Aptitude
1. Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus 2. Which of the following numbers will replace the question mark (?) in the given series?
167, 117, ?, 47, 27
3. In a code language, 'TREE' is written as 'WSHF', and 'BALL' is written as 'EBOM'.How will 'WALL' be written in that lang 4. Which of the following terms will replace the question mark (?) in the given series?
DIQ, EJR, FKS,?
5. In a code language, 'SERIES' is coded as 87 and 'DISMAY' is coded as 91 . How will 'SPRINT' be coded in the same languag 6.
By what per cent were the total exports of computers, by the company, in 2013, 2014 and 2018 less than the total produc 7.
The total production of computers in 2013, 2015 and 2018 is $x \%$ of the total exports of computers by the company dur 8. Two statements are given, followed by three conclusions numbered as I, II and III.
Assuming the statements to be true, e 9. Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to 10. The questions given below consist of a question followed by two statements numbered as I and II. We have to decide wheth
Chemistry
1. In the following redox reaction, what will be the sum of $x, y$, and $z$ ?
$$ \begin{aligned} x \mathrm{Cr}_2 \mathrm{O} 2. Under isothermal condition, a gas at 300 K expands from 0.1 L to 0.25 L against a constant external pressure of 2 bar. T 3. The freezing points of 0.01 M solutions of glucose, $\mathrm{NaNO}_3$, and $\mathrm{AlCl}_3$ would be
4. Among the following, the strongest nucleophile in aqueous medium is
5. Which of the following ethers cannot be prepared efficiently by Williamson synthesis?
6. Among the following, the species having same bond order are
7. Arrange the energy of $2 s$ orbitals in increasing order for the atoms $\mathrm{C}, \mathrm{B}, \mathrm{N}$ and O .
8. Identify the final product $C$ in the following sequence.
$$ \begin{aligned} \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}+(\t 9. The osmotic pressure of a solution prepared by dissolving 48 mg of $\mathrm{MgCl}_2$ in 500 mL water at $25^{\circ} \mat 10. Which of the following compounds on reaction with $\mathrm{CH}_3 \mathrm{MgBr}$ followed by acid hydrolysis gives a tert 11. $$ \text { Match List-I with List-II. } $$
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.tg td{border-color:blac 12. A 2 M aqueous solution of HCl has density $1.08 \mathrm{~g} / \mathrm{mL}$. What is the molality of the solution? 13. Which of the following does not give a white precipitate with sodium bisulphide?
14. Which of the following molecules has the maximum dipole moment?
15. The number of radial nodes in $4 s$ and $3 p$ orbitals respectively is
16. The activation energy for a reaction is $9.0 \mathrm{kcal} / \mathrm{mol}$. The increase in the rate constant when the t 17. 6.35 g of copper (Atomic mass $=635 \mathrm{u}$ ) is deposited at the cathode from a $\mathrm{Cu}^{2+}$ solution using a 18. When $\mathrm{H}_2 \mathrm{O}_2$ is added to a solution of acidified sodium dichromate, a deep blue colour is observed d 19. How long should water be electrolysed using 50 A current to release enough $\mathrm{H}_2$ gas to completely reduce 8.0 g 20. $$ \text { Match List-I with List-II. } $$
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.tg td{border-color:blac 21. How many moles of $\mathrm{KMnO}_4$ are required to oxidise 1 mole of oxalic acid in acidic medium?
22. Which of the following complexes can show both facial ( $f a c$ ) and meridional (mer) isomerism?
23. In the diazotisation of aniline with sodium nitrite and hydrochloric acid the excess of hydrochloric acid is used primar 24. Identify the product $Q$ in the following reaction sequence,
25. Which of the following complex ions is expected to appear colourless in aqueous solution?
26. A 0.05 M solution of aniline hydrochloride has a pH of 3.85 . Calculate the ionisation constant ( $K_b$ ) of aniline.
27. Which of the following oxides of nitrogen has a lone pair and is paramagnetic?
28. The product $(X)$ formed in the given reaction. 29. Arrange the following in the correct increasing order of atomic size.
