] $$

Which from following statements is NOT correct regarding tannins?

Calculate the solubility of gas in solvent at $25^{\circ} \mathrm{C}$ and 0.8 atm if Henry's law constant for solvent is $6.8 \times 10^{-4} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~atm}^{-1}$.

Identify the correct order of acidity of hydrides of $16^{\text {th }}$ group elements from the following.

Which from following elements belongs to inner transition elements?

Which of the following is NOT a characterstic of chemisorption?

Identify a side chain (R) group present in Leucine, an amino acid.

What is half life of a first order reaction if time required to decrease concentration of reactant from 0.4 M to 0.1 M is $x$ hour?

$$ \text { Identify ' } \mathrm{A} \text { ' in the following reaction. } $$

$$ \mathrm{A}+\text { Acetyl chloride } \xrightarrow[\mathrm{AlCl}_3]{\text { anhydrous }} \text { 2-Chloroacetophenone + 4-Chloroacetophenone }$$

Calculate osmotic pressure of 0.1 M aqueous solution of an electrolyte at 300 K if van't Hoff factor is 1.125. $\left[\mathrm{R}=0.0821 \mathrm{~atm} \mathrm{dm}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

Which from following gases causes the depletion of ozone layer in upper atmosphere?

Which from following complexes contains anionic ligand?

Find principle of green chemistry to show protection of selective group is not advantageous.

What is the name of monomer used in the formation of a polymer

Which of the following is obtained as major product when excess of methane is treated with limited chlorine in presence of UV light?

What type of alcohol is the crotonyl alcohol?

What type of solution is the $\mathrm{H}_2$ in palladium?

Identify conjugate acid and conjugate base for $\mathrm{HCO}_3^{-}$ion respectively

Which from following complexes does $\mathrm{NO}_{\uparrow}$ obey EAN rule?

Identify catalyst used in following reaction.

$$ \mathrm{CO}_{(\mathrm{g})}+\mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \xrightarrow{623 \mathrm{~K}} \mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} $$

Which of the following reagents is used in the preparation of nitroalkane from haloalkane?

What is percent dissociation of $\mathrm{NH}_4 \mathrm{OH}$ if molar conductance at zero concentration for $\mathrm{NH}_4 \mathrm{Cl}$, NaCl and NaOH are 130, 109 and $213 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ respectively and molar conductivity of $0.01 \quad \mathrm{M} \quad \mathrm{NH}_4 \mathrm{OH}$ is $9.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ ?

Identify the reagent used for Rosenmund reduction.

Calculate the work done in the oxidation of one mole $\mathrm{HCl}_{(\mathrm{g})}$ at $27^{\circ} \mathrm{C}$, according to reaction.

$$ \begin{aligned} & 4 \mathrm{HCl}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \\ & \left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right) \end{aligned} $$

Find the concentration of sodium acetate when added to 0.1 M solution of acetic acid to form a buffer solution of $\mathrm{pH}=5.5$ ?

( $\mathrm{pK}_{\mathrm{a}}$ of $\mathrm{CH}_3 \mathrm{COOH}=4.5$ )

Which actinoid from following in its +3 state has largest size?

Which of the following halogens does always show oxidation state -1 ?

Which from following carbohydrates produces glucose, galactose and fructose on hydrolysis?

What is degree of dissociation of $\mathrm{CH}_3 \mathrm{COOH}$ if, $\wedge^{\circ}\left(\mathrm{CH}_3 \mathrm{COO}^{-}\right)=50 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, $\wedge^{\circ}\left(\mathrm{H}^{+}\right)=350 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and molar conductivity of $5 \times 10^{-2} \mathrm{M} \mathrm{CH}_3 \mathrm{COOH}$ is $20 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ ?

Identify the reaction so that carbonyl group of aldehydes and ketones is reduced to methylene group on treatment with Zinc-amalgam and concentrated hydrochloric acid.

Which of the following dopant is added in silicon to obtain n-type semiconductor?

Which from following is an example of an intensive property of the system?

What is the number of hydrogen atoms present in 5.4 g of urea?

What is the order of reactivity of alkyl halides with ammonia?

For the reaction,

$$ 2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \longrightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} $$

$\mathrm{N}_2 \mathrm{O}_5$ disappears at a rate of $x \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$

Find the rate of formation of $\mathrm{O}_2$ ?

$$ \text { Which among the following is haloarene? } $$

Which of the following molecules does not obey octet rule?

