VITEEE 2021

The efficiency of a Carnot engine kept at the temperatures of $$27^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$ is

The Young's modulus of a rope of $$10 \mathrm{~m}$$ length and having diameter of $$2 \mathrm{~cm}$$ is $$200 \times 10^{11} \mathrm{~dyne} / \mathrm{cm}^2$$. If the elongation produced in the rope is $$1 \mathrm{~cm}$$, the force applied on the rope is

The power $$(P)$$ of an engine lifting a mass of $$100 \mathrm{~kg}$$ upto a height of $$10 \mathrm{~m}$$ in $$1 \mathrm{~min}$$ is

The distance of moon form the earth is $$3.8 \times 10^5 \mathrm{~km}$$. Supposing that the eye is most sensitive to the light of wavelength $$550 \mathrm{~nm}$$, the separation of two points on the moon that can be resolved by a $$500 \mathrm{~cm}$$ telescope is

If two slits in Young's experiment are $$0.4 \mathrm{~mm}$$ apart and fringe width on a screen $$200 \mathrm{~cm}$$ away is $$2 \mathrm{~mm}$$ the wavelength of light illuminating the slits is

Unpolarised light falls on two polarising sheets placed one on top of other. If the intensity of transmitted light is one fourth of the incident light, the angle between them is

The net electric force on a charge of $$+3 \mu \mathrm{C}$$ at the mid-point on the line joining two charges of magnitude $$+2 \mu \mathrm{C}$$ and $$-2 \mu \mathrm{C}$$ separated by the distance of $$6 \mathrm{~mm}$$, is

A silver wire of radius $$0.1 \mathrm{~cm}$$ carries a current of $$2 \mathrm{~A}$$. If the charge density in silver is $$5.86 \times 10^{28} \mathrm{~m}^{-3}$$, the drift velocity is

When an object is placed $$40 \mathrm{~cm}$$ from a diverging lens, its virtual image is formed $$20 \mathrm{~cm}$$ from the lens. The focal length and power of lens are

An object is $$8 \mathrm{~cm}$$ high. It is desired to form a real image $$4 \mathrm{~cm}$$ high at $$60 \mathrm{~cm}$$ from the mirror. The type of mirror needed with the focal length is

A person has a minimum distance of distinct vision as $$50 \mathrm{~cm}$$. The power of lenses required to read a book at a distance of $$25 \mathrm{~cm}$$ is

The temperature coefficient of the resistance of a wire is 0.00125 per $${ }^{\circ} \mathrm{C}$$. At $$300 \mathrm{~K}$$ its resistance is $$1 \Omega$$. The resistance of wire will be $$2 \Omega$$ at

The magnetic field at a point on the axis of a long solenoid having 5 turns per $$\mathrm{cm}$$ length when a current of $$0.8 \mathrm{~A}$$ flows through it is

If the alternating current $$I=I_1 \cos \omega t+ I_2 \sin \omega t$$ then the rms current is given by

An electron revolves in a circle at the rate of $$10^{19}$$ rounds per second. The equivalent current is $$\left(e=1.6 \times 10^{-19} \mathrm{C}\right)$$

Two straight wires each $$10 \mathrm{~cm}$$ long are parallel to one another and separated by $$2 \mathrm{~cm}$$. When the current flowing in them is $$30 \mathrm{~A}$$ and $$40 \mathrm{~A}$$ respectively, the force experienced by either of the wires is

A long straight wire is carrying a current of $$12 \mathrm{~A}$$. The magnetic field at a distance of $$8 \mathrm{~cm}$$ is $$\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~N} / \mathrm{A}^2\right)$$

A bar magnet of pole strength $$10 \mathrm{~Am}$$ is cut into two equal parts breadthwise. The pole strength of each magnet is

The Brewster's law is given by the expression

24 cells of emf $$1.5 \mathrm{~V}$$ each having internal resistance of $$1 \mathrm{~ohm}$$ are connected to an external resistance of $$1.5 \mathrm{~ohms}$$. To get maximum current

Which of the following oxides of group 16 has the highest boiling point?

