The degeneracy of a hydrogen atom whose energy equals $-R_{\mathrm{H}}$ / 16

A 1 molar aqueous solution of magnesium nitrate is $40 \%$ dissociated at 298 K . Calculate the osmotic pressure of the solution. $\left(R=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$

$$ \text { The product } Z \text { formed in the given reaction is } $$

In a cyclic $p V$ process forming $A$ square loop from $(p=1 \mathrm{~atm}, V=2 \mathrm{~L})$ to $(p=3 \mathrm{~atm}$, $V=4 \mathrm{~L})$, Then, the net heat absorbed by the gas is

Balance the following redox reaction in acidic medium and determine the stoichiometric coefficient of $\mathrm{H}_2 \mathrm{O}$ in the final balanced equation.

$$ \mathrm{MnO}_4^{-}(a q)+\mathrm{Fe}^{2+}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Fe}^{3+}(a q) $$

If the de-Broglie wavelength of a particle is equal to $10 \sqrt{h / m}$, then what is the ratio of its speed to mass?

Electron affinity is maximum when

The bond dissociation energies of $A_2, B_2$ and $A B$ are in the ratio $1: 4: 2$. If $\Delta H$ for formation of $A B$ from $A_2$ and $B_2$ is $-100 \mathrm{~kJ} / \mathrm{mol}$, calculate the bond dissociation energy of $B_2$.

Among aqueous 1 N solutions, the pH of HCl , $\mathrm{HNO}_2$ and $\mathrm{CH}_3 \mathrm{COOH}$ follows the order

The ionic radii of $\mathrm{N}^{3-}, \mathrm{O}^{2-}$ and $\mathrm{F}^{-}$follow the trend

30 mL of 0.1 M acetic acid is mixed with 60 mL of 0.1 M sodium acetate. If $K_a=1.8 \times 10^{-5}$ what will be the pH of the solution?

0.1 m of urea and 0.05 m of $\mathrm{CaCl}_2$ are dissolved separately in equal volumes of water. Which solution will have higher elevation in boiling point?

How many geometrical (cis-trans) isomers are possible for the compound?

$$ \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_2 $$

$$ \text { The product } X \text { and } Y \text { respectively are } $$

A current of 4.0 A is passed through 0.5 L of 0.2 M NaCl solution for 1200 s . Calculate the pH of the solution after electrolysis.

Intramolecular hydrogen bonding is predominantly observed in

The approximate time duration in hours to electroplate 20 g of calcium from molten calcium chloride using a current of 4 A is (Atomic mass of $\mathrm{Ca}=40$ )

The central atom shows $d$-orbital participation in hybridisation in

Identify the compound that undergoes self-aldol condensation in the presence of cold dilute alkali, forming a $\beta$-hydroxy aldehyde:

Calculate the volume of $M / 10 \mathrm{KMnO}_4$ needed to react with 20 mL of $M / 2 \mathrm{FeSO}_4$ in acidic medium.

Angular stomatitis and cracked lips are caused by deficiency of

$$ \text { The major product formed in the given reaction is } $$

For the reaction,

$$ 2 \mathrm{SO}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{SO}_3 $$

if the rate of disappearance of $\mathrm{O}_2$ is $2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, determine the rate of appearance of $\mathrm{SO}_3$.

If for a first-order reaction, the frequency factor $A=4 \times 10^{13} \mathrm{~s}^{-1}$ and activation energy $E_a=98.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$, at what temperature will the half-life be 10 minutes?

A tetrapeptide is formed from four amino acids: alanine, serine, glycine, and valine. The C-terminal is fixed as alanine, and the N-terminal amino acid is chiral. Determine the number of possible sequences.

Among the following transition metal ions, how many have the same number of unpaired electrons, and thus approximately the same magnetic moment?

