Aptitude
1. In the given series one number incorrect. Identify the incorrect number from among the options given.
$$3,5,7,6,10,14,12 2. Select the number that can replace the question mark (?) in the following series.
$$105,107,103, ?, 101,111$$ 3. If each of the letters of the English alphabet is assigned an odd numerical value beginning with $$\mathrm{A}=1, \mathrm 4. In a certain code language, GOURD is written as 21-4-5-10-24. How will BRINJAL be written in the same code language? 5. 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 6. Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even 7. If the imports of Company X in 2007 were increased by $$40 \%$$, what would be the ratio of exports to the increased imp 8. In 2005, the exports of Company $$\mathrm{X}$$ were doubled that of Company Y in that year. If the imports of Company $$ 9. Who amongst $$\mathrm{L}, \mathrm{M}, \mathrm{N}, \mathrm{O}$$ and $$\mathrm{P}$$ is the shortest?
I. O is shorter than 10. Point A is towards which direction from Point B?
I. If a person walks $$4 \mathrm{~m}$$ towards the North from Point $$\
Chemistry
1. Which of the following is false regarding shielding effect? 2. In which of the following photoelectric effect is observed? 3. An electron in H-atom in its ground state absorbs 1.50 times as much as energy as the minimum required for its escape $$ 4. If $$\mathrm{AgI}$$ crystallises in zinc blende structure with $$\mathrm{I}^{-}$$ ions at lattice points then the fracti 5. Which is largest in size in aqueous solution? 6. What will be the molarity of solution when $$30 \mathrm{~mL}$$ of $$0.5 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ is dil 7. Arrange the following in order of their electronegativity. 8. A colourless solid $$(X)$$ on heating evolved $$\mathrm{CO}_2$$ and also gave a white residue, soluble in water. Residue 9. Consider the following boron halides.
1. $$\mathrm{BF}_3$$
2. $$\mathrm{BCl}_3$$
3. $$\mathrm{BBr}_3$$
4. $$\mathrm{BI}_ 10. Which of the following defect lowers the density of a solid? 11. Which of the following option is correct regarding $$\mathrm{OF}$$ and $$\mathrm{F}_2$$ ? 12. Match the species given in column I with the shape given in column II and assign the correct code.
.tg {border-collaps 13. Among the given species the isostructural pairs is 14. The half-life period of a radioactive element '$$X$$' is same as the mean life time of another radioactive element '$$Y$ 15. Which of the following lanthanides are used in TV screens? 16. Which type of isomerism is exhibited by $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}$$? 17. Which of the following isotopes is used to treat cancer? 18. What is the degree of dissociation of $$0.05 \mathrm{~M~NH}_3$$ if its $$\mathrm{pK}{ }_a$$ is 4.75 and $$\mathrm{pH}$$ 19. 1 mole of $$\mathrm{CO}_2$$ gas at $$300 \mathrm{~K}$$ is expanded under adiabatic conditions such that its volume becom 20. The correct stability order of the following free radicals is 21. Choose the correct structure of picric acid. 22. Dehydration of methyl alcohol with conc. $$\mathrm{H}_2 \mathrm{SO}_4$$ yields 23. Which of the following will not give a primary amine? 24. Arrange the following compounds in decreasing order of their boiling points.
$$\mathrm{CH}_3 \mathrm{CHO}, \mathrm{CH}_3 25. $$0.20 \mathrm{~g}$$ of an organic compound gave $$0.12 \mathrm{~g}$$ of $$\mathrm{AgBr}$$. By using Carius method, the 26.
The catalyst 'X' can be 27. The following compound is used as
28. $$\mathrm{C}_6 \mathrm{H}_{12}(A)$$ has chirality but on hydrogenation '$$A$$' is converted into $$\mathrm{C}_6 \mathrm{ 29. 30. In a set of reactions $$m$$-bromobenzoic acid gave a product $$D$$. Identify the product $$D$$.
31. In the given reaction,
The product P is 32. Optical rotations of some compounds alongwith their structures are given below.
Point out the structures which have D-c 33. Which of the following is the structure of glutaric acid? 34. Match the following and choose the correct code.
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.tg td{border-color: 35. Consider the following statements.
A. Ocean is sink for $$\mathrm{CO}_2$$.
B. Green house effect causes lowering of temp
English
1. Mother loves you 2. 'Whatever makes you glad'. Here, 'glad' is 3. Fill in the blank with most suitable word. When we went there, we found that the lion _________. 4. Select the antonym for the word 'Chaotic'. 5. Pick out the correct synonym of the word 'Infatuation'.
