VITEEE 2022
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Aptitude

In the given series one number incorrect. Identify the incorrect number from among the options given. $$3,5,7,6,10,14,12
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Select the number that can replace the question mark (?) in the following series. $$105,107,103, ?, 101,111$$
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If each of the letters of the English alphabet is assigned an odd numerical value beginning with $$\mathrm{A}=1, \mathrm
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In a certain code language, GOURD is written as 21-4-5-10-24. How will BRINJAL be written in the same code language?
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A person stands at point A and needs to reach point D by the shortest path possible. Points A and D are on opposite ends
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Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even
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If the imports of Company X in 2007 were increased by $$40 \%$$, what would be the ratio of exports to the increased imp
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In 2005, the exports of Company $$\mathrm{X}$$ were doubled that of Company Y in that year. If the imports of Company $$
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Who amongst $$\mathrm{L}, \mathrm{M}, \mathrm{N}, \mathrm{O}$$ and $$\mathrm{P}$$ is the shortest? I. O is shorter than
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Point A is towards which direction from Point B? I. If a person walks $$4 \mathrm{~m}$$ towards the North from Point $$\
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Chemistry

Which of the following is false regarding shielding effect?
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In which of the following photoelectric effect is observed?
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An electron in H-atom in its ground state absorbs 1.50 times as much as energy as the minimum required for its escape $$
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If $$\mathrm{AgI}$$ crystallises in zinc blende structure with $$\mathrm{I}^{-}$$ ions at lattice points then the fracti
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Which is largest in size in aqueous solution?
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What will be the molarity of solution when $$30 \mathrm{~mL}$$ of $$0.5 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ is dil
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Arrange the following in order of their electronegativity.
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A colourless solid $$(X)$$ on heating evolved $$\mathrm{CO}_2$$ and also gave a white residue, soluble in water. Residue
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Consider the following boron halides. 1. $$\mathrm{BF}_3$$ 2. $$\mathrm{BCl}_3$$ 3. $$\mathrm{BBr}_3$$ 4. $$\mathrm{BI}_
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Which of the following defect lowers the density of a solid?
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Which of the following option is correct regarding $$\mathrm{OF}$$ and $$\mathrm{F}_2$$ ?
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Match the species given in column I with the shape given in column II and assign the correct code. .tg {border-collaps
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Among the given species the isostructural pairs is
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The half-life period of a radioactive element '$$X$$' is same as the mean life time of another radioactive element '$$Y$
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Which of the following lanthanides are used in TV screens?
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Which type of isomerism is exhibited by $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}$$?
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Which of the following isotopes is used to treat cancer?
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What is the degree of dissociation of $$0.05 \mathrm{~M~NH}_3$$ if its $$\mathrm{pK}{ }_a$$ is 4.75 and $$\mathrm{pH}$$
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1 mole of $$\mathrm{CO}_2$$ gas at $$300 \mathrm{~K}$$ is expanded under adiabatic conditions such that its volume becom
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The correct stability order of the following free radicals is
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Choose the correct structure of picric acid.
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Dehydration of methyl alcohol with conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ yields
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Which of the following will not give a primary amine?
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Arrange the following compounds in decreasing order of their boiling points. $$\mathrm{CH}_3 \mathrm{CHO}, \mathrm{CH}_3
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$$0.20 \mathrm{~g}$$ of an organic compound gave $$0.12 \mathrm{~g}$$ of $$\mathrm{AgBr}$$. By using Carius method, the
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The catalyst 'X' can be
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The following compound is used as
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$$\mathrm{C}_6 \mathrm{H}_{12}(A)$$ has chirality but on hydrogenation '$$A$$' is converted into $$\mathrm{C}_6 \mathrm{
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In a set of reactions $$m$$-bromobenzoic acid gave a product $$D$$. Identify the product $$D$$.
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In the given reaction, The product P is
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Optical rotations of some compounds alongwith their structures are given below. Point out the structures which have D-c
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Which of the following is the structure of glutaric acid?
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Match the following and choose the correct code. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:
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Consider the following statements. A. Ocean is sink for $$\mathrm{CO}_2$$. B. Green house effect causes lowering of temp
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English

