WB JEE 2025
JEE 2025 Previous Year
3 hDuration
200Total Marks
155Questions
3Sections
Instructions
General instructions for this test:
- Duration: 3 h. The timer starts as soon as you begin and cannot be paused.
- Total questions: 155 across 3 section(s); maximum marks: 200.
- You are allowed 1 attempt(s) at this test.
- Use the question palette on the right to navigate. Answered questions are highlighted in green; questions marked for review are highlighted in yellow.
- Each question's marking scheme (correct / wrong) is shown on the question card. Unanswered questions receive zero marks.
- Switching tabs, exiting full-screen, or attempting to copy text is monitored. Repeated tab-switching may auto-submit the test.
- Your answers autosave as you navigate. Click Submit Test when you are done. The test will be auto-submitted when the timer expires.
No exam-specific instructions were provided for this paper.
Paper Structure
Chemistry
Chemistry
Q1.
mcq single
+1 / 0.25
The major product (F) in the following reaction is
Q2.
mcq single
+1 / 0.25
The number of lone pair of electrons and the hybridization of Xenon ( Xe ) in $\mathrm{XeOF}_2$ are
Q3.
mcq single
+1 / 0.25
The number of terminal and bridging hydrogens in $\mathrm{B}_2 \mathrm{H}_6$ are respectively
Q4.
mcq single
+1 / 0.25
The common stable oxidation states of Eu and Gd are respectively
Q5.
mcq single
+1 / 0.25
How many electrons are needed to reduce $\mathrm{N}_2$ to $\mathrm{NH}_3 ?$
Q6.
mcq single
+1 / 0.25
What is the four-electron reduced form of $\mathrm{O}_2$ ?
Q7.
mcq single
+1 / 0.25
Equal volume of two solutions $A$ and $B$ of a strong acid having $\mathrm{pH}=6.0$ and $\mathrm{pH}=4.0$ respectively are mixed together to form a new solution. The pH of the new solution will be in the range
Q8.
mcq single
+2 / 0.5
As per the following equation, 0.217 g of HgO (molecular mass $=217 \mathrm{~g} \mathrm{~mol}^{-1}$ ) reacts with excess iodide. On titration of the resulting solution, how many mL of 0.01 M HCl is required to reach the equivalence point?
$\mathrm{HgO}+4 \mathrm{I}^{-}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{HgI}_4{ }^{2-}+2 \mathrm{OH}^{-}$
Q9.
mcq multi
+2 / 0
Which pair of ions among the following can be separated by precipitation method?
Q10.
mcq single
+1 / 0.25
Increasing order of solubility of AgCl in (i) $\mathrm{H}_2 \mathrm{O}$, (ii) 1 M NaCl (aq.), (iii) 1 M CaCl 2 (aq.) and (iv) $1 \mathrm{M}~ \mathrm{NaNO}_3$ (aq.) solution
Q11.
mcq multi
+2 / 0
Which of the following statement(s) is/are correct about the given compound?
Q12.
mcq single
+2 / 0.5
Compound given below will produce effervescence when mixed with aqueous sodium bicarbonate solution
Q13.
mcq single
+1 / 0.25
Which of the following oxides is paramagnetic?
Q14.
mcq single
+1 / 0.25
The bond order of $\mathrm{HeH}^{+}$is
Q15.
mcq single
+1 / 0.25
Which of the following hydrogen bonds is likely to be the weakest?
Q16.
mcq single
+2 / 0.5
An egg takes 4.0 minutes to boil at sea level where the boiling point of water is $T_1 K$, where as it takes 8.0 minutes to boil on a mountain top where the boiling point of water is $\mathrm{T}_2 \mathrm{~K}$. The activation energy for the reaction that takes place during the boiling of egg is
Q17.
mcq single
+1 / 0.25
For a chemical reaction, half-life period $\left(t_{\frac{1}{2}}\right)$ is 10 minutes. How much reactant will be left after 20 minutes if one starts with 100 moles of reactant and the order of the reaction be (i) zero, (ii) one and (iii) two?