Mathematics
1. If the real numbers $$x, y, z, t$$ be in GP then the value of $$(x^2+y^2+z^2)(y^2+z^2+t^2)$$ is euqal to 2. The value of $$\frac{4}{1 !}+\frac{11}{2 !}+\frac{22}{3 !}+\frac{37}{4 !}+\frac{56}{5 !}+\ldots \infty$$ is 3. There are 50 intermediate stations on a railway line from one terminus to another. The number of ways a train can stop a 4. If the 2nd, 3rd and 4th terms in the expansion of $$(a+b)^n$$ be $$240,720$$ and 1080 respectively, then the value of $$ 5. If $$0 6. The condition in order that $$Z_1, Z_2, Z_3$$ are vertices of an isosceles triangle right angled at $$z_2$$, is 7. If the tangent at point $$P$$ on the circle $$x^2+y^2+6 x+6 y-2=0$$ meets the straight line $$5 x-2 y+6=0$$ at a point $ 8. The image of the point $$(2,-3,4)$$ with respect to the plane $$4 x+2 y-4 z+3=0$$, is 9. If a variable plane cuts the coordinate axes in $$A, B, C$$ and is at constant distance $p$ from the origin, then the lo 10. If the tangent at $$P$$ on $$y^2=4 a x$$ meets the tangent at the vertex in $$Q$$ and $$S$$ is the focus of the parabola 11. For all values of $$\lambda$$, rank of matrix
$$A=\left[\begin{array}{ccc}
{ }^h C_0 & { }^4 C_3 & { }^5 C_4 \\
\lambda 12. The area between $$y=x^2$$ and $$y=8-x^2$$ 13. The roots of the equation $$\cos x+\sqrt{3} \sin x=2 \cos 2 x$$, are 14. A force of magnitude $$\sqrt{6}$$ acting along, the line joining points $$A(2,-1,1)$$ and $$B(3,1,2)$$ displaces a parti 15. The domain of
$$f(x)=\sqrt{\log \frac{1}{4}\left(\frac{5 x-x^2}{4}\right)}+{ }^{10} C_x$$ is 16. Through a fixed point $$P(\alpha, \beta), a$$, variable line is drawn to cut the coordinate axes at $$A$$ and $$B$$. The 17. If a man running around a race-course notes that the sum of the distances of two flag-posts from him is always $$10 \mat 18. If a circle of constant radius '$$r$$' passes through the origin and meets the coordinate axes at points $$A$$ and $$B$$ 19. A ray of light is sent along the line $$x-2 y+5=0$$. Upon reaching the line $$3 x-2 y+7=0$$, the ray is reflected from i 20. A unit vector perpendicular to both the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$\hat{\mathbf{j}}+\hat{\mathb 21. Find the solution of equation $$\frac{d y}{d x}=\frac{1}{\cos (x+y)}$$ 22. Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$ 23. 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 24. The value of
$$\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x}, 25. If $$f(x)=\left\{\begin{array}{cc}(\sin x+\cos x)^{\operatorname{cosec} x} & ,-\frac{\pi}{2} 26. The image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ is 27. The value of $$\lim _\limits{t \rightarrow \infty} \frac{\ln \left(\frac{3}{2} t\right)}{t^2}$$ 28. The value of $$f(x) = \mathop {\lim }\limits_{x \to 2} {{{x^3} - 3{x^2} + 4} \over {{x^4} - 7x - 2}}$$ 29. The solution of the equation $$\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1$$ is 30. If $$\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, where $$|x| 31. If $$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}{ 32. 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 33. The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is 34. $$\cos (x+y), \cos x, \cos (x-y)$$ are in HP, then $$\cos x \sec \frac{y}{2}$$ is 35. 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 36. Find the area enclosed by $$y=x^2$$ and $$y=x+2$$ 37. $$f$$ and $$g$$ are differentiable function in $$(0,1)$$ satisfying $$f(0)=2=g(\mathrm{l}), g(0)=0$$ and $$f(l)=6$$, the 38. 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 39. The integral $$\int \frac{d x}{x^2\left(x^4+1\right)^{3 / 4}}$$ equals 40. The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x$$ occurs at the point
Physics