Mother loves you
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'Whatever makes you glad'. Here, 'glad' is
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Fill in the blank with most suitable word. When we went there, we found that the lion _________.
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Select the antonym for the word 'Chaotic'.
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Pick out the correct synonym of the word 'Infatuation'.
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Mathematics

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
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The value of $$\frac{4}{1 !}+\frac{11}{2 !}+\frac{22}{3 !}+\frac{37}{4 !}+\frac{56}{5 !}+\ldots \infty$$ is
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There are 50 intermediate stations on a railway line from one terminus to another. The number of ways a train can stop a
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If the 2nd, 3rd and 4th terms in the expansion of $$(a+b)^n$$ be $$240,720$$ and 1080 respectively, then the value of $$
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The condition in order that $$Z_1, Z_2, Z_3$$ are vertices of an isosceles triangle right angled at $$z_2$$, is
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If the tangent at point $$P$$ on the circle $$x^2+y^2+6 x+6 y-2=0$$ meets the straight line $$5 x-2 y+6=0$$ at a point $
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The image of the point $$(2,-3,4)$$ with respect to the plane $$4 x+2 y-4 z+3=0$$, is
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If a variable plane cuts the coordinate axes in $$A, B, C$$ and is at constant distance $p$ from the origin, then the lo
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If the tangent at $$P$$ on $$y^2=4 a x$$ meets the tangent at the vertex in $$Q$$ and $$S$$ is the focus of the parabola
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For all values of $$\lambda$$, rank of matrix $$A=\left[\begin{array}{ccc} { }^h C_0 & { }^4 C_3 & { }^5 C_4 \\ \lambda
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The area between $$y=x^2$$ and $$y=8-x^2$$
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The roots of the equation $$\cos x+\sqrt{3} \sin x=2 \cos 2 x$$, are
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A force of magnitude $$\sqrt{6}$$ acting along, the line joining points $$A(2,-1,1)$$ and $$B(3,1,2)$$ displaces a parti
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The domain of $$f(x)=\sqrt{\log \frac{1}{4}\left(\frac{5 x-x^2}{4}\right)}+{ }^{10} C_x$$ is
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Through a fixed point $$P(\alpha, \beta), a$$, variable line is drawn to cut the coordinate axes at $$A$$ and $$B$$. The
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If a man running around a race-course notes that the sum of the distances of two flag-posts from him is always $$10 \mat
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If a circle of constant radius '$$r$$' passes through the origin and meets the coordinate axes at points $$A$$ and $$B$$
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A ray of light is sent along the line $$x-2 y+5=0$$. Upon reaching the line $$3 x-2 y+7=0$$, the ray is reflected from i
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A unit vector perpendicular to both the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$\hat{\mathbf{j}}+\hat{\mathb
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Find the solution of equation $$\frac{d y}{d x}=\frac{1}{\cos (x+y)}$$
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Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$
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An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be dr
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The value of $$\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x},
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If $$f(x)=\left\{\begin{array}{cc}(\sin x+\cos x)^{\operatorname{cosec} x} & ,-\frac{\pi}{2}
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The image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ is
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The value of $$\lim _\limits{t \rightarrow \infty} \frac{\ln \left(\frac{3}{2} t\right)}{t^2}$$
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The value of $$f(x) = \mathop {\lim }\limits_{x \to 2} {{{x^3} - 3{x^2} + 4} \over {{x^4} - 7x - 2}}$$
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The solution of the equation $$\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1$$ is
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If $$\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, where $$|x|
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If $$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}{
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Two dices are rolled. If both dices have six faces numbered $$1,2,3,5,7$$ and $$11$$ then the probability that the sum o
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The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is
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$$\cos (x+y), \cos x, \cos (x-y)$$ are in HP, then $$\cos x \sec \frac{y}{2}$$ is
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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
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Find the area enclosed by $$y=x^2$$ and $$y=x+2$$
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$$f$$ and $$g$$ are differentiable function in $$(0,1)$$ satisfying $$f(0)=2=g(\mathrm{l}), g(0)=0$$ and $$f(l)=6$$, the
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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
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The integral $$\int \frac{d x}{x^2\left(x^4+1\right)^{3 / 4}}$$ equals
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The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x$$ occurs at the point
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Physics