Q18.
mcq single
+1 / 0.25
In the following reaction, the major product $(\mathrm{H})$ is
Q19.
mcq single
+1 / 0.25
Which of the following compounds is most reactive in $\mathrm{S}_{\mathrm{N}} 1$ reaction?
Q20.
mcq single
+1 / 0.25
The coagulating power of electrolytes having ions $\mathrm{Na}^{+}, \mathrm{Al}^{3+}$ and $\mathrm{Ba}^{2+}$ for $\mathrm{As}_2 \mathrm{S}_3$ sol increases in the order
Q21.
mcq single
+1 / 0.25
How many oxygen atoms are present in 0.36 g of a drop of water at STP?
Q22.
mcq single
+2 / 0.5
Consider the following gas phase dissociation, $\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ with equilibrium constant $K_P$ at a particular temperature and at pressure $P$. The degree of dissociation ( $\alpha$ ) for $\mathrm{PCl}_5(\mathrm{~g})$ is
Q23.
mcq multi
+2 / 0
$X$ is an extensive property and $x$ is an intensive property of a thermodynamic system. Which of the following statement(s) is (are) correct?
Q24.
mcq single
+1 / 0.25
An LPG (Liquified Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure of 3.0 atm . In the course of usage at $27^{\circ} \mathrm{C}$, the mass of the full cylinder is reduced to $24 \cdot 2 \mathrm{~kg}$. The volume of the used gas in cubic metre at the normal usage condition ( atm and $27^{\circ} \mathrm{C}$ ) is (assume LPG to be normal butane and it behaves ideally)
Q25.
mcq single
+1 / 0.25
Adiabatic free expansion of ideal gas must be
Q26.
mcq single
+1 / 0.25
$360 \mathrm{~cm}^3$ of a hydrocarbon diffuses in 30 minutes, while under the same conditions $360 \mathrm{~cm}^3$ of $\mathrm{SO}_2$ gas diffuses in one hour. The molecular formula of the hydrocarbon is
Q27.
mcq single
+1 / 0.25
Increasing order of the nucleophilic substitution of following compounds
Q28.
mcq single
+1 / 0.25
Arrange the following compounds in order of their increasing acid strength
Q29.
mcq single
+1 / 0.25
Identify the major product (G) in the following reaction
Q30.
mcq single
+1 / 0.25
$P$ and $Q$ combines to form two compounds $\mathrm{PQ}_2$ and $\mathrm{PQ}_3$. If $1 \mathrm{~g} ~\mathrm{PQ}{ }_2$ is dissolved in 51 g benzene the depression of freezing point becomes $0 \cdot 8^{\circ} \mathrm{C}$. On the other hand if $1 \mathrm{~g} ~\mathrm{PQ}_3$ is dissolved in 51 g of benzene, the depression of freezing point becomes $0.625^{\circ} \mathrm{C}$. The atomic mass of P and Q are $\left(\mathrm{K}_{\mathrm{f}}\right.$ of benzene $=5 \cdot 1 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1})$
Q31.
mcq single
+2 / 0
Identify 'P' and 'Q' in the following reaction
Q32.
mcq single
+1 / 0.25
$$\begin{aligned}
&{ }_5 \mathrm{~B}^{10}+{ }_2 \mathrm{He}^4 \rightarrow \mathrm{X}+{ }_0 \mathrm{n}^1\\\\
&\text { In the above nuclear reaction ' } X \text { ' will be }
\end{aligned}$$
Q33.
mcq multi
+2 / 0
The compound(s) showing optical activity is/are
Q34.
mcq single
+1 / 0.25
Kjeldahl's method cannot be used for the estimation of nitrogen in which compound?
Q35.
mcq single
+1 / 0.25
An optically active alkene having molecular formula $\mathrm{C}_8 \mathrm{H}_{16}$ gives acetone as one of the products on ozonolysis. The structure of the alkene is
Q36.
mcq single
+1 / 0.25
Which of the following hydrocarbons reacts easily with $\mathrm{MeMgBr}$ to give methane?