$\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$ 30. Given, $\Delta G^{\circ}=-502 \mathrm{~kJ} \mathrm{~mol}^{-1}$ for the dissociation of ,
$\mathrm{Mg}(\mathrm{OH})_2(s) 31. Which of the following is a water-soluble vitamin?
32. In a first-order reaction, the initial concentration of $A$ is $0.5 \mathrm{~mol} \mathrm{~L}^{-1}$. After 20 minutes, t 33. An unknown ester is hydrolysed to give ethanol as one of the products. Which chemical test can be used to confirm the id 34. Which of the following pairs form the same osazone?
35. Ozone is quantitatively determined by bubbling it through an excess of acidic potassium iodide solution, which liberates
English
1. Select the most appropriate idiom to fill in the blank. The team always $\_\_\_\_$ to come up with unique advertisements 2. Select the most appropriate synonym of the given word.
Prudent
3. Select the most appropriate antonym of the underlined word in the following sentence. The woman in the crowd broke down 4. Biofuels are not made from $\_\_\_\_$
5. Why have major airline companies pledged to reach net-zero carbon emissions by mid-century?
Mathematics
1. The distance between the point with position vector $-\hat{i}-5 \hat{j}-10 \hat{k}$ and the point of intersection of the 2. The equation of the line, where length of the perpendicular segment from the origin to the line is 4 and the inclination 3. In a $\triangle A E X, T$ is the mid-point of $X E$ and $P$ is the mid-point of $E T$. If the $\triangle A P E$ is equil 4. Let $f$ be a non-negative function defined on the interval $[0,1]$. If $\int_0^x \sqrt{1-(f(t))^2} d t =\int_0^x f(t) d 5. The set of real value of $x$ for which $\log _{0.2} \frac{x+2}{x} \leq 1$ is
6. Sum to 10 terms of the series $1+2(1 \cdot 1)+3(1 \cdot 1)^2+4(1 \cdot 1)^3+$ $\_\_\_\_$ is
7. The equation of the straight line through the origin and parallel to the line
$$ \begin{aligned} & (b+c) x+(c+a) y+(a+b) 8. The point $(-2 m, m+1)$ is an interior point of the smaller region bounded by circle $x^2+y^2=4$ and the parabola $y^2=4 9. Total number of 3 letters word that can be formed from the letters of the word 'SAHARANPUR' is equal to
10. For any four vectors $\mathbf{a , b , c , d}$ the expression $(\mathrm{b} \times \mathrm{c}) \cdot(\mathrm{a} \times \ma 11. If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{(1+x)^{3 / 2}-\left(1+\frac{1}{2} x 12. The focal chord of $y^2=16 x$ is a tangent to $(x-6)^2+y^2=2$, then the possible values of the slope of this chord are
13. Let $f(x)$ be a polynomial of degree 6 divisible by $x^3$ and having a point of extremum at $x=2$. If $f^{\prime}(x)$ is 14. If $\hat{\mathbf{a}} \cdot \hat{\mathbf{b}}=0$, where $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ are unit vectors and the 15. In the given figure, the equation of the large circle is $x^2+y^2+4 y-5=0$ and the distance between centre is 4 . Then, 16. If $a$ is the root of equation $z^n+2 z^{n-1}+3 z^{n-2}+12-18 z=0$ which lies inside $|z|=1$, then
17. The equation of a straight line passing through $(1,2)$ and having intercept of length 3 between the straight lines $3 x 18. The differential equation for all family of line which are at a unit distance from the origin is
19. If $[x]$ denotes the integral part of $x$ and $k=\sin ^{-1}\left(\frac{1+t^2}{2 t}\right)>0$, then number of values of $ 20. $\int \frac{e^{x^2}\left(2 x+x^3\right)}{\left(3+x^2\right)^2} d x$ is equal to
21. If $a$ and $b$ are two complex numbers, then the sum of $(n+1)$ terms of the series $a c_0-(a+d) c_1+(a+2 d) c_2-(a+3 d) 22. Let $f: R \rightarrow R, f(x)=x^3-3 x^2+3 x-2$, then $f^{-1}(x)$ is given by