Which of the following on reaction with Grignards reagent followed by hydrolysis forms tertiary alcohol?

In an ionic solid anions are arranged in hcp array and cations occupy $\frac{2}{3}$ of octahedral voids.

What is the formula of ionic compound? [consider $\mathrm{A}=$ cation; $\mathrm{B}=$ anion]

For a certain reaction $\Delta \mathrm{H}=-225 \mathrm{~kJ}$ and $\Delta S=-150 \mathrm{JK}^{-1}$. Find the temperature so that $\Delta G$ is zero.

Calculate the ionisation constant of $0.08 \mathrm{~mol} \mathrm{dm}{ }^{-3}$ of a monobasic acid having $\mathrm{pH}=2$.

What is the number of moles of ' C ' and ' H ' atoms respectively present in n mole molecule represented by following structure?

Identify the product obtained when nitro ethane is treated with $\mathrm{Sn}-\mathrm{HCl}$ under ideal conditions.

What is the SI unit of resistivity?

Which of the following is trihydric phenol?

The negation of statement pattern $(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow(\mathrm{p} \vee \sim \mathrm{q})$ is

If the line $3 x+4 y-24=0$ intersects X and Y axes in points A and B respectively then incentre of the triangle OAB where O is origin is

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $x y=\mathrm{a}^2$ at the point $\left(x_1, y_1\right)$ is _______ sq. units (where a, $x_1$ and $y_1$ are non-zero)

The co-ordinates of the point in which line joining $(1,1,1)$ and $(2,2,2)$ intersects the plane $x+y+\mathrm{z}=9$ are

The minimum value of the slope of the tangent to curve $y=x^3-3 x^2+2 x+93$ is

If $\quad f(x)=\left\{\begin{array}{cc}\frac{9^x-2 \cdot 3^x+1}{\log (1+3 x) \cdot \tan 2 x} & , \text { if } x \neq 0 \\ a(\log b)^c & , \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $\mathrm{a}+\mathrm{b}+\mathrm{c}=$

If $x=\tan ^{-1}\left\{\frac{\sqrt{1+t^2}-1}{t}\right\}, y=\cos ^{-1}\left\{\frac{1-t^2}{1+t^2}\right\}, \quad$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

Define $f(x)=\left\{\begin{array}{cl}b-a x & , \text { if } x<2 \\ 3 & , \text { if } x=2 \\ a+2 b x & , \text { if } x>2\end{array}\right.$ and if $\lim _{x \rightarrow 2} f(x)$ exists, then $\frac{a}{b}=$

The function $\mathrm{f}(x)=\sec \left[\log \left(x+\sqrt{1+x^2}\right)\right]$ is________function

The value of ${ }^{47} \mathrm{C}_4+\sum\limits_{\mathrm{j}=1}^5{ }^{(52-\mathrm{j})} \mathrm{C}_3$ is

Derivative of

$y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \ldots \ldots \ldots \ldots \ldots \infty}}}$ is

The feasible region for the constraints $x-y \geq 0, x-5 y \leq-5, x \geq 0, y \geq 0$ is shown by the figure:

The area of the triangle whose vertices are $i, \omega$ and $\omega^2$ is (Where $\omega$ is a complex cube root of unity other than $1, i$ is an imaginary number)__________ sq.units

Three numbers are chosen at random from numbers 1 to 20 . The probability that they are consecutive is

The approximate value of $\frac{1}{(2.002)^2}$ is

The equation of plane passing through $(1,0,0)$ and $(0,1,0)$ and making an angle $45^{\circ}$ with the plane $x+y-3=0$ is

The distance of the point $(5,3,-1)$ from the plane passing through points $(2,1,0),(3,-2,4)$ and $(1,-3,3)$ is

$$ \int \frac{d x}{\cos x(1+\cos x)}= $$

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then $\mathrm{E}\left(\mathrm{X}^2\right)=$

The eccentric angle of the point $\mathrm{P}(-6,2)$ of the ellipse $\frac{x^2}{48}+\frac{y^2}{16}=1$ is

If one of the diameters of the circle, given by the equation $x^2+y^2-4 x+6 y-12=0$, is a chord of a circle, ' S ', whose centre is at $(-3,2)$, then the length of radius of ' S ' is _______ units.

The area of the region bounded by the parabola $y^2=27 x$ and the line $x=1$ is ________ sq.units.