Q37.
mcq single
+1 / 0.25
If three elements $A, B, C$ crystalise in a cubic solid lattice with $B$ atoms at the cubic centres, $C$ aton at the centre of edges and A atoms at the corners, then formula of the compound is
Q38.
mcq single
+1 / 0.25
The molar conductances of $\mathrm{Ba}(\mathrm{OH})_2, \mathrm{BaCl}_2$ and $\mathrm{NH}_4 \mathrm{Cl}$ at infinite dilution are $523 \cdot 28,280 \cdot 0$ and $129.8 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ respectively. The molar conductance of $\mathrm{NH}_4 \mathrm{OH}$ at infinite dilution will be
Q39.
mcq single
+1 / 0.25
Which one among the following compounds will most readily be dehydrated under acidic condition?
Q40.
mcq single
+2 / 0.5
The major product 'P' and 'Q' in the above reactions are
The major product 'P' and 'Q' in the above reactions areMathematics
Mathematics
Q1.
mcq single
+2 / 0.5
If $a, b, c$ are in A.P. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, then
Q2.
mcq single
+1 / 0.25
The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112. If its first term is 11, then the number of terms is
Q3.
mcq single
+1 / 0.25
If the sum of ' $n$ ' terms of an A.P. is $3 n^2+5 n$ and its $m$ th term is 164 , then the value of $m$ is
Q4.
mcq single
+1 / 0.25
Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors. Suppose $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$. Then $\vec{a}$ is
Q5.
mcq single
+1 / 0.25
If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the parallelogram for which $\vec{\alpha}$ and $\vec{\beta}$ are adjacent sides is
Q6.
mcq single
+1 / 0.25
If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{a} \times \vec{b}|^2=k^2-(\vec{a} \cdot \vec{b})^2$, then the values of $k$ and $\theta$ are
Q7.
mcq single
+1 / 0.25
If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}, \lambda \vec{b}+4 \vec{c}$ and $(2 \lambda-1) \vec{c}$ are non-coplanar for
Q8.
mcq single
+1 / 0.25
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ is $\alpha, \vec{b}$ and $\vec{c}$ is $\beta$ and $\vec{c}$ and $\vec{a}$ is $\gamma$. Then the minimum value of $\cos \alpha+\cos \beta+\cos \gamma$ is
Q9.
mcq single
+2 / 0
Three numbers are chosen at random without replacement from $\{1,2, \ldots 10\}$. The probability that the minimum of the chosen numbers is 3 or their maximum is 7 , is
Q10.
mcq single
+1 / 0.25
If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E / F)-P(F / E)$ equals
Q11.
mcq single
+2 / 0.5
The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is
Q12.
mcq single
+1 / 0.25
For what value of ' $a$ ', the sum of the squares of the roots of the equation $x^2-(a-2) x-a+1=0$ will have the least value?
Q13.
mcq single
+1 / 0.25
If the sum of the squares of the roots of the equation $x^2-(a-2) x-(a+1)=0$ is least for an appropriate value of the variable parameter $a$, then that value of ' $a$ ' will be
Q14.
mcq single
+1 / 0.25
The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is
Q15.
mcq single
+1 / 0.25
Let $f(x)=|1-2 x|$, then
Q16.
mcq single
+1 / 0.25
Let $f(x)$ be continuous on $[0,5]$ and differentiable in $(0,5)$. If $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq \frac{1}{5}$ for all $x$ in $(0,5)$, then $\forall x$ in $[0,5]$
Q17.
mcq single
+1 / 0.25
A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect?
