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viteee-2025

VITEEE 2025

JEE 2025 Previous Year

3 hDuration
500Total Marks
125Questions
5Sections
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Instructions

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  • Total questions: 125 across 5 section(s); maximum marks: 500.
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Paper Structure

Chemistry

Chemistry

Q1. mcq single +4 / 1
The product $(X)$ formed in the given reaction.
Q2. mcq single +4 / 1
In the diazotisation of aniline with sodium nitrite and hydrochloric acid the excess of hydrochloric acid is used primarily to
Q3. mcq single +4 / 1
When $\mathrm{H}_2 \mathrm{O}_2$ is added to a solution of acidified sodium dichromate, a deep blue colour is observed due to the formation of a peroxo complex. This change signifies that
Q4. mcq single +4 / 1
Which of the following molecules has the maximum dipole moment?
Q5. mcq single +4 / 1
Among the following, the species having same bond order are
Q6. mcq single +4 / 1
The number of radial nodes in $4 s$ and $3 p$ orbitals respectively is
Q7. mcq single +4 / 1
Arrange the energy of $2 s$ orbitals in increasing order for the atoms $\mathrm{C}, \mathrm{B}, \mathrm{N}$ and O .
Q8. mcq single +4 / 1
A 0.05 M solution of aniline hydrochloride has a pH of 3.85 . Calculate the ionisation constant ( $K_b$ ) of aniline.
Q9. mcq single +4 / 1
The activation energy for a reaction is $9.0 \mathrm{kcal} / \mathrm{mol}$. The increase in the rate constant when the temperature is increased from 298 K to 308 K is
Q10. mcq single +4 / 1
In a first-order reaction, the initial concentration of $A$ is $0.5 \mathrm{~mol} \mathrm{~L}^{-1}$. After 20 minutes, the concentration reduces to $0.4 \mathrm{~mol} \mathrm{~L}^{-1}$. The rate constant is (in $\mathrm{min}^{-1}$ ).
Q11. mcq single +4 / 1
In the following redox reaction, what will be the sum of $x, y$, and $z$ ? $$ \begin{aligned} x \mathrm{Cr}_2 \mathrm{O}_7^{2-}(a q) & +y \mathrm{SO}_3^{2-}(a q)+z \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{SO}_4^{2-}(a q)+\mathrm{H}_2 \mathrm{O}(l) \end{aligned} $$
Q12. mcq single +4 / 1
How many moles of $\mathrm{KMnO}_4$ are required to oxidise 1 mole of oxalic acid in acidic medium?
Q13. mcq single +4 / 1
Ozone is quantitatively determined by bubbling it through an excess of acidic potassium iodide solution, which liberates iodine. The liberated iodine is then titrated with sodium thiosulphate solution. If 25.0 mL of the iodine-containing solution required 20.0 mL of 0.01 M sodium thiosulphate for complete titration, calculate the number of moles of ozone that reacted.
Q14. mcq single +4 / 1
Identify the final product $C$ in the following sequence. $$ \begin{aligned} \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}+(\text { alc. } \mathrm{KOH}) & \xrightarrow{h \nu} A+\mathrm{Br}_2 \longrightarrow B+(\text { alc. } \mathrm{KCN}) \longrightarrow C \end{aligned} $$
Q15. mcq single +4 / 1
Arrange the following in the correct increasing order of atomic size. $\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$
Q16. mcq single +4 / 1
$$ \text { Match List-I with List-II. } $$ List I (Atoms) List II (Properties) A. F I. Highest electronegativity B. Cs II. Lowest ionisation energy C. Na III. Strong reducing agent D. O IV. Forms strong hydrogen bonds Choose the correct match from the options given below
