VITEEE 2022

The system is pushed by a force $$F$$ as shown in figure. All surfaces are smooth except between $$B$$ and $$C$$. Friction coefficient between $$B$$ and $$C$$ is $$\mu$$. Minimum value of $$F$$ to prevent block $$B$$ from downward slipping is

A cone filled with water is revolved in a vertical circle of radius $$4 \mathrm{~m}$$ and the water does not fall down. What must be the maximum period of revolution?

A person is standing at some point between two parallel cliffs (not exactly at the centre). He claps, and hears two echoes: the first after $$1 \mathrm{~s}$$ and the second after $$2 \mathrm{~s}$$. If the speed of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$, the distance between the two cliffs is

A particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ under a centripetal force given by $$\left(-k / r^2\right)$$, where $$k$$ is a constant. Then

A wire of cross-section $$A$$ is stretched horizontally between two clamps located $$2 l$$ metre apart. A weight $$w \mathrm{~kg}$$ is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance $$x<1$$, the strain produced is

A train has to negotiate a curve of radius $$400 \mathrm{~m}$$. By how much should the outer rail be raised with respect to the inner rail for a speed of $$48 \mathrm{~km} / \mathrm{h}$$ ? The distance between the rails is $$1 \mathrm{~m}$$.

An electrically heated coil is immersed in a calorimeter containing $$360 \mathrm{~g}$$ of water at $$10^{\circ} \mathrm{C}$$. The coil consumes energy at the rate of $$90 \mathrm{~W}$$. The water equivalent of calorimeter and coil is $$40 \mathrm{~g}$$. The temperature of water after $$10 \mathrm{~min}$$ is

If $$\mathrm{AgI}$$ crystallises in zinc blende structure with $$\mathrm{I}^{-}$$ ions at lattice points then the fraction of tetrahedral voids occupied by $$\mathrm{Ag}^{+}$$ ions is

If an object of height $$6 \mathrm{~cm}$$ is viewed through a liquid of refractive index $$\frac{4}{3}$$ vertically at a depth of $$10 \mathrm{~cm}$$. Then what will be its apparent height and apparent distance from the surface of liquid.

What is the degree of dissociation of $$0.05 \mathrm{~M~NH}_3$$ if its $$\mathrm{pK}{ }_a$$ is 4.75 and $$\mathrm{pH}$$ is 11 ?

$$0.20 \mathrm{~g}$$ of an organic compound gave $$0.12 \mathrm{~g}$$ of $$\mathrm{AgBr}$$. By using Carius method, the percentage of bromine in the compound will be

A plane glass mirror of thickness $$3 \mathrm{~cm}$$ of material of $$\mu=\frac{3}{2}$$ is silvered on the back surface. When a point object is placed $$9 \mathrm{~cm}$$ from the front surface of the mirror, then the position of the brightest image from the front surface is

If two metallic plates of equal thickness and thermal conductivities $$K_1$$ and $$K_2$$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

A quantity $X$ is given by $$\frac{\varepsilon_0 A}{L} \frac{\Delta V}{\Delta t}$$, where $$\varepsilon_0$$ is the permittivity of free space, $$L$$ is the length, $$A$$ is area, $$\Delta V$$ is the potential difference and $$\Delta t$$ is time interval. The dimensional formula for $$X$$ is the same as that of

Consider the following boron halides.

1. $$\mathrm{BF}_3$$

2. $$\mathrm{BCl}_3$$

3. $$\mathrm{BBr}_3$$

4. $$\mathrm{BI}_3$$

The Lewis acid characters of these halides are in the order of

The value of $$\lim _\limits{t \rightarrow \infty} \frac{\ln \left(\frac{3}{2} t\right)}{t^2}$$

A colourless solid $$(X)$$ on heating evolved $$\mathrm{CO}_2$$ and also gave a white residue, soluble in water. Residue also gave $$\mathrm{CO}_2$$ when treated with dilute acid. $$(X)$$ is

The value of $$f(x) = \mathop {\lim }\limits_{x \to 2} {{{x^3} - 3{x^2} + 4} \over {{x^4} - 7x - 2}}$$

A particle of mass $$m$$ is allowed to fall freely under gravity from a point $$P$$ as shown in the figure. If the vector position $$Q$$ of the particle from the origin is represented by $$\mathbf{r}$$, the magnitude of torque acting on the particle at time $$t$$ with respect to the origin $$O$$ is.