Q18.
mcq single
+1 / 0.25
$\lim\limits_{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right)}{\sin ^2 x}$ equals
Q19.
mcq single
+2 / 0
Let $f:[0,1] \rightarrow \mathbb{R}$ and $g:[0,1] \rightarrow \mathbb{R}$ be defined as follows :
$\left.\begin{array}{rl}f(x) & =1 \text { if } x \text { is rational } \\ & =0 \text { if } x \text { is irrational }\end{array}\right]$ and
$\left.\begin{array}{rl}g(x) & =0 \text { if } x \text { is rational } \\ & =1 \text { if } x \text { is irrational }\end{array}\right]$ then
Q20.
mcq single
+1 / 0.25
A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$.
If the function ' $f$ ' is differentiable at $x=0$, then $f$ is
Q21.
mcq single
+2 / 0.5
Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of points in $[\alpha,\beta]$ at which $f$ is not differentiable is
Q22.
mcq single
+2 / 0.5
Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $\lim \limits_{n \rightarrow \infty} \frac{\left(a_n\right) n!}{{ }^{3 n} P_n}$ equals
Q23.
mcq single
+1 / 0.25
If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then :
Q24.
mcq single
+1 / 0.25
If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then
Q25.
mcq multi
+2 / 0
Let $f(x)=x^3, x \in[-1,1]$. Then which of the following are correct?
Q26.
mcq single
+2 / 0.5
Let $f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|$.
Suppose $A$ and $B$ are respectively maximum and minimum values of $f(\theta)$.Then $(A,B)$ is equal to
Q27.
mcq single
+1 / 0.25
Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$, then
Q28.
mcq single
+1 / 0.25
The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has
Q29.
mcq single
+1 / 0.25
Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is
Q30.
mcq single
+2 / 0.5
The maximum number of common normals of $y^2=4 a x$ and $x^2=4 b y$ is equal to :
Q31.
mcq single
+1 / 0.25
Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :
Q32.
mcq single
+1 / 0.25
If $\operatorname{adj} B=A,|P|=|Q|=1$, then $\operatorname{adj}\left(Q^{-1} B P^{-1}\right)=$
Q33.
mcq single
+1 / 0.25
If the matrix $\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)$ is orthogonal, then the values of $a, b, c$ are
Q34.
mcq single
+1 / 0.25
Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $|A|^2=25$, then $|\alpha|$ equals to
Q35.
mcq single
+1 / 0.25
Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then the rank of the matrix $\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right)$ is
Q36.
mcq single
+1 / 0.25
If for a matrix $A,|A|=6$ and adj $A=\left[\begin{array}{ccc}1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]$, then $k$ is equal to
Q37.
mcq single
+1 / 0.25
If $a, b, c$ are positive real numbers each distinct from unity, then the value of the determinant $\left|\begin{array}{ccc}1 & \log _a b & \log _a c \\ \log _b a & 1 & \log _b c \\ \log _c a & \log _c b & 1\end{array}\right|$ is
Q38.
mcq single
+2 / 0
If $P$ is a non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is 1 , then the sum of the elements of each row in $P^{-1}$ is
Q39.
mcq single
+1 / 0.25
An $n \times n$ matrix is formed using 0, 1 and $-$1 as its elements. The number of such matrices which are skew symmetric is
Q40.
mcq single
+1 / 0.25
The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is
Q41.
mcq single
+1 / 0.25
Let $f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)$, then
Q42.
mcq single
+2 / 0
If $0 \leq a, b \leq 3$ and the equation $x^2+4+3 \cos (a x+b)=2 x$ has real solutions, then the value of $(a+b)$ is
Q43.
mcq multi
+2 / 0
If the equation $\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0$ has a solution, the $p$ must lie in the interval
Q44.
mcq single
+2 / 0
The solution set of the equation $\left(x \in\left(0, \frac{\pi}{2}\right)\right) \tan (\pi \tan x)=\cot (\pi \cot x)$, is
Q45.
mcq single
+2 / 0.5
If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}, 0<\theta, \phi<\frac{\pi}{4}$, then $\cot (2 \theta)$ has the value
Q46.
mcq single
+1 / 0.25
The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $X P \cdot X Q$ is
Q47.
mcq single
+2 / 0.5
The number of solutions of $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$ is
Q48.