(i) $\mathrm{Cr}^{3+}$

(ii) $\mathrm{Fe}^{3+}$

(iii) $\mathrm{Mn}^{2+}$

(iv) $\mathrm{Co}^{2+}$

(v) $\mathrm{Ni}^{2+}$

The $\mathrm{Fe}^{3+}$ ion, having five unpaired electrons, shows a spin-only magnetic moment closest to

The hybridisation and geometry of the complex $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are

Match List-I with List-II for oxidation number of central metal atom.

$$ \begin{array}{llcc} \hline \begin{array}{c} \text { List-I } \\ (\text { Complex }) \end{array} & & \begin{array}{c} \text { List-II } \\ \text { (Oxidation number) } \end{array} \\ \hline \text { A. } \mathrm{Ni}(\mathrm{CO})_4 & \text { I. } & +1 \\ \hline \text { B. }\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right]^{2+} & \text { II. } & \text { Zero } \\ \hline \begin{array}{l} \text { C. }\left[\mathrm{Co}(\mathrm{CO})_5\right]^{2-} \\ (\mathrm{Each} \mathrm{Cr}) \end{array} & \text { III. } & -1 \\ \hline \begin{array}{l} \text { D. }\left[\mathrm{Cr}(\mathrm{CO})_{10}\right]^{2-} \\ (\mathrm{Each}) \end{array} & \text { IV. } & -2 \\ \hline \end{array} $$

Choose the correct match from the options given below

The major product of the reaction between $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{ONa}$ and $\left(\mathrm{CH}_3\right)_3 \mathrm{CCl}$ in ethanol is

Select the most appropriate option that can substitute the underlined segment in the given sentence.

They had eaten an apple every day for breakfast.

Select the most appropriate option to fill in the blank.

Though he is stout, he runs $\_\_\_\_$

Select the option that expresses the given sentence in active voice.

The door was opened by the children for their father.

Select the most appropriate antonym of the given word.

Famous

Select the most appropriate synonym of the given word. Austere

Select the option that can be used as a one-word substitute for the given group of words. One thing that can be divided

Select the option that can be used as a one-word substitute for the given group of words.

Unselfish interest in the welfare of others

Select the most appropriate meaning of the highlighted idiom.

The actress' daughter is just a chip off the old block.

Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.

A. Two astronomers - Johannes Kepler from Germany and Galileo from Italy-supported the Copernicus theory after nearly a century passed by.

B. Copernicus' view was that the Sun was stationary and the Earth and the planets moved in orbits around the Sun.

C. Nicholas Copernicus, a Polish priest, proposed a model in 1514.

D. There are many popular theories about the solar system. Ancient people believed that the Sun moved around the Earth and the Earth was static.

Select the option that expresses the given sentence in passive voice.

I am going to ask all employees about the incident that took place in the canteen yesterday.

Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter-cluster.

Which figure from the given options would replace the question mark (?) if the following figure series were to be continued?

Which of the following numbers will replace the question mark (?) in the given series? 270, 241, 212, ?, 154, 125

Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.

$25: 18:: 37: ?:: 49: 36$

Select the option that is related to the third word in the same way as the second word is related to the first word.

Pressure : Barometer :: Electricity : ?

Select the option figure in which the given figure is embedded as its part (Rotation is not allowed.)

Select the set in which the numbers are related in the same way as are the numbers of the following sets.

$$ (112,327,215),(98,254,156) $$

Which letter-cluster will replace the question mark (?) to complete the given series?

BRCQ, EPFO, ?, KLLK, NJOI

Select the option in which the given figure is embedded (Rotation is not allowed).

$\mathrm{Q}+\mathrm{J}$ means " Q is the Husband of J "

Q - J means "Q is the Father of J"

$\mathrm{Q} \times \mathrm{J}$ means " Q is the Mother of J "

Q * J means " Q is the Daughter of J "

If $\mathrm{D} * \mathrm{~V}+\mathrm{B} \times \mathrm{U}$, how is D related to U?

When the following figure is folded to form a cube, which letter-number will be on the face opposite to the face showing the letter-number ‘Al’?

(The elements are shown to indicate the sides only.)

Six characters A, B, C, 1, 2 and 3 are written on different faces of a dice. Two positions of this dice are shown in the figure. Find the character on the face opposite to $\boldsymbol{C}$.

Stanley starts cycling from point $A$. He cycles $x$ km towards the West and then turns right and cycles 3 km . He again turns right and cycles for $x+1 \mathrm{~km}$. He again turns right and cycles for $2 x+1 \mathrm{~km}$. He takes a final right turn and cycles for 1 km to stop at point $B$. Point $B$ is 6 km South of point $\boldsymbol{A}$. What is the value of $x$ ?