1. A toy gun uses a spring of force constant $$k$$. When charged before being triggered in the upward direction, the spring 2. A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a 3. In which of the following photoelectric effect is not observed? 4. An electrically heated coil is immersed in a calorimeter containing $$360 \mathrm{~g}$$ of water at $$10^{\circ} \mathrm 5. A quantity $X$ is given by $$\frac{\varepsilon_0 A}{L} \frac{\Delta V}{\Delta t}$$, where $$\varepsilon_0$$ is the permi 6. A nuclide at rest emits an $\alpha$-particle. In this process 7. If 2 moles of an ideal monoatomic gas at temperature $$T_0$$ is mixed with 4 moles of another ideal monoatomic gas at te 8. The system is pushed by a force $$F$$ as shown in figure. All surfaces are smooth except between $$B$$ and $$C$$. Fricti 9. A parallel plate capacitor with plate area $$A$$ and separation between the plates $$d$$ is charged by a constant curren 10. A projectile is launched vertically from the earth with speed $$v_1$$ hits a satellite at the height $$h$$ moving with s 11. A cone filled with water is revolved in a vertical circle of radius $$4 \mathrm{~m}$$ and the water does not fall down. 12. Consider a rod of mass $$M$$ and length $$L$$ pivoted at its centre free to rotate in a vertical plane. The rod is at re 13. In a cathode ray tube, a potential difference of 3000 volts is maintained between the deflector plates whose separation 14. A wire of cross-section $$A$$ is stretched horizontally between two clamps located $$2 l$$ metre apart. A weight $$w \ma 15. A stream of electrons is projected horizontally to the right. A straight conductor carrying, a current is supported para 16. 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 17. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in inte 18. A coil of 100 turns and area $$2 \times 10^{-2} \mathrm{~m}^2$$ is pivoted about a vertical diameter in a uniform magnet 19. A man stands between two parallel cliffs (not in middle). When he claps his hands, he hears two echoes one after is and 20. Light of wavelength $$\lambda$$ strikes a photoelectric surface and electrons are ejected with kinetic energy $$K$$. If 21. When in $$p$$-$$n$$ junction diode, $$p$$ is connected to the positive terminal and $$n$$ is connected to the negative t 22. If an object of height $$6 \mathrm{~cm}$$ is viewed through a liquid of refractive index $$\frac{4}{3}$$ vertically at a 23. The half-life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$. 24. 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 25. A particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ under a centripetal force given by $$\left(-k 26. A plane glass mirror of thickness $$3 \mathrm{~cm}$$ of material of $$\mu=\frac{3}{2}$$ is silvered on the back surface. 27. A skylab or mass $$m \mathrm{~kg}$$ is first launched from the surface of the earth in a circular orbit of radius $$2 R$ 28. A train has to negotiate a curve of radius $$400 \mathrm{~m}$$. By how much should the outer rail be raised with respect 29. From Wien's displacement law, $$\lambda_m T=$$ constant $$=0.00289 \mathrm{~m}-\mathrm{K}$$
Radiation from moon givens $ 30. A disc of $$10.0 \mathrm{~cm}$$ diameter is rotated at speed of $$3600 \mathrm{~rpm}$$ inside a long solenoid of 1200 tu 31. If two metallic plates of equal thickness and thermal conductivities $$K_1$$ and $$K_2$$ are put together face to face a 32. Which of the following is arranged in forward bias? 33. A TV tower has a height of $$75 \mathrm{~m}$$. What is the maximum distance upto which this TV transmission can be recei 34. Which of the following is deflected by the magnetic field? 35. A particle of mass $$m$$ is allowed to fall freely under gravity from a point $$P$$ as shown in the figure. If the vecto
1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0
Find the solution of equation $$\frac{d y}{d x}=\frac{1}{\cos (x+y)}$$
A
$$\cot \left(\frac{x+y}{2}\right)+c$$
B
$$\sec \left(\frac{x+y}{2}\right)+c$$
C
$$\tan \left(\frac{x+y}{2}\right)+c$$
D
$$-\cot \left(\frac{x-y}{2}\right)+c$$
2
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0
Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$
A
$$-\cot \left(\frac{x+y}{2}\right)+c$$
B
$$\operatorname{cosec}^2\left(\frac{x+y}{2}\right)+c$$
C
$$\tan \left(\frac{x+y}{2}\right)+c$$
D
$$\cot \left(\frac{x-y}{2}\right)+c$$
3
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0
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
A
590
B
490
C
430
D
510
4
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0
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
A
$$(\text {pqrs})^3$$
B
$$(p q r s)^{3 / 2}$$
C
$$(\text {pqrs})^{3 / 4}$$
D
None of these
Paper analysis
Total Questions
Aptitude
10
Chemistry
35
English
5
Mathematics
40
Physics
35
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