Q17. mcq single +4 / 1
Given, $\Delta G^{\circ}=-502 \mathrm{~kJ} \mathrm{~mol}^{-1}$ for the dissociation of , $\mathrm{Mg}(\mathrm{OH})_2(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)$ at 298 K . Find the $K_{\mathrm{sp}}$ value. $(R=8314 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K})$
Q18. mcq single +4 / 1
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. The work done by the gas is (Given that, 1 L bar $=100 \mathrm{~J}$ )
Q19. mcq single +4 / 1
Among the following, the strongest nucleophile in aqueous medium is
Q20. mcq single +4 / 1
A 2 M aqueous solution of HCl has density $1.08 \mathrm{~g} / \mathrm{mL}$. What is the molality of the solution?
Q21. mcq single +4 / 1
The osmotic pressure of a solution prepared by dissolving 48 mg of $\mathrm{MgCl}_2$ in 500 mL water at $25^{\circ} \mathrm{C}$ is (Assuming complete dissociation). (Molar mass of $\mathrm{MgCl}_2=95 \mathrm{~g} / \mathrm{mol}, R=0.0821 \mathrm{L} \cdot \mathrm{atm} / \mathrm{mol} \cdot \mathrm{K}$ )
Q22. mcq single +4 / 1
The freezing points of 0.01 M solutions of glucose, $\mathrm{NaNO}_3$, and $\mathrm{AlCl}_3$ would be
Q23. mcq single +4 / 1
Which of the following oxides of nitrogen has a lone pair and is paramagnetic?
Q24. mcq single +4 / 1
Which of the following complexes can show both facial ( $f a c$ ) and meridional (mer) isomerism?
Q25. mcq single +4 / 1
Which of the following complex ions is expected to appear colourless in aqueous solution?
Q26. mcq single +4 / 1
An unknown ester is hydrolysed to give ethanol as one of the products. Which chemical test can be used to confirm the identity of this alcohol?
Q27. mcq single +4 / 1
$$ \text { Match List-I with List-II. } $$ List I (Mixture) List II (Distinguishing test) A. Ethanal, propanone I. Brady's reagent B. Benzaldehyde, acetophenone II. Tollen's reagent C. Phenol, aniline III. Neutral $\mathrm{FeCl}_3$ D. Cyclohexene, cyclohexane IV. Baeyer's reagent Choose the correct match from the options given below
Q28. mcq single +4 / 1
Which of the following ethers cannot be prepared efficiently by Williamson synthesis?
Q29. mcq single +4 / 1
Which of the following pairs form the same osazone?
Q30. mcq single +4 / 1
Which of the following is a water-soluble vitamin?
Q31. mcq single +4 / 1
How long should water be electrolysed using 50 A current to release enough $\mathrm{H}_2$ gas to completely reduce 8.0 g of CuO ? $\left(\mathrm{CuO}+\mathrm{H}_2 \longrightarrow \mathrm{Cu}+\mathrm{H}_2 \mathrm{O}\right.$; Atomic mass of $\mathrm{Cu}=635 \mathrm{u}$ )
Q32. mcq single +4 / 1
6.35 g of copper (Atomic mass $=635 \mathrm{u}$ ) is deposited at the cathode from a $\mathrm{Cu}^{2+}$ solution using a certain quantity of electric charge. The volume of oxygen gas liberated at STP from water electrolysis using the same quantity of electric charge is
Q33. mcq single +4 / 1
Identify the product $Q$ in the following reaction sequence,
Q34. mcq single +4 / 1
Which of the following compounds on reaction with $\mathrm{CH}_3 \mathrm{MgBr}$ followed by acid hydrolysis gives a tertiary alcohol?
Q35. mcq single +4 / 1
Which of the following does not give a white precipitate with sodium bisulphide?
Mathematics