The zeroth law of thermodynamics for three systems $$A, B$$ and $$C$$ in contact demands that

The velocity of sound in a gas is $$1300 \mathrm{~m} / \mathrm{s}$$ at STP and specific heat at constant pressure is $$6.84 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$. The rms velocity at STP is $$(R=1.98 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1})$$

A $$50 \mathrm{~Hz}$$ $$\mathrm{AC}$$ signal is applied in a circuit of inductance of $$(1 / \pi) \mathrm{H}$$ and resistance $$2100 \Omega$$. The impedance offered by the circuit is

The horizontal and vertical components of earth's magnetic field at a place are $$0.3 \mathrm{G}$$ and $$0.52 \mathrm{G}$$. The earth's magnetic field and the angle of dip are

Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is

A parallel plate capacitor of capacitance $$5 \mu \mathrm{F}$$ is charged to $$120 \mathrm{~V}$$ and then connected to another uncharged capacitor. If the potential falls to $$40 \mathrm{~V}$$, and capacitance of the second capacitor is

The alternating current in a circuit is given by $$I=50 \sin 314 t$$. The peak value and frequency of the current are

The induced emf in a coil of $$10 \mathrm{H}$$ inductance in which current varies from $$9 \mathrm{~A}$$ to $$4 \mathrm{~A}$$ in $$0.2 \mathrm{~s}$$ is

A conductor of length $$5 \mathrm{~cm}$$ is moved parallel to itself with a speed of $$2 \mathrm{~m} / \mathrm{s}$$, perpendicular to a uniform magnetic field of $$10^{-3} \mathrm{~Wb} / \mathrm{m}^3$$. The induced e.m.f. generated is

Einstein's photoelectric equation is

Polonium has a half-life of 140 days. If we take $$20 \mathrm{~g}$$ of polonium initially then the amount of it that remains after 280 days is

The Rutherford scattering experiment proves that an atom consists of

According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition

Which component of electromagnetic spectrum have maximum wavelength?

Which of the following logic gates are also known as the Universal gates?

Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in

Calculate the wavelength associated with an electron moving with a velocity of $$10^6 \mathrm{~m} / \mathrm{s}$$ (mass of electron $$=9.1 \times 10^{-31} \mathrm{~kg}, h=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$$ )

Which of the following pairs is not correctly matched?

The orbital diagram in which Aufbau principle is violated is

The demodulator or detector circuit consists of a

What is the total number of electrons that can have the values $$n=2, l=1, s=1 / 2$$ in the electronic configuration $$1 s^2 2 s^2 2 p^3$$ ?

A catalyst is a substance which

When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal is known as

The solubility of $$\mathrm{Fe}(\mathrm{OH})_3$$ is $$x \mathrm{~mol} \mathrm{~L}^{-1}$$. Its $$K_{\mathrm{sp}}$$ would be

If $$\Delta H$$ and $$\Delta S$$ are positive for a reaction, the reaction will be spontaneous only when

The $$[\mathrm{OH}]^{-}$$ in a solution is $$1 \mathrm{~mol} \mathrm{~L}^{-1}$$. The $$\mathrm{pH}$$ of the solution is

In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called

Electrolysis of an aqueous solution of sodium ethanoate gives

Which of the following statements is correct?

When an electrolytic solution conducts electricity, the current is carried by

An electrochemical cell has two half cell reactions as,

$$\begin{aligned} A^{2+}+2 e^{-} & \longrightarrow A ; E_{A^{2+} / A}^0=0.34 \mathrm{~V} \\ X & \longrightarrow X^{2+}+2 e^{-} ; E_{X^{2+} / X}^0=-2.37 \mathrm{~V} \end{aligned}$$

The cell voltage will be

Consider the reaction,

$$2 \mathrm{~N}_2 \mathrm{O}_5(g) \longrightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$

The rate law for this reaction is rate $$=k\left[\mathrm{~N}_2 \mathrm{O}_5\right]$$.

