Aptitude
1. Four letter-clusters have been given, out of which three are alike in same manner and one is different. Select the lette 2. Select the number from among the given options that can replace the question mark (?) in the following series.
$$38,77,2 3. In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written as in that language? 4. From the given options, choose the correct one that will replace the question mark (?) in the following series.
ZBO, YEJ 5. In a certain code language, 'HONEY' is coded as ' $65^{\prime}$ ' and 'MONEY' is coded as ' $70^{\prime}$ '. How will 'S 6. What is the ratio of total sale of branch $B_2$ for both year to the total sale of branch $B_4$ for both year? 7. What is the average sales of all the branches (in thousand numbers) for the year of 2010? 8. Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even 9. Select the letter that is related to the third letter in the same way as the second letter is related to the first lette 10. The questions given below consist of a question followed by two statements labelled as I and II. We have to decide wheth
Chemistry
1. For the given redox reaction, what will be the sum of $x, y, m$ and $n$ ?
$$\begin{aligned}
x \mathrm{MnO}_4^{-}+y \math 2. The bond dissociation energies for $\mathrm{Cl}_2, \mathrm{I}_2$ and ICl are $242.3,151.0$ and $211.3 \mathrm{~kJ} / \ma 3. The boiling points of 0.01 M aqueous solution of sucrose, NaCl and $\mathrm{CaCl}_2$ would be 4. Which of the following species has highest nucleophilicity? 5. Which of the following cannot be made by using Williamson synthesis? 6. Among the following, the molecules /ions having same bond order are 7. Arrange in decreasing order, the energy of $2 s$ orbital in the following atoms $\mathrm{H}, \mathrm{Li}, \mathrm{Na}$ a 8. Identify the product $C$ in the following given reaction?
$$\mathrm{C}_2 \mathrm{H}_5 \mathrm{I} \xrightarrow{\mathrm{KO 9. The osmotic pressure of solution prepared by dissolving 25 mg of $\mathrm{K}_2 \mathrm{SO}_4$ in 2 litre of water at $25 10. Which of the following compounds on reaction with $\mathrm{CH}_3 \mathrm{MgBr}$ will give a tertiary alcohol? 11. Match List I with List II.
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.tg td{border-color:black;border-style:sol 12. The density of 3 M solution of NaCl is $1.25 \mathrm{~g} / \mathrm{mL}$. What is the molality of solution? 13. Which of the following compounds does not react with sodium bisulphate? 14. Which of the following has maximum dipole moment? 15. The number of radial nodes in 3s and 2p respectiely are 16. The activation energy for a reaction is $9.0 \mathrm{~K} \mathrm{cal} \mathrm{mol}^{-1}$. The increase in the rate const 17. 4.5 g of aluminium (Atomic mass 27 amu ) is deposited at cathode from $\mathrm{Al}^{3+}$ solution by a certain quantity 18. When diluted $\mathrm{H}_2 \mathrm{SO}_4$ is added to aqueous solution of potassium chromate, yellow colour solution tur 19. How long should water be electrolysed by passing through 100 amperes current so that oxygen released can completely burn 20. Match List I with List II.
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.tg td{border-color:black;border-style:sol 21. How many moles of potassium dichromate oxidises 1 mole of ferrous oxalate in acidic medium? 22. Among the following complexes, the one that can exist as facial ( fac ) and meridional (mer) isomers is 23. Electrophilic substitution of compound $X$ will be fastest at which position
24. In the given reaction, the final product B will be
25. Which of the following complex ions is expected to absorb visible light? 26. A 0.02 M solution of pyridinium hydrochloride has $\mathrm{pH}=3.44$. The ionisation constant of pyridine is 27. Which of the following oxide is diamagnetic? 28. In the following reaction the final product M will be
29. Which of the following order in respect to ionisation energy is correct? 30. Using the Gibbs free energy change, $\Delta G^{\circ}=+63.3 \mathrm{~kJ}$. For the reaction,
$$\mathrm{Ag}_2 \mathrm{CO} 31. Which of the following is not a fat soluble vitamin? 32. $A(g) \longrightarrow B(g)$ is a first order reaction. The initial concentration of $A$ is $0.2 \mathrm{~mol} \mathrm{~L 33. Methyl acetate and ethyl acetate can be distinguished by 34. Which of the following pairs form the same osazone? 35. Ozone is determined quantitatively by first reacting it with excess of KI at a particular pH and then titrating the $\ma