Mathematics

Q1. mcq single +4 / 1
If $\hat{\mathbf{a}} \cdot \hat{\mathbf{b}}=0$, where $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ are unit vectors and the unit vector $\hat{\complement}$ is inclined at an angle $\theta$ to both $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$. If $\hat{\mathbf{c}}=m \hat{\mathbf{a}}+n \hat{\mathbf{b}}+p(\hat{\mathbf{a}} \times \hat{\mathbf{b}})$, where, $m, n, p \in R$, then
Q2. mcq single +4 / 1
For any four vectors $\mathbf{a , b , c , d}$ the expression $(\mathrm{b} \times \mathrm{c}) \cdot(\mathrm{a} \times \mathrm{d})+(\mathrm{c} \times \mathrm{a}) \cdot(\mathrm{b} \times \mathrm{d})+(\mathrm{a} \times \mathrm{b}) \cdot(\mathrm{c} \times \mathrm{d})$ is always equal to
Q3. mcq single +4 / 1
The least positive non-integral solution of the equation $\sin \pi\left(x^2+x\right)=\sin \pi x^2$ is
Q4. mcq single +4 / 1
A five digit number (having all different digits) is formed using the digits $1,2,3,4,5$, 6,78 and 9 . The probability that the formed number either begins or ends with an odd digit is equal to
Q5. mcq single +4 / 1
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 $\alpha$ for which the equation $(x-[k])(x+\alpha)-1$ has integral roots
Q6. mcq single +4 / 1
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 of equation $2 x^2+2 q x+1=0$, then $\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right)\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)$ is equal to
Q7. mcq single +4 / 1
Sum to 10 terms of the series $1+2(1 \cdot 1)+3(1 \cdot 1)^2+4(1 \cdot 1)^3+$ $\_\_\_\_$ is
Q8. mcq single +4 / 1
$S_n=1 \cdot 3+2 \cdot 2^2+3 \cdot 3^3+4 \cdot 2^4+\ldots \ldots \ldots$ upto $n$ terms. If $S_{20}=a \cdot 3^{21}+b \cdot 2^{22}+\frac{391}{288}$, then value of $32 a-9 b$ is
Q9. mcq single +4 / 1
If $f(x)=\left(\frac{x^2+5 x+3}{x^2+x+2}\right)^x$, then $\lim _{x \rightarrow \infty} f(x)$ is
Q10. mcq single +4 / 1
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 divisible by $1+x^2$, then find the value of $\frac{3 f(2)}{f(1)}$
Q11. mcq single +4 / 1
The minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\frac{9}{v}\right)^2$, where $0 0$
Q12. mcq single +4 / 1
The function, $f(x)=(3 x-7) x^{2 / 3}, x \in R$ is increasing for all $x$ lying in
Q13. mcq single +4 / 1
The area of the region $\left\{(x, y): x y<8,1 \leq y \leq x^2\right\}$ is
Q14. mcq single +4 / 1
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 $a_{11}=109$, then $a_{22}$ is equal to
Q15. mcq single +4 / 1
The equation of the straight line through the origin and parallel to the line $$ \begin{aligned} & (b+c) x+(c+a) y+(a+b) z=k= \\ & (b-c) x+(c-a) y+(a-b) z \text { is } \end{aligned} $$
Q16. mcq single +4 / 1
The distance between the point with position vector $-\hat{i}-5 \hat{j}-10 \hat{k}$ and the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ with the plane $x-y+z=5$, is $\_\_\_\_$ (units)
Q17. mcq single +4 / 1
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 $L$ is
Q18. mcq single +4 / 1
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 $y^2=4 x$, then
Q19. mcq single +4 / 1
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
Q20. mcq single +4 / 1
$S=\cot ^{-1}\left(\frac{1+2 \times 6}{4}\right)+\cot ^{-1}\left(\frac{1+3 \times 8}{10}\right)+\cot ^{-1} \left(\frac{1+4 \times 10}{18}\right) \ldots \ldots \ldots$ upto $\infty$ terms is equal to
Q21. mcq single +4 / 1
If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{(1+x)^{3 / 2}-\left(1+\frac{1}{2} x\right)^3}{(1-x)^{1 / 2}}$ may be approximate as
Q22. mcq single +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
Q23. mcq single +4 / 1
The value of $$ 99^{50}-90 \cdot 98^{50}+\frac{99 \cdot 98}{1 \cdot 2}(97)^{50}-\ldots \ldots \ldots \ldots .+99 $$ is
Q24. mcq single +4 / 1
The set of real value of $x$ for which $\log _{0.2} \frac{x+2}{x} \leq 1$ is
Q25. mcq single +4 / 1
The value of $(016)^{\log _{25}\left(\frac{1}{3}+\frac{1}{3^2}+\ldots+\infty\right)}$ is equal to $..........$
Q26. mcq single +4 / 1
The equation of a straight line passing through $(1,2)$ and having intercept of length 3 between the straight lines $3 x+4 y=24$ and $3 x+4 y=12$ is
Q27. mcq single +4 / 1
The equation of the line, where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of $X$-axis is $30^{\circ}$.
Q28. mcq single +4 / 1
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
Q29. mcq single +4 / 1
If $\alpha$ is a root of $x^4=1$ with negative principal argument, then the principle argument of $\Delta(A)$, where $\Delta(A)=\left|\begin{array}{ccc}1 & 1 & 1 \\ \alpha^n & \alpha^{n+1} & \alpha^{n+3} \\ \frac{1}{\alpha^{n+1}} & \frac{1}{\alpha^n} & 0\end{array}\right|$
Q30. mcq single +4 / 1
Let $f: R \rightarrow R, f(x)=x^3-3 x^2+3 x-2$, then $f^{-1}(x)$ is given by
Q31. mcq single +4 / 1
The period of the function $f(x)=3 \sin \frac{\pi x}{3}+4 \cos \frac{\pi x}{4}$ is
Q32. mcq single +4 / 1
The differential equation for all family of line which are at a unit distance from the origin is
Q33. mcq single +4 / 1
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, the equation of smaller circle is
Q34. mcq single +4 / 1
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 the mid-point of $P Q$, then $M$ lies on a circle $(x-5)^2+y^2=r^2$ where ' $r$ ' is $(r>0)$
Q35. mcq single +4 / 1
Let $f(x)=\cos ^{-1}\left(2 x \sqrt{1-x^2}\right)$, then $f^{\prime}(0.6)$ equals to
Q36. mcq single +4 / 1
The number of numbers greater than a million that can be formed with the digits 2 , $3,0,3,4,2$ and 3 is
Q37. mcq single +4 / 1
Total number of 3 letters word that can be formed from the letters of the word 'SAHARANPUR' is equal to
Q38. mcq single +4 / 1
Let $f$ be a non-negative function defined on the interval $[0,1]$. If $\int_0^x \sqrt{1-(f(t))^2} d t =\int_0^x f(t) d t, 0 \leq x \leq 1$ and $f(0)=0$, then
Q39. mcq single +4 / 1
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 equilateral of side length equal to unity, then which of the following alternative is not correct?
Q40. mcq single +4 / 1
$\int \frac{e^{x^2}\left(2 x+x^3\right)}{\left(3+x^2\right)^2} d x$ is equal to
English