In a certain code language, 'SPAM' is coded as ' 36 ' and 'JUG' is coded as ' 27 '. How will 'FROCK' be coded in that language?

Six students Meera, Jigyasa, Tarun, Naina, Shambhavi and Avni are sitting around a circular table facing the centre (Not necessarily in the same order). Shambhavi is an immediate neighbour of both Jigyasa and Avni. Tarun is sitting third to the left of Jigyasa. Meera is sitting second to the right of Avni. Who is sitting second to the left of Jigyasa?

In a certain code language, 'BLOCK' is coded as LBCON and 'CABIN' is coded as ACIBQ. How will 'SUITE' be coded in the same language?

Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts,

decide which of the conclusions logically follow(s) from the statements.

Statements

All keys are locks.

No door is a lock.

Conclusions

I. Some locks are doors.

II. Some locks are keys.

III. No key is a door.

A paper is folded and cut as shown below. How will it appear when unfolded?

Which of the following numbers will replace the question mark (?) in the given series?

$$ 69,65,67,63, ?, 61 $$

Which of the following numbers will replace the question mark (?) in the given series?

$5,20,60,240,720$, ?

If $f: X \rightarrow Y$ be a function defined by $f(x)=a \sin \left(x+\frac{\pi}{4}\right)+b \cos x+c$ and $f$ is bijective, then the set $X$ with $\theta=\tan ^{-1}\left(\frac{a+\sqrt{2} b}{a}\right)$ is

The value of $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ is

The function $f(x)=\frac{x}{\sin x}$ is strictly increasing in the interval.

The value of integral $\int_a^b e^x d x$ as limit of sums is

For what values of the parameter ' $a$ ' does the function $f(x)=x^3+3(a-7) x^2+3\left(a^2-9\right) x-1$ have a positive point of maximum.

The solution of the differential equation $\frac{d y}{d x}+x \sin 2 y=x^3 \cos ^2 y$ is

If ' $a$ ' is a complex number such that $|a|=1$. Find the value of $a$, so that the equation $a z^2+z+1=0$ has one purely imaginary root.

If $\mathbf{a , b , c}$ are vectors such that $|\mathbf{b}|=|\mathbf{c}|$ then $\{(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}+\mathbf{c})\} \times(\mathbf{b} \times \mathbf{c}) \cdot(\mathbf{b}+\mathbf{c})$ is equal to

For what value of $a, 6$ lies between the roots of the equation $x^2+2(a-3) x+9=0$.

What is the probability of getting a sum of 9 in a single throw of three fair dice?

The coefficient of $x^n$ in the expansion of $\frac{1-a x-x^2}{e^x}$ is

The locus of the middle points of chords of the circle $x^2+y^2=25$ which are parallel to the line $x-2 y+3=0$ is

What is the value of the definite integral $\int_0^\pi \log (\sin x) d x$ ?

104. If $p, q, r$ are in GP and the line $p x+q y+r=0$ forms a triangle with the coordinate axes, what is the area of the triangle if $p=2, q=4$ and $r=8$ ?

What is the area enclosed by the curves $y=x^4$ and $y=x^{\frac{1}{3}}$

The number of real solution of $\sqrt{\left(7-\log _3|x|\right)}=4-\log _3|x|$ is equal to

For three numbers $a, b, c$ between 2 and 18 such that their sum is 25 , the numbers $2, a, b$ are in AP and the numbers $b, c, 18$ are in GP Then, the value of $a+b+c$ is

If ${ }^n C_{n-r}+3 \cdot{ }^n C_{n-r+1}+3 \cdot{ }^n C_{n-r+2} +{ }^n C_{n-r+3}={ }^x C_r$, then the value of $x$ is

109. If $A, B, C$ are the angles of a $\triangle A B C$, then

$$ \Delta=\left|\begin{array}{ccc} \sin 2 A & \sin C & \sin B \\ \sin C & \sin 2 B & \sin A \\ \sin B & \sin A & \sin 2 C \end{array}\right| \text { is equal to } $$

What is the coefficient of $x^{50}$ in $(1+x)^{41}\left(1-x+x^2\right)^{40}$.