English
1. Fill in the blank with the most suitable choice.
I ................ the job if you had paid me enough. 2. Pick out the correct synonym of the word 'Solitude'. 3. Select the antonym of the word 'Gregarious'.
4. The narrator call a person dull if he/she 5. The city of London appear as if it is............
Mathematics
1. If 6 letter words, with or without meaning can be formed out of these letters of the word "MATHEMATICS", repetition of l 2. If the coefficient of $x^2$ and $x^3$ in the expansion of $\left(1+8 x+b x^2\right)(1-3 x)^9$ in the power of $x$ are eq 3. If the unit vectors $\mathbf{a}$ and $\mathbf{b}$ are inclined at $2 \theta$ and $|\mathbf{a}-\mathbf{b}| 4. If the coefficients of $x^7$ and $x^8$ in the expansion of $\left[2+\frac{x}{3}\right]^n$ are equal, then value of $n$ i 5. In a triangle $A B C$ as shown in the diagram, where $A B=5, A C=10$ and $B D=1$, then perimeter of $\triangle A B C$ is 6. Given, $\frac{x^2+y^2}{x^2-y^2}+\frac{x^2-y^2}{x^2+y^2}=k$, then $\frac{x^8+y^8}{x^8-y^8}$ is equal to 7. $\log \left(\log _{a b} a+\frac{1}{\log _b a b}\right)$ is $($ where $a b \neq 1)$ 8. If two different circles $x^2+y^2+2 a x+2 b y+1$ $=0$ and $x^2+y^2+2 b x+2 a y+1=0$ touches each other, then $(a+b)^2$ i 9. 6 couples decided to form a committee of four members, the number of different committees that can be formed in which no 10. The sum of the series $1 \cdot 2^2+2 \cdot 4^2+3 \cdot 6^2+\ldots$ upto 10 terms is 11. If the tangent at the point $P$ on the circle $x^2+y^2+2 x+2 y=7$ meets the straight line $3 x-4 y=15$ at the point $Q$ 12. Coefficient of $x^3$ in the expansion of $\left(x^2-x+1\right)^{10}\left(x^2+1\right)^{15}$ is equal to 13. Consider the ellipse $\frac{x^2}{\cos ^2 \alpha}+\frac{y^2}{\sin ^2 \alpha}=1$, where $\alpha \in\left(0, \frac{\pi}{4}\ 14. If $A, B$ are two square matrices, such that $A B=A, B A=B$, then $(A+B)^7$ equals 15. $$
\int_0^\pi\left[\cos ^2\left(\frac{3 \pi}{8}-\frac{x}{4}\right)-\cos ^2\left(\frac{11 \pi}{8}+\frac{x}{4}\right)\righ 16. If the distance between the planes $8 x+12 y-14 z=2$ and $4 x+6 y-7 z=2$ can be expressed as $\frac{1}{\sqrt{N}}$, then 17. The complex number $z$ satisfying $z+|z|$ $=1+7 i$, then the value of $|z|^2$ equals 18. Two red counters, three green counters and four blue counters are placed in a row in random order. The probability that 19. The differential equation corresponding to the family of curves $y=e^x(a x+b)$ is 20. The value of $$\sin ^{-1}\left\{\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sec ^{ 21. The volume of the parallelopiped whose edges are represented by $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat 22. Period of $f(x)=\{x\}+\left\{x+\frac{1}{3}\right\}+\left\{x+\frac{2}{3}\right\}$ is equal to (where $\{\cdot\}$ is fract 23. The area of the region(s) enclosed by the curves $y=x^2$ and $y=\sqrt{|x|}$ is
24. $\lim \limits_{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ equal to 25. If $A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{ 26. The value of ' $a$ ' for which the lines $\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}$ and $\frac{x-a}{-1}=\frac{y-7}{2}$ 27. The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\righ 28. If $(\cos x)^y=(\sin y)^x$, then $\frac{d y}{d x}$ equals 29. If $a, b$ and $c$ are distinct positive numbers, not equal to unity. Such that $a b c=1$, then the value