23. The least positive non-integral solution of the equation $\sin \pi\left(x^2+x\right)=\sin \pi x^2$ is
24. $S=\cot ^{-1}\left(\frac{1+2 \times 6}{4}\right)+\cot ^{-1}\left(\frac{1+3 \times 8}{10}\right)+\cot ^{-1} \left(\frac{1 25. The area of the region $\left\{(x, y): x y
26. If $\alpha$ is a root of $x^4=1$ with negative principal argument, then the principle argument of $\Delta(A)$, where $\D 27. Let $f(x)=\cos ^{-1}\left(2 x \sqrt{1-x^2}\right)$, then $f^{\prime}(0.6)$ equals to
28. The period of the function $f(x)=3 \sin \frac{\pi x}{3}+4 \cos \frac{\pi x}{4}$ is
29. If $f(x)=\left(\frac{x^2+5 x+3}{x^2+x+2}\right)^x$, then $\lim _{x \rightarrow \infty} f(x)$ is
30. The value of
$$ 99^{50}-90 \cdot 98^{50}+\frac{99 \cdot 98}{1 \cdot 2}(97)^{50}-\ldots \ldots \ldots \ldots .+99 $$
is
31. A five digit number (having all different digits) is formed using the digits $1,2,3,4,5$, 6,78 and 9 . The probability t 32. The function, $f(x)=(3 x-7) x^{2 / 3}, x \in R$ is increasing for all $x$ lying in
33. Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in R$ and $A^4=\left[a_{i j}\right]$.
It $a_{11}=109$ 34. If $\alpha$ and $\beta$ are the roots of equation $x^2+p x+2=0$ and $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ are roots o 35. The value of $(016)^{\log _{25}\left(\frac{1}{3}+\frac{1}{3^2}+\ldots+\infty\right)}$ is equal to
$..........$
36. The number of numbers greater than a million that can be formed with the digits 2 , $3,0,3,4,2$ and 3 is
37. For the parabola $y^2=16 x$, length of a focal chord, whose on end point is $(16,16)$ is $L^2$, then absolute value of $ 38. The minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\frac{9}{v}\right)^2$, where $0 0$
39. Let $c_1: x^2+y^2=1$ and $c_2:(x-10)^2+y^2=9$ be two circles a line touching $c_1$ at $P$ and $c_2$ at $Q$. If $M$ is th 40. $S_n=1 \cdot 3+2 \cdot 2^2+3 \cdot 3^3+4 \cdot 2^4+\ldots \ldots \ldots$ upto $n$ terms. If $S_{20}=a \cdot 3^{21}+b \cd
Physics
1. Three electric bulbs of 200 W and 400 W are shown in figure. The resultant power of the combination, if rated voltage is 2. In hydrogen atom, an electron is revolving in the orbit of radius $0.53 \mathop {\rm{A}}\limits^{\rm{o}} $ with $6.6 \ti 3. To get an output 1 from the circuit shown in the figure, the input must be
4. When the ideal monoatomic gas is heated at constant pressure fraction of heat energy supplied which increases the intern 5. Two identical long solid cylinders are used to conduct heat from temperature $T_1$ to temperature $T_2$. Originally, the 6. In the fusion reaction,
$$ { }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \longrightarrow{ }_2^3 \mathrm{He}+{ }_0^1 \mathrm{n} $ 7. A steel wire of mass 4 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N , then the frequency 8. Ratio of powers of a convex and concave lens is $\frac{3}{2}$ and their equivalent focal length (when lenses are kept in 9. The radius of the orbit of an electron in a Hydrogen-like atom is $45 a_0$, where $a_0$ is the Bohr radius. Its orbital 10. A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest pos 11. If the rotational kinetic energy of a body is increased by $300 \%$, then the percentage increase in its angular momentu 12. The average depth of Indian ocean is about 3000 m . The fractional compression, $\frac{\Delta V}{V}$ of water at the bot 13. The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the larges 14. The velocity of a particle moving in a straight line varies with time in such a manner that $v$ versus $t$ graph is velo 15. A conductor of length 0.6 m is moving with a speed of $5 \mathrm{~m} / \mathrm{s}$ perpendicular to a magnetic field of 16. In given situation, force on charge $Q_3$ is