English

Q1. mcq single +4 / 1
Biofuels are not made from $\_\_\_\_$
Q2. mcq single +4 / 1
Select the most appropriate idiom to fill in the blank. The team always $\_\_\_\_$ to come up with unique advertisements for all its clients.
Q3. mcq single +4 / 1
Select the most appropriate antonym of the underlined word in the following sentence. The woman in the crowd broke down in hysterics.
Q4. mcq single +4 / 1
Select the most appropriate synonym of the given word. Prudent
Q5. mcq single +4 / 1
Why have major airline companies pledged to reach net-zero carbon emissions by mid-century?
Aptitude

Aptitude

Q1. mcq single +4 / 1
Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster does not belong to that group?
Q2. mcq single +4 / 1
The questions given below consist of a question followed by two statements numbered as I and II. We have to decide whether these statements give enough information required to answer the question or not. When is Yuvi's wedding anniversary? Statements I. On 7th day of a month. II. The month has 29 days only in a leap year.
Q3. mcq single +4 / 1
Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. ABIDE : GFKDC :: CHARM : OTCJE :: BLOOM : ?
Q4. mcq single +4 / 1
Two statements are given, followed by three conclusions numbered as I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the given statements. Statements All scanners are printers.Some scanners are copiers. Conclusions I. Some printers are copiers. II. No copier is a printer. III. Some printers are scanners.
Q5. mcq single +4 / 1
In a code language, 'TREE' is written as 'WSHF', and 'BALL' is written as 'EBOM'.How will 'WALL' be written in that language?
Q6. mcq single +4 / 1
In a code language, 'SERIES' is coded as 87 and 'DISMAY' is coded as 91 . How will 'SPRINT' be coded in the same language?
Q7. mcq single +4 / 1
Which of the following terms will replace the question mark (?) in the given series? DIQ, EJR, FKS,?
Q8. mcq single +4 / 1
Which of the following numbers will replace the question mark (?) in the given series? 167, 117, ?, 47, 27
Q9. mcq single +4 / 1
By what per cent were the total exports of computers, by the company, in 2013, 2014 and 2018 less than the total production of computers in 2015 to 2017? (correct to one decimal place)
Q10. mcq single +4 / 1
The total production of computers in 2013, 2015 and 2018 is $x \%$ of the total exports of computers by the company during the 6 yr . The value of $x$ is
Physics