of $\log _b a \ 30. Sum of first ' $n$ ' terms of a series $a_1+a_2+\ldots+a_n$ is given by $S_n=\frac{n\left(n^2-1\right)(n+2)}{4}$, then t 31. The area of circle touching parabola $y=x^2$ at $(1,1)$ and having directrix of $y=x^2$ as its normal is $125 A \pi$, th 32. The sum of the infinite terms of the series $\cot ^{-1}\left(1^2+\frac{3}{4}\right)+\cot ^{-1}\left(2^2+\frac{3}{4}\righ 33. $\lim _\limits{x \rightarrow 0} \frac{1}{x} \int_0^x(1+\sin 3 t)^{\frac{1}{t}} d t$ is equal to 34. If the curves $\frac{x^2}{a}+\frac{y^2}{4}=1$ and $y^3=16 x$ intersect at right angles, then ' $a$ ' equals to 35. $\tan 65^{\circ}, \tan 40^{\circ}+\tan 25^{\circ}$ and $\tan 25^{\circ}$ are in 36. If $P=\operatorname{cosec} \frac{\pi}{8}+\operatorname{cosec} \frac{2 \pi}{8}+\operatorname{cosec} \frac{3 \pi}{8}$ $+\o 37. Difference between the maximum and minimum values of $f(x)=-\sin ^3 x+3 \sin ^2 x+5$ in $x \in\left[0, \frac{\pi}{2}\rig 38. If $e$ is the eccentricity of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\theta$ is the angle between the asympt 39. If tangent to the curve $f(x)=x^3-\alpha x^2-x+\beta$ at point $(1,3)$ on the curve, cut equals non zero intercepts on c 40. The sum of $1+\frac{1}{4}+\frac{1 \cdot 3}{4 \cdot 8}+\frac{1 \cdot 3 \cdot 5}{4 \cdot 8 \cdot 12}+\ldots \infty$ is
Physics
1. A short bar magnet of magnetic moment of $0.15 \mathrm{~J} / \mathrm{T}$ is placed in a uniform magnetic field of 0.4 T 2. Moment of a force of magnitude 10 N acting along positive $y$-direction at point $(2 \mathrm{~m}, 0,0)$ about the point 3. Variation of internal energy with density of one mole of monoatomic gas is depicted in the below figure, corresponding v 4. The output of the given arrangement of logic gates for $A=0, B=1$ and $A=1, B=1$ will be
5. The resultant of $\mathbf{A}$ and $\mathbf{B}$ is $\mathbf{R}_1$. On reversing the vector $\mathbf{B}$, the resultant be 6. The horizontal range of a projectile is $4 \sqrt{3}$ times of its maximum height. The angle of projection will be 7. In the equation for a stationary wave given by $y=5 \cos \frac{\pi x}{25} \sin 100 \pi t$. Here, $x$ is in cm and $t$ in 8. The potential energy of a particle of mass 0.1 kg moving along the $X$-axis, is given by $U=5 x(x-4) \mathrm{J}$, where 9. If gravitational attraction between two points masses be given by $F=G \frac{m_1 m_2}{r^n}$, then the period of a satell 10. Imagine a system of unit in which the unit of mass is 10 kg , length is 1 km and time is 1 min. Then, 1 J in this system 11. A transformer has 200 windings in the primary and 400 windings in the secondary. The primary is connected to an AC suppl 12. Which of the following graphs represents the correct variation of inductive reactance $X_L$ with angular frequency $\ome 13. Eight dipoles of charges of magnitude $e$ each are placed inside a cube. The total electric flux coming out of the cube 14. In an electric circuit, a capacitor of reactance $55 \Omega$ is connected across the source of 220 V . The value of disp 15. The work done in moving a charge particle of charge $2 \times 10^{-8} \mathrm{C}$ between two points having potential di 16. A light ray of wavelength 546 nm is incident on an air-glass interface. If the speed of light in air is $3 \times 10^8 \ 17. A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3 A . A thin coil having 10 , turns of wire 18. Which of the following graph represents the variation of magnetic flux density $B$ with distance $r$ for a straight long 19. Three charges, each of $+4 \mu \mathrm{C}$, are placed at the corners $A, B, C$ of a square $A B C D$ of side 1 m . What 20. 36 cells each of internal resistance $0.5 \Omega$ and emf 1.5 V each are used to send current through an external circui 21. The magnetic field in a electromagnetic wave is given by