If $a, b, c, d$ be four positive unequal quantities and $s=a+b+c+d$, then $(s-a)(s-b)(s-c) (s-d)>k a b c d$. Then, value of $k$ is

If four lines $a x \pm b y \pm c=0$ encloses a rhombus, then the area is

If the equation $2 h x y+2 g x+2 f y+c=0$ represents two straight lines, then the area of rectangle formed with the coordinates axes is

What is the set of values of a for which the point ( $2 a, a+1$ ) is an interior point of the larger segment of the circle $x^2+y^2-2 x-2 y-8=0$ made by the chord $x-y+1=0$.

Tangents are drawn to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at points where it is intersected by the line $l x+m y+n=0$. The point of intersection of tangents at these points is

The locus of the mid-point of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9 x^2-16 y^2=144$ is $\left(x^2+y^2\right)^2=k x^2-l y^2$. Then, the sum of values of $k$ and $l$ is

If $A+B=\frac{\pi}{4}$, then $(1+\tan A)(1+\tan B)$ is equal to

The angles of a triangle are in the ratio $1: 2: 7$. The ratio of the greatest side to the least side is $(k+1):(k-1)$. The value of $k$ is

Let $A, B$ and $C$ be the angles of a triangle and $\tan \frac{A}{2}=\frac{2}{5}, \tan \frac{B}{2}=\frac{3}{7}$. Then, $\tan \frac{C}{2}$ is equal to

Roots of the equation $a x^2+b x+c=0(a, b, c>0)$ are

Consider the function $g(x)$ defined as

$$ g(x)=\left\{\begin{array}{cc} \frac{x^2-4}{x^2-2|x-2|-4}, & x \neq 2 \\ \frac{3}{4}, & x=2 \end{array}\right. $$

Which of the following statements is true about the continuity of $g(x)$ ?

The magnitude projection of line segment joining points $(1,2,3)$ and $(-1,4,2)$ on the line joining points $(-2,3,3)$ and $(0,6,-3)$ is

The Boolean expression

$$ \sim(p \wedge q) \vee(p \wedge \sim q) \vee(\sim p \wedge \sim q) $$

is equivalent to

In a binomial distribution, the mean is 10 and the variance is 6 . Then, its median is

A rectangle is inscribed in an ellipse with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

What is the maximum area of the rectangle that can be inscribed in the ellipse?

A four digit number is formed with digits $1,3,4$, 5 with no repetition. What is the probability that the number is divisible by 5 ?

If the function $f: R \rightarrow R$ is defined by $f(x)=x^2+5 x+9$, then $f^{-1}(9)$ is equal to

If $\mathop {\lim }\limits_{x \to \infty }\left\{\frac{x^2-1}{x+1}-a x-b\right\}=2$. The value of $a$ is

The slope of the curve $2 y^2=a x^2+b$ at $(1,-1)$ is -1 . Then, the value of $b$ is

Let $z$ be a complex number for which $\left|2 z \cos \theta+z^2\right|>1$, if $|z|

A beam of light travelling in water strikes a glass plate which is also immersed in water. When the angle of incidence is $60^{\circ}$, the reflected beam is found to be plane polarised. Find the refractive index of glass, if refractive index of water is $\sqrt{2}$.

Consider a hydrogen atom with its electron in the $n$th orbit. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV , then the value of $n$ is ( $h c=1242 \mathrm{eV} \mathrm{nm}$ )

A water film is made between two straight parallel wires of length 10 cm each and at a distance of 0.5 cm from each other. If the distance between the wires is increased by 1 mm , then work done (in ergs) is [Given, surface tension of water $=72$ dynes $/ \mathrm{cm}$ ]

The acceleration versus time graph of a particle moving along a straight line is shown in the figure. Draw the respective velocity time graph. (Assuming at $t=0, v=0$ )

In given lens combination, each lens is of focal length 10 cm .

Correct ray diagram for this combination is

A parallel plate capacitor with plate area $A$ and separation between plates $d$ is charged with constant current $I$. Consider a plane surface of area $\frac{5 A}{6}$ parallel to the plates and drawn between the plates. The displacement current through area is

A body is projected vertically upwards from the surface of Earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be

A current $I=10 \sin (100 \pi t) A$ is passed in the first coil, which induces a maximum emf of $5 \pi \mathrm{~V}$ in second coil. The mutual inductance between the coil is

A dielectric slab of dielectric constant $k=3$ is filling $\frac{3}{4}$ th space of the capacitor.