If $\sin (\alpha+\beta)=1, \sin (\alpha-\beta)=\frac{1}{2}, \alpha, \beta \in\left[0, \frac{\pi}{2}\right]$, then $\tan (\alpha+2 \beta) \cdot \tan (2 \alpha+\beta)=$

The value of $\int_0^\pi\left|\sin ^3 x\right| \mathrm{d} x$ is

The population $p$ of the city at time $t$ is given by $\frac{\mathrm{dp}}{\mathrm{dt}}=\frac{\mathrm{p}}{2}-100$. If initial population is 100 then $\mathrm{p}=$

$$ \int_0^1 \log (x+1) d x= $$

If $A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ where $a=7^x, b=7^{7^x}, c=7^{7^{7^x}}$ then $\int|A| d x$, (Where $|A|$ is the determinant of the matrix $A$ ) is equal to

$\int \frac{\sin 7 x}{\cos 9 x \cos 2 x} \mathrm{~d} x$ is equal to

The solution of the equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1}{x+y+1}$ is

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage has begun, is

If $x \cdot \log _e\left(\log _e x\right)-x^2+y^2=4(y>0)$, then $\frac{d y}{d x}$ at $x=\mathrm{e}$ is

If p : switch $\mathrm{S}_1$ is closed, q : switch $\mathrm{S}_2$ is closed then correct interpretation from the following circuit is

The solution of $\log \left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)=2 x-5 y, y(0)=0$ is

The integrating factor of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y \log x=x \cdot \mathrm{e}^x x^{-\frac{1}{2}} \log x(x>0)$ is

ABCD is a quadrilateral with $\overline{\mathrm{AB}}=\overline{\mathrm{a}}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}$ and $\overline{\mathrm{AC}}=2 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$. If its area is $\alpha$ times the area of the parallelogram with $\mathrm{AB}, \mathrm{AD}$ as adjacent sides, then the value of $\alpha$ is

The equation of a line passing through the point $(-1,2,3)$ and perpendicular to the lines $\frac{x}{2}=\frac{y-1}{-3}=\frac{z+2}{-2}$ and $\frac{x+3}{-1}=\frac{y+3}{2}=\frac{z-1}{3}$ is

If $A=\left[\begin{array}{rrr}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]$ then $A(I+\operatorname{adj} A)=$

A line L is passing through points $\mathrm{A}(1,3,2)$ and $\mathrm{B}(2,2,1)$. If mirror image of point $\mathrm{P}(1,1,-1)$ in the line L is $(x, y, z)$ then $x+y+\mathrm{z}=$

If $\overline{\mathrm{c}}=5 \overline{\mathrm{a}}+6 \overline{\mathrm{~b}}$ and $3 \overline{\mathrm{c}}=\overline{\mathrm{a}}-4 \overline{\mathrm{~b}}$ then

The equation $x^2-3 x y+2 y^2+3 x-5 y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to

$$ \cot ^{-1}\left(2 \cdot 1^2\right)+\cot ^{-1}\left(2 \cdot 2^2\right)+\cot ^{-1}\left(2 \cdot 3^2\right)+\ldots \ldots \ldots \infty= $$

With usual notation, in a triangle ABC $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$, then the value of $\cos B$ is equal to

If $\overline{\mathrm{a}}=\frac{1}{\sqrt{10}}(3 \hat{\mathrm{i}}+\hat{\mathrm{k}}), \overline{\mathrm{b}}=\frac{1}{7}(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}})$, then the value of $(\overline{\mathrm{a}}-2 \overline{\mathrm{~b}}) \cdot\{(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times(2 \overline{\mathrm{a}}+\overline{\mathrm{b}})\}$ is

The vectors $\bar{p}=\hat{i}+a \hat{j}+a^2 \hat{k}, \bar{q}=\hat{i}+b \hat{j}+b^2 \hat{k}$ and $\overline{\mathrm{r}}=\hat{\mathrm{i}}+\mathrm{c} \hat{\mathrm{j}}+\mathrm{c}^2 \hat{\mathrm{k}}$ are non-coplanar and $\left|\begin{array}{lll}a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3\end{array}\right|=0$ then the value of $(a b c)$ is

Two adjacent sides of a parallelogram $A B C D$ are given by $\overline{\mathrm{AB}}=2 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}$ and $\overline{\mathrm{AD}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. The side AD is rotated by an acute angle $\alpha$ in the plane of parallelogram so that AD becomes $\mathrm{AD}^{\prime}$. If $\mathrm{AD}^{\prime}$ makes a right angle with the side AB , then $\cos \alpha=$