$$B_y=2 \times 10^{-7} \sin \left(0.5+10^3 x+1.5 \times 10^{11} 22. An electromagnetic wave with poynting vector $6 \mathrm{Wm}^{-2}$ is absorbed by a surface area $12 \mathrm{~m}^2$. The 23. Two point charges of $+3 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at a certain distance apart from each other. 24. The primary of a transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 25. The maximum power rating of a $20 \Omega$ resistor is 2 kW . Then, it cannot be used with 300 V DC source because the 26. A metal surface is illuminated with photons of energies $E_1=4 \mathrm{eV}$ and $E_2=2.5 \mathrm{eV}$ respectively. The 27. A germanium crystal is doped with arsenic atoms and indium atoms simultaneously. Number of arsenic atoms used $=5 \times 28. In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of 5.0 cm . This pressure is transm 29. The magnitude of resistance $X$ in the circuit shown below in the figure, when no current flows through the $5 \Omega$ r 30. A current carrying conductor experiences maximum force in magnetic field when the angle between current element and dire 31. Two different ideal diatomic gases $A$ and $B$ are initially in the same state. $A$ and $B$ are then expanded to same fi 32. The distance of the centres of Moon and the Earth is $D$. The mass of the Earth is 81 times the mass of the Moon. At wha 33. A cyclic process for 1 mole of an ideal is shown in the $V-T$ diagram. The work done in $A B, B C$ and $C A$ respectivel 34. The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be 35. A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. If the mass o
1
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0
If $A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]$, then $\left(B B^T A\right)^5$ is equal to
A
$\left[\begin{array}{cc}2+\sqrt{3} & 1 \\ -1 & 2-\sqrt{3}\end{array}\right]$
B
$\frac{1}{2}\left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right]$
C
$\left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right]$
D
$\left[\begin{array}{ll}5 & 1 \\ 0 & 1\end{array}\right]$
2
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0
The value of ' $a$ ' for which the lines $\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}$ and $\frac{x-a}{-1}=\frac{y-7}{2}$ $=\frac{z+2}{-3}$ intersect, is
A
$-5$
B
$-2$
C
$5$
D
$-3$
3
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0
The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\right)$ of the trapezium is
A
$75 \sqrt{2}$
B
$50 \sqrt{2}$
C
$50 \sqrt{3}$
D
$75 \sqrt{3}$
4
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0
If $(\cos x)^y=(\sin y)^x$, then $\frac{d y}{d x}$ equals
A
$\frac{\log \sin y-y \tan x}{\log \cos x+x \cot y}$
B
$\frac{\log \sin y+y \tan x}{\log \cos x-x \cot y}$
C
$\frac{\log \sin y+y \tan x}{\log \cos x+x \cot y}$
D
$\frac{\log \sin y+y \tan x}{\log \cos y-y \cot x}$
Paper analysis
Total Questions
Aptitude
10
Chemistry
35
English
5
Mathematics
40
Physics
35
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