Which of the following statements is true regarding the above reaction?

How does electron affinity change when we move from left to right in a period in the Periodic Table?

Specify the coordination number of cobalt in $$\left[\mathrm{Co}(\mathrm{CN})\left(\mathrm{H}_2 \mathrm{O}\right)(\mathrm{e n})^2\right]^{2+}$$

Which of the following statements is not correct?

Which of the following complexes is square planar and diamagnetic?

The number of optical isomers of the compound $$\mathrm{CH}_3 \mathrm{CHBrCHBrCOOH}$$ is

Which type of isomerism is exhibited by $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$$ ?

The hybridization of carbon atoms in $$\mathrm{C}-\mathrm{C}$$ single bond of $$\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_2$$ is

Identify Z in the following sequence

$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{I} \xrightarrow{\mathrm{KCN}} X \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+} / \mathrm{H}_2 \mathrm{O}} \mathrm{Y} \xrightarrow[\Delta]{\mathrm{H}_3 \mathrm{O}^{+} / \mathrm{H}_2 \mathrm{O}} Z$$

Phenol on treatment with conc. $$\mathrm{HNO}_3$$ gives

Which of the following groups is ortho and para directing?

When ethanol and $$\mathrm{I}_2$$ are heated in the presence of $$\mathrm{Na}_2 \mathrm{CO}_3$$, the yellow crystals obtained are of

The reaction given below is an example of which of the following?

$$2 \mathrm{CH}_3 \mathrm{Br}+2 \mathrm{Na} \xrightarrow{\text { dry ether }} \mathrm{C}_2 \mathrm{H}_6+2 \mathrm{NaBr}$$

Which of the following compounds will exhibit cis-trans (geometrical) isomerism?

Which of the following compounds will be formed when methoxy benzene is reacted with $$\mathrm{HBr}$$ ?

Which of the following compounds has maximum acidic character?

Propanal on reaction with lithium aluminium hydride gives

Identify B in the following series of reaction

$$\mathrm{CH}_3 \mathrm{CHO} \xrightarrow{\mathrm{CH}_3 \mathrm{MgX}} A \xrightarrow{\mathrm{HOH}} B$$

Among the following, the least reactive aldehyde is

$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl} \xrightarrow{\mathrm{NH}_3} X \xrightarrow{\mathrm{P}_2 \mathrm{O}_5} Y \xrightarrow[\mathrm{H}_2]{\mathrm{Ni}} Z$$

the end product in the above sequence of reactions is

Treatment of aniline with bromine water produces

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is

Nucleic acids are polymers of

Which of the following is least reactive to nitration?

Chlorobenzene can be prepared by reacting aniline with

Which of the following enzymes helps in digestion of proteins?

Which of the following is the correct principle of Mathematical induction?

If $$S=\{(a, b): b=|a-1|, a \in Z$$ and $$|a|<3\}$$, where $$Z$$ denotes the set of integers. Then, the range set of $$S$$ is

The coefficient of the term independent of $$x$$ in the expansion $$\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$$ is

If $$(3,4,-1)$$ and $$(-1,2,3)$$ be end points of the diameter of a sphere, then the radius of the sphere is

A bag contains 50 tickets numbered $$1,2,3, ..., 50$$ of which five are drawn at random and arranged in ascending order of magnitude $$\left(x_1 < x_2 < x_3 < x_4< x_5\right)$$, then the probability that $x_3=30$ is

The cartesian product $$A \times A$$ has 9 elements among which are found $$(-1,0)$$ and $$(0,1)$$, then set $$A$$ is equal to

The position vector of a point $$R$$ which divides the line joining $$P(6,3,-2)$$ and $$Q(3,1,-4)$$ in the ratio $$2 : 1$$ externally is