mcq single
+1 / 0.25
If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ is equal to
Q49.
mcq single
+1 / 0.25
If $\left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12}$, then the value of $a_2+a_4+a_6+\ldots+a_{12}$ is
Q50.
mcq single
+1 / 0.25
The line parallel to the $x$-axis passing through the intersection of the lines $a x+2 b y+3 b=0$ and $b x-2 a y-3 a=0$ where $(a, b) \neq(0,0)$ is
Q51.
mcq single
+1 / 0.25
Consider three points $P(\cos \alpha, \sin \beta), Q(\sin \alpha, \cos \beta)$ and $R(0,0)$, where $0<\alpha, \beta<\frac{\pi}{4}$. Then
Q52.
mcq single
+1 / 0.25
The number of reflexive relations on a set $A$ of $n$ elements is equal to
Q53.
mcq single
+1 / 0.25
Let $\omega(\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\left\{\mid a+b \omega+c \omega^2\right\}^2 ; a, b, c$ are distinct non-zero integers} equals
Q54.
mcq single
+2 / 0.5
If $\left|Z_1\right|=\left|Z_2\right|=\left|Z_3\right|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose vertices are $Z_1, Z_2, Z_3$ is
Q55.
mcq single
+1 / 0.25
If $z_1, z_2$ are complex numbers such that $\frac{2 z_1}{3 z_2}$ is a purely imaginary number, then the value of $\left|\frac{z_1-z_2}{z_1+z_2}\right|$ is
Q56.
mcq single
+2 / 0.5
Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to
Q57.
mcq single
+2 / 0.5
If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be
Q58.
mcq single
+2 / 0.5
If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x+1$, then
Q59.
mcq single
+1 / 0.25
If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then
Q60.
mcq single
+1 / 0.25
If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to
Q61.
mcq single
+2 / 0
The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation
$$\frac{d p(t)}{d t}=0.5 p(t)-450$$
If $p(0)=850$, then the time at which the population becomes zero is
Q62.
mcq single
+2 / 0.5
The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is
Q63.
mcq single
+2 / 0.5
Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to
Q64.
mcq single
+1 / 0.25
If ' $f$ ' is the inverse function of ' $g$ ' and $g^{\prime}(x)=\frac{1}{1+x^n}$, then the value of $f^{\prime}(x)$ is
Q65.
mcq single
+1 / 0.25
Let $f(x)$ be a second degree polynomial. If $f(1)=f(-1)$ and $p, q, r$ are in A.P., then $f^{\prime}(p), f^{\prime}(q), f^{\prime}(r)$ are
Q66.
mcq single
+1 / 0.25
If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is
Q67.
mcq single
+1 / 0.25
The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is
Q68.
mcq single
+1 / 0.25
The expression $2^{4 n}-15 n-1$, where $n \in \mathbb{N}$ (the set of natural numbers) is divisible by
Q69.
mcq single
+2 / 0
If $f(x)=\int\limits_0^{\sin ^2 x} \sin ^{-1} \sqrt{t} d t$ and $g(x)=\int\limits_0^{\cos ^2 x} \cos ^{-1} \sqrt{t} d t$, then the value of $f(x)+g(x)$ is
Q70.
mcq single
+1 / 0.25
The value of the integral $\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x$ is
Q71.
mcq single
+1 / 0.25
The value of the integral $\int\limits_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is
Q72.
mcq single
+1 / 0.25
$\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to
Q73.
mcq single
+2 / 0.5
Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{-3}^3 f(x) d x$ has the value
Q74.
mcq single
+1 / 0.25
$\int\limits_0^{1 \cdot 5}\left[x^2\right] d x$ is equal to
Q75.
mcq single
+2 / 0
The value of $\int\limits_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x$ is
Physics
Physics
Q1.
mcq single
+1 / 0.25
The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds of motion is :
Q2.
mcq single
+1 / 0.25
Which logic gate is represented by the following combinations of logic gates?