A projectile is launched vertically from the earth with speed $$v_1$$ hits a satellite at the height $$h$$ moving with speed $$v_2$$. If both have the same mass $$m$$, then what is the common velocity if they move together after the collision?

Consider a rod of mass $$M$$ and length $$L$$ pivoted at its centre free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass $$M$$ moving horizontal at a speed $$v$$ strikes and gets embedded in one end of the rod. The angular velocity of the rod just after the collision will be

One end of a spring of force constant $$k$$ is fixed to a vertical wall and other to a body of mass $$m$$ resting on a smooth horizontal surface. There is another wall at a distance $$x_0$$ from the body. The spring is then compressed by $$2 x_0$$ and released. The time taken to stike the wall is

A toy gun uses a spring of force constant $$k$$. When charged before being triggered in the upward direction, the spring is compressed by a distance $$x$$. If the mass of the shot is $$m$$, on being triggered it will go upto a height of

A skylab or mass $$m \mathrm{~kg}$$ is first launched from the surface of the earth in a circular orbit of radius $$2 R$$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $$3 R$$. The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of the given mass of gas, when the volume changes from $$V$$ to $$2 V$$ at constant pressure $$p$$ is

A parallel plate capacitor with plate area $$A$$ and separation between the plates $$d$$ is charged by a constant current $$i$$. Consider a plane surface of area $$A / 2$$ parallel to the plates and drawn simultaneously between the plates. The displacement current through this area is

If 2 moles of an ideal monoatomic gas at temperature $$T_0$$ is mixed with 4 moles of another ideal monoatomic gas at temperature $$2 T_0$$, then the temperature of the mixture is

From Wien's displacement law, $$\lambda_m T=$$ constant $$=0.00289 \mathrm{~m}-\mathrm{K}$$

Radiation from moon givens $$\lambda_m=4700 \mathop A\limits^o$$ and another wavelength of $$14 \times 10^{-6} \mathrm{~m}$$. Out of the following which conclusion(s) drawn is/are correct with the given information regarding the moon and the sun?

1. Sun radiations are reflected from moon's disc.

2. The temperature of moon's surface is $$207 \mathrm{~K}$$

3. The temperature of the sun is $$6160 \mathrm{~K}$$.

A stream of electrons is projected horizontally to the right. A straight conductor carrying, a current is supported parallel to the electron stream and above it. If the current in the conductor is from left to right, what will be the effect on the electron stream?

A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a) and then in Fig.(b). Then ratio of the capacitor in the two arrangements is

A coil of 100 turns and area $$2 \times 10^{-2} \mathrm{~m}^2$$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of $$5 \mathrm{~A}$$. When the coil is held with its plane in North-South direction, it experiences a couple of $$0.33 \mathrm{~N}-\mathrm{m}$$. When the plane is East-West, the corresponding couple is $$0.4 \mathrm{~N}-\mathrm{m}$$. The value of magnetic induction is [Neglect earth's magnetic field]

Which of the following is deflected by the magnetic field?

In a cathode ray tube, a potential difference of 3000 volts is maintained between the deflector plates whose separation is $$2 \mathrm{~cm}$$. A magnetic field of $$2.5 \times 10^{-3} \mathrm{~Wb} / \mathrm{m}^2$$ at right angles to electric field gives no deflection of the electron beam, which received an initial acceleration by a potential difference of $$10000 \mathrm{~V}$$. Calculate $$(\mathrm{e} / \mathrm{m})$$ of an electron.