17. $$ \text { A } 2 \mu \mathrm{~F} \text { capacitor is charged as shown, } $$
When switch $S$ is shifted to position $2, 18. The displacement from mean position of a particle in SHM at 3 s is $\frac{\sqrt{3}}{2}$ of the amplitude, then its time 19. A cylindrical magnet has a length of 15 cm and diameter 3 cm . If it has uniform magnetisation of $4.0 \times 10^3 \math 20. A parallel beam of fast moving electrons is incident normally on a narrow slit. If the speed of the electrons is decreas 21. When a ball of mass 5 kg hits a bat with a velocity $3 \mathrm{~m} / \mathrm{s}$, in positive direction and it moves bac 22. A flask contains argon and chlorine in the ratio of $2: 1$ by mass, the temperature of mixture is $27^{\circ} \mathrm{C} 23. When a beam of 10.6 eV photons of intensity $2.0 \mathrm{~W} / \mathrm{m}^2$ falls on a platinum surface of area $1.0 \t 24. If the magnetic field in plane electromagnetic wave is
$$ \mathbf{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^3 x+48 \t 25. A laser beam of cross-sectional area $5 \mathrm{~mm}^2$ is 30 mW . Find the magnitude of maximum electric field in this 26. A body of mass $M$ is moving with a uniform speed of $10 \mathrm{~m} / \mathrm{s}$ on frictionless surface under the inf 27. An object is projected from surface of Earth with a kinetic energy twice that of escape energy ' $K$ ', from surface of 28. If the Earth is assumed to be a sphere of uniform mass density and its weight on the surface is 200 N , then the weight 29. A liquid film is formed over a frame $A B C D$ as shown in figure. Wire $C D$ can slide without friction. Maximum value 30. A car of mass 500 kg is lifted by a hydraulic jack that consist of two pistons. If the diameter of large and small pisto 31. A network of four capacitors of capacity equal to $C_1=C, C_2=2 C, C_3=3 C$ and $C_4=4 C$ are connected to a battery, as 32. Capacity of a parallel plate capacitor in the absence of dielectric medium is $C_0$. A sheet of dielectric constant $k$ 33. Which of the following statement is correct regarding the AC circuit shown in the adjacent figure?
34. The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding 35. A ball is projected horizontally with a velocity of $5 \mathrm{~ms}^{-1}$ from the top of a building 19.6 m high. How lo
1
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1
$\int \frac{e^{x^2}\left(2 x+x^3\right)}{\left(3+x^2\right)^2} d x$ is equal to
A
$\frac{e^{x^2}}{\left(3+x^2\right)}+c$
B
$\frac{1}{4} \frac{e^{x^2}}{\left(3+x^2\right)}+c$
C
$\frac{1}{8} \frac{e^{x^2}}{\left(3+x^2\right)}+c$
D
$\frac{1}{2} \frac{e^{x^2}}{\left(3+x^2\right)}+c$
2
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1
If $a$ and $b$ are two complex numbers, then the sum of $(n+1)$ terms of the series $a c_0-(a+d) c_1+(a+2 d) c_2-(a+3 d) c_3+$ $\_\_\_\_$ is
A
$\frac{a}{2^n}$
B
na
C
0
D
None of these
3
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1
Let $f: R \rightarrow R, f(x)=x^3-3 x^2+3 x-2$, then $f^{-1}(x)$ is given by
A
$1+\sqrt[3]{x+1}$
B
$1-\sqrt[3]{x+1}$
C
$\sqrt[3]{x+1}-1$
D
$\sqrt[3]{x-1}-1$
4
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1
The least positive non-integral solution of the equation $\sin \pi\left(x^2+x\right)=\sin \pi x^2$ is
A
Rational
B
Irrational of form $\sqrt{p}$
C
Irrational of the form $\frac{\sqrt{p}-1}{4}$, where $p$ is an odd integer
D
Irrational of the form $\frac{\sqrt{p}+1}{4}$, where $p$ is an even integer
Paper Analysis
Total Questions
Aptitude 10
Chemistry 35
English 5
Mathematics 40
Physics 35
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