If $$A^{-1}=\left[\begin{array}{rr}5 & -2 \\ -7 & 3\end{array}\right]$$ and $$B^{-1}=\frac{1}{2}\left[\begin{array}{rr}9 & -7 \\ -8 & 6\end{array}\right]$$, then $$(A B)^{-1}$$ is equal to

The following lines are

$$\begin{aligned} \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\ \text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \end{aligned}$$

The negation of $$\sim s \vee(\sim r \wedge s)$$ is equivalent to

The angle between the lines $$\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0}, \frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}$$ is

If $$A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$$, then $$\left(A-A^{\prime}\right)$$ is equal to (where, $$A^{\prime}$$ is transpose of matrix $$A$$ )

The non-zero solutions of the equation $$z^2+|z|=0$$, where $$z$$ is a complex number, are

Find the value of $$\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{3}{5}\right)$$.

The value of $$\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left\{\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right\}$$ is

If $$(1+i)(2 i+1)(1+3 i) \ldots(1+n i)=x+i y$$, then $$2 \cdot 5 \cdot 10 \ldots\left(1+n^2\right)$$ is equal to

If $$\theta=\frac{\pi}{2^n+1}$$, then the value of $$2^n \cos \theta \cos 2 \theta \cos 2^2 \theta \ldots \cos 2^{n-1} \theta$$ is

Using the principal values, the value of $$\sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}+\tan ^{-1}\left\{\tan \frac{\pi}{6}\right\}$$ is equal to

Which of the following is not a function?

If $$f(x)=\left\{\begin{array}{cc}\frac{(1-\cos 4 x)}{x^2}, & \text { if } x < 0 \\ a, & \text { if } x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & \text { if } x > 0\end{array}\right.$$ then $$f(x)$$ is continuous at $$x=0$$, for $$a$$

The value of $$\lim _\limits{n \rightarrow \infty}\left\{\frac{1+2+3+\ldots+n}{n+2}-\frac{n}{2}\right\}$$ is

$$\lim _\limits{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}$$ is equal to

If $$y=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots$$, then $$\frac{d y}{d x}$$ is equal to

The quotient of the identity function by the reciprocal function is given by

The area bounded by the circle $$x^2+y^2=16$$ and the line $$y=x$$ in the first quadrant is

The value of $$\frac{d}{d x}\left(x^n \log _a x e^x\right)$$ is

The interval in which the function $$f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi$$ is strictly decreasing, is

The value of $$\int\limits_0^{\pi / 2} \frac{d x}{1+\tan x}$$ is

Evaluate $$\int \frac{3 x-2}{(x+3)(x+1)^2} d x$$.

The slope of normal to the curve $$y=x^3+2 x+6$$ which is parallel to line $$x+14 y+4=0$$ is

The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpendicular is 3/4 is

The radius of the circle $$(x \cos \theta+y \sin \theta-a)^2+(x \sin \theta-y \cos \theta-b)^2=k^2$$ is

On solving the differential equation $$x^2 y d x-\left(x^3+y^3\right) d y=0$$, the value of $$\log y$$ is

The particular solution of the differential equation $$\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x$$, such that $$y(\pi / 2)=0$$ is

The equation of a straight line which cuts off intercept on $$X$$-axis which is twice that on $$Y$$-axis and is at a unit distance from origin is given by

The general solution of the linear differential equation $$\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \frac{\pi}{2}\right)$$ is

The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents

The focal distance of the point $$(x, y)$$ from the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$$ is

Your friend ............. too much.

The eccentricity of the ellipse $$25 x^2+9 y^2-150 x-90 y+225=0$$ is

We bought ............. books.

According to equipartition law of energy each particle in a system of particles have thermal energy $$E$$ equal to

An electric charge does not have which of the following properties?

A hollow sphere of radius $$0.1 \mathrm{~m}$$ has a charge of $$5 \times 10^{-8} \mathrm{C}$$. The potential at a distance of 5 $$\mathrm{cm}$$ from the centre of the sphere is $$\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)$$

Select the antonym for the word 'Bane'.

Pick out the correct synonym of the word 'Treason'.