A bar magnet suspended by a horse's hair lies in the magnetic meridian where there is no twist in the hair, on turning the upper end of the hair through $$150^{\circ}$$, the magnet is deflected through $$30^{\circ}$$ from the meridian. Then the angle through which upper end of the hair has to be twisted to deflect the magnet through $$90^{\circ}$$ from the meridian is

The half-life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$. Initially, both of them have the same number of atoms. Then,

A disc of $$10.0 \mathrm{~cm}$$ diameter is rotated at speed of $$3600 \mathrm{~rpm}$$ inside a long solenoid of 1200 turns per metre on the axis of the solenoid and perpendicular to the plane of the disc. When a current of $$1.5 \mathrm{~A}$$ is passed through the solenoid, the difference in the potential between axes and circumference of the disc is nearly

In which of the following photoelectric effect is not observed?

Light of wavelength $$\lambda$$ strikes a photoelectric surface and electrons are ejected with kinetic energy $$K$$. If $$K$$ is to be increased to exactly twice its original value, the wavelength must be changed to $$\lambda^{\prime}$$, such that

When in $$p$$-$$n$$ junction diode, $$p$$ is connected to the positive terminal and $$n$$ is connected to the negative terminal, then it is

A nuclide at rest emits an $\alpha$-particle. In this process

Which of the following is arranged in forward bias?

A TV tower has a height of $$75 \mathrm{~m}$$. What is the maximum distance upto which this TV transmission can be received? (Take, radius of the earth $$=6.4 \times 10^6 \mathrm{~m}$$)

An electron in H-atom in its ground state absorbs 1.50 times as much as energy as the minimum required for its escape $$(13.6 \mathrm{~eV})$$ from the atom. Thus, KE given to emitted electron is

Which of the following defect lowers the density of a solid?

In which of the following photoelectric effect is observed?

The half-life period of a radioactive element '$$X$$' is same as the mean life time of another radioactive element '$$Y$$'. Initially, both of them have the same number of atoms, then

Which of the following isotopes is used to treat cancer?

1 mole of $$\mathrm{CO}_2$$ gas at $$300 \mathrm{~K}$$ is expanded under adiabatic conditions such that its volume becomes 27 times. What is work done?

Which is largest in size in aqueous solution?

Match the species given in column I with the shape given in column II and assign the correct code.

Which of the following option is correct regarding $$\mathrm{OF}$$ and $$\mathrm{F}_2$$ ?

Which of the following is false regarding shielding effect?

Among the given species the isostructural pairs is

Which of the following lanthanides are used in TV screens?

$$\mathrm{C}_6 \mathrm{H}_{12}(A)$$ has chirality but on hydrogenation '$$A$$' is converted into $$\mathrm{C}_6 \mathrm{H}_{14}(B)$$ in which chirality disappears. Hence '$$A$$' is

Which type of isomerism is exhibited by $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}$$?

The correct stability order of the following free radicals is

Consider the following statements.

A. Ocean is sink for $$\mathrm{CO}_2$$.

B. Green house effect causes lowering of temperature of earth's surface.

C. To control $$\mathrm{CO}$$ emission by automobiles, usually catalytic convertor are fitted into exhaust pipes.

D. $$\mathrm{H}_2 \mathrm{SO}_4$$, herbicides and insecticides form mist.

Choose the correct statements and mark the option accordingly.

Arrange the following in order of their electronegativity.

Optical rotations of some compounds alongwith their structures are given below.

Point out the structures which have D-configuration.

Dehydration of methyl alcohol with conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ yields

In a set of reactions $$m$$-bromobenzoic acid gave a product $$D$$. Identify the product $$D$$.

Choose the correct structure of picric acid.

In the given reaction,

The product P is

The catalyst 'X' can be

Arrange the following compounds in decreasing order of their boiling points.

$$\mathrm{CH}_3 \mathrm{CHO}, \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}, \mathrm{CH}_3 \mathrm{OCH}_3, \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_3$$

Which of the following will not give a primary amine?

The following compound is used as

Which of the following is the structure of glutaric acid?

Match the following and choose the correct code.