Physics

Q1. mcq single +4 / 1
The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension, when the same tension is applied?
Q2. mcq single +4 / 1
The average depth of Indian ocean is about 3000 m . The fractional compression, $\frac{\Delta V}{V}$ of water at the bottom of the ocean (given, that the Bulk modulus of the water $=2.2 \times 10^9 \mathrm{Nm} { }^{-2}$ and $g=10 \mathrm{~ms}^{-2}$ ) is
Q3. mcq single +4 / 1
The displacement from mean position of a particle in SHM at 3 s is $\frac{\sqrt{3}}{2}$ of the amplitude, then its time period is
Q4. mcq single +4 / 1
If the rotational kinetic energy of a body is increased by $300 \%$, then the percentage increase in its angular momentum will be
Q5. mcq single +4 / 1
A conductor of length 0.6 m is moving with a speed of $5 \mathrm{~m} / \mathrm{s}$ perpendicular to a magnetic field of intensity $0.8 \mathrm{~Wb} / \mathrm{m}^2$. The induced emf across the conductor is
Q6. mcq single +4 / 1
A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest position are equal. The angle $\theta$ of thread deflection in the extreme position will be
Q7. mcq single +4 / 1
When the ideal monoatomic gas is heated at constant pressure fraction of heat energy supplied which increases the internal energy of gas is
Q8. mcq single +4 / 1
Two identical long solid cylinders are used to conduct heat from temperature $T_1$ to temperature $T_2$. Originally, the cylinders are connected in series and the rate of heat transfer is $H$. If the cylinders are connected in parallel, then the rate of heat transfer will be
Q9. mcq single +4 / 1
A flask contains argon and chlorine in the ratio of $2: 1$ by mass, the temperature of mixture is $27^{\circ} \mathrm{C}$, the ratio of root mean square ( $U_{\mathrm{rms}}$ ) of the molecule of two gases (Given, Atomic mass of argon $=39.9 v$, Molecular mass of chlorine $=70.9 u$ )
Q10. mcq single +4 / 1
A parallel beam of fast moving electrons is incident normally on a narrow slit. If the speed of the electrons is decreased, the angular width of central maxima
Q11. mcq single +4 / 1
When a beam of 10.6 eV photons of intensity $2.0 \mathrm{~W} / \mathrm{m}^2$ falls on a platinum surface of area $1.0 \times 10^{-4} \mathrm{~m}^2$ and work function $5.6 \mathrm{eV} .0 .53 \%$ of the incident photons eject photoelectrons. The number of photoelectrons emitted per second is
Q12. mcq single +4 / 1
In given situation, force on charge $Q_3$ is
Q13. mcq single +4 / 1
An object is projected from surface of Earth with a kinetic energy twice that of escape energy ' $K$ ', from surface of Earth. It's kinetic energy when it reaches far away from Earth is
Q14. mcq single +4 / 1
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 of the body at a depth halfway to the Earth's center will be
Q15. mcq single +4 / 1
Capacity of a parallel plate capacitor in the absence of dielectric medium is $C_0$. A sheet of dielectric constant $k$ and thickness of one-fourth of the plate separation is inserted between the plates. If the new capacity is $C$, then $\frac{C}{C_0}$ is
Q16. mcq single +4 / 1
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 shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is $\_\_\_\_$
Q17. mcq single +4 / 1
$$ \text { A } 2 \mu \mathrm{~F} \text { capacitor is charged as shown, } $$ When switch $S$ is shifted to position $2, \%$ of energy lost is
Q18. mcq single +4 / 1
Ratio of powers of a convex and concave lens is $\frac{3}{2}$ and their equivalent focal length (when lenses are kept in constant) is 30 cm . Focal lengths of lenses are