Q3.
mcq single
+1 / 0.25
A diode is connected in parallel with a resistance as shown in Figure. The most probable current (I) - voltage (V) characteristic is
Q4.
mcq single
+1 / 0.25
Manufacturers supply a zener diode with zener voltage $\mathrm{V}_{\mathrm{z}}=5.6 \mathrm{~V}$ and maximum power dissipation $P_{\mathrm{z}, \max }=\frac{1}{4} \mathrm{~W}$. This zener diode is used in the following circuit. Calculate the minimum value of the resistance $R_s$ in the circuit so that the zener diode will not burn when the input voltage is $\mathrm{V}_{\mathrm{in}}=10 \mathrm{~V}$.
Q5.
mcq single
+1 / 0.25
Six vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}$ and $\vec{f}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true?
Q6.
mcq single
+1 / 0.25
A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then
Q7.
mcq single
+1 / 0.25
A simple pendulum is taken at a place where its distance from the earth's surface is equal to the radius of the earth. Calculate the time period of small oscillations if the length of the string is 4.0 m . (Take $g=\pi^2 \mathrm{~ms}^{-2}$ at the surface of the earth.)
Q8.
mcq single
+1 / 0.25
The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass $m$ is represented by $y=2 \sin \left(\frac{\pi t}{2}+\phi\right) \mathrm{cm}$. The maximum acceleration of the particle is
Q9.
mcq single
+1 / 0.25
A ball falls from a height $h$ upon a fixed horizontal floor. The co-efficient of restitution for the collision between the ball and the floor is ' $e$ '. The total distance covered by the ball before coming to rest is [neglect the air resistance]
Q10.
mcq single
+1 / 0.25
The variation of density of a solid cylindrical rod of cross sectional area $\alpha$ and length $L$ is $\rho=\rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from one end $(x=0)$ is
Q11.
mcq single
+2 / 0.5
Temperature of a body $\theta$ is slightly more than the temperature of the surrounding $\theta_0$. Its rate of cooling $(R)$ versus temperature of the body $(\theta)$ is plotted. Its shape would be
Q12.
mcq multi
+2 / 0
Let $\bar{V}, V_{m s}, V_p$ denotes the mean speed, root mean square speed and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement(s) is/are correct?
Q13.
mcq single
+1 / 0.25
For an ideal gas, a cyclic process ABCA as shown in P-T diagram, when presented in P-V plot, would be
Q14.
mcq single
+2 / 0.5
A piece of granite floats at the interface of mercury and water contained in a beaker as in figure. If the densities of granite, water and mercury are $\rho, \rho_1$ and $\rho_2$ respectively, the ratio of the volume of granite in water to the volume of granite in mercury is
Q15.
mcq single
+1 / 0.25
One end of a stecl wire is fixed to the ceiling of an elevator moving up with an acceleration $2 \mathrm{~m} / \mathrm{s}^2$ and a load of 10 kg hangs from the other end. If the cross section of the wire is $2 \mathrm{~cm}^2$, then the longitudinal strain in the wire will be ( $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\mathrm{Y}=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )
Q16.
mcq single
+2 / 0.5
The apparent coefficient of expansion of a liquid, when heated in a copper vessel is $C$ and when heated in silver vessel is $S$. If $A$ is linear coefficient of expansion of copper, then linear coefficient of expansion of silver is
Q17.
mcq single
+1 / 0.25
Three different liquids are filled in a U-tube as shown in figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ respectively. From the figure we may conclude that
Q18.
mcq single
+1 / 0.25
An electron in Hydrogen atom jumps from the second Bohr orbit to the ground state and the difference between the energies of the two states is radiated in the form of a photon. This photon strikes a material. If the work function of the material is 4.2 eV , then the stopping potential is (Energy of electron in $n$-th orbit $\left.=-\frac{13 \cdot 6}{n^2} \mathrm{eV}\right)$
Q19.
mcq single
+1 / 0.25
The de-Broglie wavelength of a moving bus with speed $v$ is $\lambda$. Some passengers left the bus at a stoppage. Now when the bus moves with twice of its initial speed, its kinetic energy is found to be twice of its initial value. What is the de-Broglie wavelength of the bus now?