	List I		List II
A.		(i)	Veronal
B.		(i)	Chloroxylenol
C.		(iii)	Dulcin
D.		(iv)	Histamine

If the real numbers $$x, y, z, t$$ be in GP then the value of $$(x^2+y^2+z^2)(y^2+z^2+t^2)$$ is euqal to

The value of $$\frac{4}{1 !}+\frac{11}{2 !}+\frac{22}{3 !}+\frac{37}{4 !}+\frac{56}{5 !}+\ldots \infty$$ is

If the 2nd, 3rd and 4th terms in the expansion of $$(a+b)^n$$ be $$240,720$$ and 1080 respectively, then the value of $$(n, b, a)$$ is

A unit vector perpendicular to both the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ is

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is

There are 50 intermediate stations on a railway line from one terminus to another. The number of ways a train can stop at 3 of these intermediate stations if no two of these stopping stations are to be consecutive, are

Two dices are rolled. If both dices have six faces numbered $$1,2,3,5,7$$ and $$11$$ then the probability that the sum of the number on the top faces is less than or equal to 8 is

The image of the point $$(2,-3,4)$$ with respect to the plane $$4 x+2 y-4 z+3=0$$, is

If a variable plane cuts the coordinate axes in $$A, B, C$$ and is at constant distance $p$ from the origin, then the locus of the centroid of the tetrahedron $$A B C$$ is equal to

$$\cos (x+y), \cos x, \cos (x-y)$$ are in HP, then $$\cos x \sec \frac{y}{2}$$ is

If $$0< a<5,0< b<5$$ and $$\frac{x^2+5}{2}=x-2[\cos (a+b x)]$$ is satisfied for atleast one real $$x$$, then the least value of $$\frac{a+b}{\pi}$$ is equal to

A force of magnitude $$\sqrt{6}$$ acting along, the line joining points $$A(2,-1,1)$$ and $$B(3,1,2)$$ displaces a particle from $$A$$ to $$B$$. The work done by the force is

The condition in order that $$Z_1, Z_2, Z_3$$ are vertices of an isosceles triangle right angled at $$z_2$$, is

For all values of $$\lambda$$, rank of matrix

$$A=\left[\begin{array}{ccc} { }^h C_0 & { }^4 C_3 & { }^5 C_4 \\ \lambda & 8 & 8 \lambda-6 \\ 1+\lambda^2 & 8 \lambda+4 & 2 \lambda+21 \end{array}\right]$$

The roots of the equation $$\cos x+\sqrt{3} \sin x=2 \cos 2 x$$, are

If $$f(x)=\left\{\begin{array}{cc}(\sin x+\cos x)^{\operatorname{cosec} x} & ,-\frac{\pi}{2}< x<0 \\ a & ,x=0 \\ \frac{e^{1 / x}+e^{2 / x}+e^{3 / x}}{a e^{-2+\frac{1}{x}}+b e^{-1+\frac{3}{x}}} & , 0< x<\frac{\pi}{2}\end{array}\right.$$ is continuous at $$x=0$$, then the value of $$(b, a)$$ is

The domain of $$f(x)=\sqrt{\log \frac{1}{4}\left(\frac{5 x-x^2}{4}\right)}+{ }^{10} C_x$$ is

If $$\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, where $$|x|< \frac{1}{\sqrt{3}}$$ then value of $$y$$ is

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha$$ where $$-1 \leq x \leq 1, -2 \leq y \leq 2, x \leq \frac{y}{2}$$, then for all $$x, y, 4 x^2-4 x y \cos \alpha+y^2$$ is equal to

The value of $$\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x}, p, q, r, s>0 \text {, }$$ is

The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x$$ occurs at the point

$$f$$ and $$g$$ are differentiable function in $$(0,1)$$ satisfying $$f(0)=2=g(\mathrm{l}), g(0)=0$$ and $$f(l)=6$$, then for some $$c \in] 0,1[$$

If $$X \phi(x)=\int_\limits5^x 3 t^2-2 \phi(t) d t, x>-2$$ and $$\phi(0)=4$$, then $$\phi(2)$$ is