Q19. mcq single +4 / 1
A ball is projected horizontally with a velocity of $5 \mathrm{~ms}^{-1}$ from the top of a building 19.6 m high. How long will the ball take to hit the ground?
Q20. mcq single +4 / 1
The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=8 t-5 t^2 \mathrm{~m}$ and $x=6 t \mathrm{~m}$, where $t$ is in seconds. The velocity with which the projectile is projected is
Q21. mcq single +4 / 1
The velocity of a particle moving in a straight line varies with time in such a manner that $v$ versus $t$ graph is velocity is $v_m$ and the total time of motion is $t_0$ (i) Average velocity of the particle is $\frac{\pi}{4} v_m$ (ii) Such motion cannot be realized in practical terms Choose the correct option on the basis of above two statements.
Q22. mcq single +4 / 1
In hydrogen atom, an electron is revolving in the orbit of radius $0.53 \mathop {\rm{A}}\limits^{\rm{o}} $ with $6.6 \times 10^{15} \mathrm{rps}$. Magnetic field produced at the centre of the orbit is
Q23. mcq single +4 / 1
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 of mass that can be hanged from $C D$ without breaking the liquid film is
Q24. mcq single +4 / 1
A car of mass 500 kg is lifted by a hydraulic jack that consist of two pistons. If the diameter of large and small pistons are 2 m and 20 cm , respectively. Then force required (in N ) to lift the car by smaller piston is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )
Q25. mcq single +4 / 1
In the fusion reaction, $$ { }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \longrightarrow{ }_2^3 \mathrm{He}+{ }_0^1 \mathrm{n} $$ the masses of deuteron, helium and neutron expressed in amu are 2.015, 3.017 and 1.009, respectively. If 1 kg of deuterium undergoes complete fusion, then find the amount of total energy released. ( $1 \mathrm{amu}=9315 \mathrm{MeV}$ )
Q26. mcq single +4 / 1
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 angular momentum is $\frac{3 h}{2 \pi}$. It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)
Q27. mcq single +4 / 1
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 of fourth harmonic is
Q28. mcq single +4 / 1
When a ball of mass 5 kg hits a bat with a velocity $3 \mathrm{~m} / \mathrm{s}$, in positive direction and it moves back with a velocity $4 \mathrm{~m} / \mathrm{s}$, find the impulse in SI units.
Q29. mcq single +4 / 1
A cylindrical magnet has a length of 15 cm and diameter 3 cm . If it has uniform magnetisation of $4.0 \times 10^3 \mathrm{Am}^{-1}$, then magnetic dipole moment is
Q30. mcq single +4 / 1
A body of mass $M$ is moving with a uniform speed of $10 \mathrm{~m} / \mathrm{s}$ on frictionless surface under the influence of two forces $F_1$ and $F_2$. The net power of the system is
Q31. mcq single +4 / 1
Three electric bulbs of 200 W and 400 W are shown in figure. The resultant power of the combination, if rated voltage is applied across the combination is
Q32. mcq single +4 / 1
If the magnetic field in plane electromagnetic wave is $$ \mathbf{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^3 x+48 \times 10^{10} t\right) \hat{\mathbf{j}} \mathrm{T}, $$ then find the expression of electric field?
Q33. mcq single +4 / 1
A laser beam of cross-sectional area $5 \mathrm{~mm}^2$ is 30 mW . Find the magnitude of maximum electric field in this electromagnetic wave.
Q34. mcq single +4 / 1
To get an output 1 from the circuit shown in the figure, the input must be
Q35. mcq single +4 / 1
Which of the following statement is correct regarding the AC circuit shown in the adjacent figure?