The general solutions of the equation $\tan ^2 \theta+\sec 2 \theta=1$ are

In a triangle $A B C$, with usual notations, the sides $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are such that they are roots of the equation $x^3-11 x^2+38 x-40=0$ then $\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{\cos \mathrm{C}}{\mathrm{c}}=$

The value of $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]$ is

If $\mathrm{X} \sim \mathrm{B}(35, \mathrm{p})$ such that $7 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$ then the value of $\frac{\mathrm{P}(\mathrm{X}=15)}{\mathrm{P}(\mathrm{X}=20)}$ is equal to

A student studies for X number of hours during a randomly selected school day. The probability that X can take the values, has the following form, where k is some constant.

$$ \mathrm{P}(\mathrm{X}=x)= \begin{cases}0.2, & \text { if } x=0 \\ \mathrm{k} x, & \text { if } x=1 \text { or } 2 \\ \mathrm{k}(6-x), & \text { if } x=3 \text { or } 4 \\ 0, & \text { otherwise }\end{cases} $$

The probability that the student studies for at most two hours is

In an LC circuit, angular frequency at resonance is $\omega$. The new angular frequency when inductance is made four times and capacitance is made eight times is

$$ \text { The electric flux through the surface } $$

A person observes two moving trains. First reaching the station and another leaves the station with equal speed of $30 \mathrm{~m} / \mathrm{s}$. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air $330 \mathrm{~m} / \mathrm{s}$ )

An open organ pipe and closed organ pipe of same length produce 2 beats per second, when they are set into vibrations together, in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled.

The number of beats produced per second will be (neglect end correction)

A beam of light of intensity $I_0$ falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through $60^{\circ}$ with respect to preceding one. The fraction of the incident light intensity that passes through the system is $\left(\cos 60^{\circ}=\frac{1}{2}\right)$

The angular momentum of a rotating body is ' $L$ '. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

An electric dipole of length 2 cm is placed with its axis making an angle of $60^{\circ}$ to a uniform electric field of $10^{+5} \mathrm{~N} / \mathrm{C}$. If it experiences a torque of $9 \sqrt{3} \mathrm{Nm}$, the magnitude of the charge on the dipole is $\left(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)$

Two inductors of 80 mH each are joined in parallel. The current passing through the combination is 2.1 A . The energy stored in this combination of inductors is

The liquid (mercury) meniscus in capillary tube will be convex if the angle of contact is

A 2.5 V battery is connected to a potentiometer wire. A cell of e.m.f. 1.08 V is balanced by the voltage drop across 2.16 m of wire. The length of the potentiometer wire is

A stone of mass ' m ' kg is tied to a string of length ' $L$ ' $m$ and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take $\pi^2=10$ and acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

A photosensitive surface has work function $\phi$. If photon of energy $3 \phi$ falls on this surface, the electron comes out with maximum velocity of $4 \times 10^6 \mathrm{~m} / \mathrm{s}$ When photon energy is increased to $7 \phi$ then maximum velocity of photoelectron will be

A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' $a$ ' and hole ' $Q$ ' is a circle of radius ' $r$ '. The water flowing out per second from both the holes is same, then side ' $a$ ' of hole ' $P$ ' is

A wire of length ' $L$ ' carries a current ' $I$ '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field $(\overrightarrow{\mathrm{B}})$ is

A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The moment of inertia of a thin uniform rod of mass ' $M$ ' and length ' $L$ ', about an axis perpendicular to length of the rod and at a distance ' $L / 4$ ' from one end is

The potential difference across the 4 capacitor in the following circuit is

The relation between efficiency $(\eta)$ of Carnot engine and coefficient of performance $\left(\eta_1\right)$ of refrigerator is

A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

500 gram of a diatomic gas is enclosed at a pressure of $10^5 \mathrm{Nm}^{-2}$. The density of the gas is $5 \mathrm{kgm}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

In metre-bridge experiment the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$. A shunt of $\mathrm{x} \Omega$ is added to $3 \Omega$ resistor to shift the balance point by 22.5 cm . The value of x is

All the springs in fig. (a), (b) and (c) are identical, each having force constant K each. Mass m is attached to each system. If $\mathrm{T}_a, \mathrm{~T}_b$ and $\mathrm{T}_{\mathrm{c}}$ are the time periods of oscillations of the three systems in fig. (a), (b) and (c) respectively, then