When capacitor is charged, then \% of total energy stored in dielectric is

A string of length $L$ and force constant $k$ is stretched to obtain extension $l$. It is further stretched to obtain extension $l_1$. The work done in second stretching is

A block of mass 10 kg slides down a rough slope which is inclined at an angle of $45^{\circ}$ to the horizontal. The coefficient of sliding friction is 0.30 . When the block has slide 5 m , the work done on the block by the force of friction is nearly

In a Young's double slit experiment for a particular wavelength of light the distance between third dark and fifth bright fringe is 1.63 mm . If the distance between two slit is 1 mm and distance between slit and screen is 1 metre. Then, the wavelength of light is

A mass $M$ is broken into two parts of masses $m_1$ and $m_2$. How are $m_1$ and $m_2$ related, so that force of gravitational attraction between the two parts is maximum?

The frequency of a light wave in a material is $2 \times 10^{14} \mathrm{~Hz}$ and wavelength is $5000 \mathop {\rm{A}}\limits^{\rm{o}} $. The refractive index of material will be

A man with a mass of 80 kg is standing on the rim to a circular platform with a mass of 200 kg . The circular platform is rotating at 12 revolutions per minute (rpm) about its axis. The man moves from the rim towards the centre of the platform. The new angular velocity of the system will be (Assuming that the man's moment of inertia at the centre of the plateform is negligible)

Two wires of the same material (Young's modulus $=Y$ ) and same length $L$ but radii $R$ and $2 R$ respectively are joined end to end and a weight $w$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

A pure resistive circuit element $X$, when connected to an AC supply of peak voltage 200 V , gives a peak current of 5 A . A second circuit element $Y$, when connected to the same AC supply also gives the same value of peak current but the current lags behind by $90^{\circ}$. If the series combination of $X$ and $Y$ is connected to the same supply, what will be the rms value of current?

The equivalent resistance of the circuit across $A B$ is given by

The fundamental frequency of a closed organ pipe is same as the first overtone frequency of an open organ pipe. If the length of open organ pipe is 50 cm , then the length of closed organ pipe is

A vessel is filled with a gas at a pressure of 76 cm of mercury at a certain temperature. The mass of gas is increased by $50 \%$ introducing more gas in the vessel at the same temperature. Now the resultant pressure of the gas is

A cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2 R$ made of a material of thermal conductivity $k_2$. The two ends of a combined system are maintained at two different temperature. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

The mass of proton is 1.0073 u and that of neutron is $1.0087 \mathrm{u}(\mathrm{u}=$ atomic mass unit). The binding energy of ${ }_2 \mathrm{He}^4$ is

In a certain process, 400 cal of heat is supplied to a system and at the same time 105 J of mechanical work was done on the system. The increase in its internal energy is

A standing wave $y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$ is maintained in a taught string, where $y$ and $x$ are in metres. The distance between two successive points oscillating with the amplitude $\frac{A}{2}$ across a node is

Two rods $P$ and $Q$ have equal lengths. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$. When the temperature at ends of each rod are $T_1$ and $T_2$ respectively, the rate of flow of heat through $P$ and $Q$ will be equal, if

A bar magnet has magnetic moment of $0.05 \mathrm{Am}^2$ which is suspended in uniform magnetic field of 0.2 T . Calculate the work done in rotating the magnet from its most stable to most unstable position in the magnetic field.

The frequency of oscillation of the spring mass system is

A body is projected with a speed $u \mathrm{~ms}^{-1}$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $(3 / 4)$ th of the initial kinetic energy. The value of $\beta$ is

The temperature $(T)$ dependence of resistivity ( $\rho$ ) of a semiconductor is represented by

A large block of ice 10 cm thick with a vertical hole drilled through it is floating in a lake. The minimum length of the rope required to scoop out a bucket full of water through the hole is (density of ice $=0.9 \mathrm{~g} / \mathrm{cm}^3$ )