The integral $$\int \frac{d x}{x^2\left(x^4+1\right)^{3 / 4}}$$ equals

The area between $$y=x^2$$ and $$y=8-x^2$$

Find the area enclosed by $$y=x^2$$ and $$y=x+2$$

Find the solution of equation $$\frac{d y}{d x}=\frac{1}{\cos (x+y)}$$

The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is

A ray of light is sent along the line $$x-2 y+5=0$$. Upon reaching the line $$3 x-2 y+7=0$$, the ray is reflected from it. The equation of the line containing the reflected ray, is

The solution of the equation $$\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1$$ is

If $$p$$ and $$q$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+4 \frac{\left(\frac{d^2 y}{d x^2}\right)^2}{\left(\frac{d^3 y}{d x^3}\right)^3}+\frac{d^3 y}{d x^3}=x^2-1$$, then

Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$

If a circle of constant radius '$$r$$' passes through the origin and meets the coordinate axes at points $$A$$ and $$B$$ respectively, then the locus of the centroid of triangle $$O A B$$, '$$O$$' being the origin, is

If a man running around a race-course notes that the sum of the distances of two flag-posts from him is always $$10 \mathrm{~m}$$ and the distance between the flag-posts is $$8 \mathrm{~m}$$, then the area of the path he encloses in square metres is

If the tangent at point $$P$$ on the circle $$x^2+y^2+6 x+6 y-2=0$$ meets the straight line $$5 x-2 y+6=0$$ at a point $$Q$$ on $$Y$$-axis, the length of $$P Q$$ is

If the tangent at $$P$$ on $$y^2=4 a x$$ meets the tangent at the vertex in $$Q$$ and $$S$$ is the focus of the parabola, then $$\angle S Q P$$ is equal to

Who amongst $$\mathrm{L}, \mathrm{M}, \mathrm{N}, \mathrm{O}$$ and $$\mathrm{P}$$ is the shortest?

I. O is shorter than P, but taller than N.

II. M is not as tall as L.

Through a fixed point $$P(\alpha, \beta), a$$, variable line is drawn to cut the coordinate axes at $$A$$ and $$B$$. The locus of the mid-point of $$A B$$ is

In 2005, the exports of Company $$\mathrm{X}$$ were doubled that of Company Y in that year. If the imports of Company $$\mathrm{X}$$ during the year were ₹ ~180 crore, what was the amount (in ₹ crore) of imports of Company Y during the year?

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements

1. Some chimpanzees are tigers.

2. All tigers are elephants.

Conclusions

I. Some elephants are tigers.

II. Some elephants are chimpanzees.

If the imports of Company X in 2007 were increased by $$40 \%$$, what would be the ratio of exports to the increased imports?

In a certain code language, GOURD is written as 21-4-5-10-24. How will BRINJAL be written in the same code language?

In the given series one number incorrect. Identify the incorrect number from among the options given.

$$3,5,7,6,10,14,12,24,28,24,40,56$$

Select the number that can replace the question mark (?) in the following series.

$$105,107,103, ?, 101,111$$

'Whatever makes you glad'. Here, 'glad' is

If each of the letters of the English alphabet is assigned an odd numerical value beginning with $$\mathrm{A}=1, \mathrm{~B}=3$$ and so on, what will be the total value of the letters of the word RADICAL?

Select the antonym for the word 'Chaotic'.

Mother loves you

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

What will be the molarity of solution when $$30 \mathrm{~mL}$$ of $$0.5 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ is diluted to $$500 \mathrm{~mL}$$ ?

The image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ is

Fill in the blank with most suitable word. When we went there, we found that the lion _________.

Point A is towards which direction from Point B?

I. If a person walks $$4 \mathrm{~m}$$ towards the North from Point $$\mathrm{A}$$ and takes two consecutive right turns, each after walking $$4 \mathrm{~m}$$, he would reach Point C, which is $$8 \mathrm{~m}$$ away from Point B.

II. Point $$\mathrm{D}$$ is $$2 \mathrm{~m}$$ towards the East of point A and $$4 \mathrm{~m}$$ towards the West of point B.