A physical quantity ' X ' is related to four measurable quantities ' $a$ ', ' $b$ ', ' $c$ ' and ' $d$ ' as $\mathrm{X}=\mathrm{a}^2 \mathrm{~b}^3 \mathrm{c}^{5 / 2} \mathrm{~d}^{-2}$. The percentage error in the measurement of 'a', 'b', 'c' and 'd' are $1 \%$, $2 \%, 2 \%$ and $4 \%$ respectively. The percentage error in measurement of quantity ' X ' is

A coil of effective area $3 \mathrm{~m}^2$ is placed at right angles to a magnetic field of induction $0.05 \mathrm{~Wb} / \mathrm{m}^2$ If the field is decreased to $20 \%$ of its original value in 10 second, the e.m.f. induced in the coil will be

Two vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other. When $3 \mathrm{a}+2 \mathrm{~b}=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is

Three immiscible transparent liquids with refractive indices $3 / 2,4 / 3$ and $6 / 5$ are arranged one above the other in a container. The depths of the liquids are $3 \mathrm{~cm}, 4 \mathrm{~cm}$ and 6 cm respectively. The apparent depth of the vessel is

A spherical liquid drop splits in to 729 identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of resulting drops, then $\frac{E}{U}=\frac{1}{x}$. The value of $x$ is

A circular coil carrying current has radius ' $R$ '. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$ th of its value at the centre of the coil is

A point particle of mass 200 gram is executing S.H.M. of amplitude 0.2 m . When the particle passes through the mean position, its kinetic energy is $16 \times 10^{-3} \mathrm{~J}$. The equation of motion of this particle is (Initial phase of oscillation $=0^{\circ}$ )

An inductor of $\left(\frac{100}{\pi}\right) \mathrm{mH}$, capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) \mathrm{F}$ and resistance of $10 \Omega$ are connected in series with an AC voltage source of $110 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The tangent of the phase angle ' $\phi$ ' between voltage and current is

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

A charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up, the total electric flux coming out of the surface

Resolving power of a telescope can be increased by increasing

The ratio of the total energy of the $2^{\text {nd }}$ orbit electron for the hydrogen atom ($^1\mathrm{H}$) to that of a helium ion ($\mathrm{He}^+$) is :

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' $R$ ' from the centre of a star of radius ' $r$ ' is $(R>r)(\sigma=$ Stefan's constant $)$

The magnetic field (B) inside a long solenoid having ' $n$ ' turns per unit length and carrying current ' i ' when iron core is kept in it, is ( $\mu_0=$ permeability of vacuum, $\chi=$ magnetic susceptibility)

A gas having $\gamma=\frac{5}{2}$ and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

In Young's double slit experiment, the intensity on screen at a point, where path difference is $\frac{\lambda}{4}$ is $\frac{K}{4}$. The intensity at a point when path difference is ' $\lambda$ ' will be $\left[\cos \frac{\pi}{2}=0, \cos 2 \pi=1\right]$

When LED is manufactured by using aluminium gallium arsenide (AlGaAs), it emits

A simple pendulum starts oscillating simple harmonically from its mean position ( $\mathrm{x}=0$ ) with amplitude ' $a$ ' and periodic time ' $T$ '. The magnitude of velocity of pendulum at $x=\frac{a}{2}$ is

A coil having ' $N$ ' turns and resistance ' $R$ ' $\Omega$ is connected to a galvanometer of resistance ' 6 R ' $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time ' t ' second. The induced current in the circuit is

Energy of the incident photons on the metal surface is initially 4 W and then 6 W where $W$ is the work function of that metal. The ratio of velocities of emitted photoelectrons is

A ball is dropped on the floor from a height of 20 m . It rebounds to a height of 5 m . Ball remains in contact with floor for 1 s . The average acceleration during contact is (acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )

Which of the following figure represents forward bias diode?

The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

An AND gate is followed by a NOT gate in series. With two inputs ' $A$ ' and ' $B$ ', the Boolean expression for the output ' Y ' will be

A uniform sphere has radius ' $R$ ' and mass ' $M$ '. The magnitude of gravitational field at distances ' $\mathrm{r}_1$ ' and ' $\mathrm{r}_2$ ' from the centre of the sphere are ' $E_1$ ' and ' $E_2$ ' respectively. The ratio $E_1: E_2$ is $\left(r_1>R\right.$ and $\left.r_2