A toy gun uses a spring of force constant $$k$$. When charged before being triggered in the upward direction, the spring
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A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a
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In which of the following photoelectric effect is not observed?
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An electrically heated coil is immersed in a calorimeter containing $$360 \mathrm{~g}$$ of water at $$10^{\circ} \mathrm
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A quantity $X$ is given by $$\frac{\varepsilon_0 A}{L} \frac{\Delta V}{\Delta t}$$, where $$\varepsilon_0$$ is the permi
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A nuclide at rest emits an $\alpha$-particle. In this process
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If 2 moles of an ideal monoatomic gas at temperature $$T_0$$ is mixed with 4 moles of another ideal monoatomic gas at te
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The system is pushed by a force $$F$$ as shown in figure. All surfaces are smooth except between $$B$$ and $$C$$. Fricti
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A parallel plate capacitor with plate area $$A$$ and separation between the plates $$d$$ is charged by a constant curren
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A projectile is launched vertically from the earth with speed $$v_1$$ hits a satellite at the height $$h$$ moving with s
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A cone filled with water is revolved in a vertical circle of radius $$4 \mathrm{~m}$$ and the water does not fall down.
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Consider a rod of mass $$M$$ and length $$L$$ pivoted at its centre free to rotate in a vertical plane. The rod is at re
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In a cathode ray tube, a potential difference of 3000 volts is maintained between the deflector plates whose separation
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A wire of cross-section $$A$$ is stretched horizontally between two clamps located $$2 l$$ metre apart. A weight $$w \ma
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A stream of electrons is projected horizontally to the right. A straight conductor carrying, a current is supported para
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A bar magnet suspended by a horse's hair lies in the magnetic meridian where there is no twist in the hair, on turning t
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If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in inte
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A coil of 100 turns and area $$2 \times 10^{-2} \mathrm{~m}^2$$ is pivoted about a vertical diameter in a uniform magnet
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A man stands between two parallel cliffs (not in middle). When he claps his hands, he hears two echoes one after is and
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Light of wavelength $$\lambda$$ strikes a photoelectric surface and electrons are ejected with kinetic energy $$K$$. If
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When in $$p$$-$$n$$ junction diode, $$p$$ is connected to the positive terminal and $$n$$ is connected to the negative t
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If an object of height $$6 \mathrm{~cm}$$ is viewed through a liquid of refractive index $$\frac{4}{3}$$ vertically at a
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The half-life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$.
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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 s
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A particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ under a centripetal force given by $$\left(-k
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A plane glass mirror of thickness $$3 \mathrm{~cm}$$ of material of $$\mu=\frac{3}{2}$$ is silvered on the back surface.
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A skylab or mass $$m \mathrm{~kg}$$ is first launched from the surface of the earth in a circular orbit of radius $$2 R$
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A train has to negotiate a curve of radius $$400 \mathrm{~m}$$. By how much should the outer rail be raised with respect
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From Wien's displacement law, $$\lambda_m T=$$ constant $$=0.00289 \mathrm{~m}-\mathrm{K}$$ Radiation from moon givens $
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A disc of $$10.0 \mathrm{~cm}$$ diameter is rotated at speed of $$3600 \mathrm{~rpm}$$ inside a long solenoid of 1200 tu
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If two metallic plates of equal thickness and thermal conductivities $$K_1$$ and $$K_2$$ are put together face to face a
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Which of the following is arranged in forward bias?
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A TV tower has a height of $$75 \mathrm{~m}$$. What is the maximum distance upto which this TV transmission can be recei
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Which of the following is deflected by the magnetic field?
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A particle of mass $$m$$ is allowed to fall freely under gravity from a point $$P$$ as shown in the figure. If the vecto
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