Q20.
mcq single
+2 / 0.5
$10^{20}$ photons of wavelength 660 nm are emitted per second from a lamp. The wattage of the lamp is (Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )
Q21.
mcq single
+1 / 0.25
Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $E(t)=E_0 \sin \omega t$ in the $x$-direction, where $E_0=2$ Newton/Coulomb and $\omega=1000 \mathrm{rad} / \mathrm{sec}$. The maximum speed attained by the particle is
Q22.
mcq single
+1 / 0.25
Two charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance $2 L_{\mathrm{p} p a t}$ $C$ is the mid point of $A$ and $B$. The workdone in moving a charge $+Q$ along the semicircle $\operatorname{CSD}\left(W_V\right)$ and along the line $\mathrm{CBD}\left(W_2\right)$ are
Q23.
mcq single
+1 / 0.25
What are the charges stored in the $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ capacitors in the circuit as shown in figure once the current (I) become steady?
Q24.
mcq single
+1 / 0.25
Acceleration-time $(a-t)$ graph of a body is shown in the figurd. Corresponding velocity-time $(v-t)$ graph is
Q25.
mcq single
+1 / 0.25
Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity $v_1$ in time $t_1$. On other day if she remains stationary on the escalator moving with velocity $v_2$, then escalator takes her up in time $t_2$. The time taken by her to walk up with velocity $v_1$ on the moving escalator will be
Q26.
mcq single
+1 / 0.25
Figure shows the graph of angle of deviation $\delta$ versus angle of incidence i for a light ray striking a prism. The prism angle is
Q27.
mcq single
+1 / 0.25
The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(25 \pm 0.4)$ Volt and $\mathrm{I}=(200 \pm 3)$ Ampere. The percentage error in ' $R$ ' is
Q28.
mcq multi
+2 / 0
If the dimensions of length are expressed as $G^x C^y h^z$, where $G, C$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then
Q29.
mcq single
+1 / 0.25
A quantity $X$ is given by $\varepsilon_0 L \frac{\Delta V}{\Delta t}$, where $\varepsilon_0$ is the permittivity of free space, $L$ is the length, $\Delta V$ is a potential difference and $\Delta t$ is a time interval. The dimension of $X$ is same as that of
Q30.
mcq single
+1 / 0.25
The number of undecayed nuclei $N$ in a sample of radioactive material as a function of time $(t)$ is shown in the figure. Which of the following graphs correctly show the relationship between $N$ and the activity ' $A$ '?
Q31.
mcq multi
+2 / 0
Let the binding energy per nucleon of nucleus is denoted by ' $E_{b n}$ ' and radius of the nucleus is denoted by ' $r$ '. If mass number of nuclei $A$ and $B$ are 64 and 125 respectively, then
Q32.
mcq single
+1 / 0.25
The minimum wavelength of Lyman series lines is $P$, then the maximum wavelength of these lines is
Q33.
mcq single
+1 / 0.25
A radioactive nucleus decays as follows :
$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 $$
If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the atomic number and mass number of ' $X$ ' are
Q34.
mcq multi
+2 / 0
A wave disturbance in a medium is described by $y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)$ where $x, y$ are in meters and $t$ is in second. Which statement(s) is/are correct?
Q35.
mcq single
+2 / 0.5
The equation of a stationary wave along a stretched string is given by $y=5 \sin \frac{\pi x}{3} \cos 40 \pi t$.
Here $x$ and $y$ are in cm and $t$ in second. The separation between two adjacent nodes is
Q36.
mcq single
+1 / 0.25
The minimum force required to start pushing a body up a rough (having co-efficient of friction $\mu$ ) inclined plane is $\vec{F}_1$ while the minimum force needed to prevent it from sliding is $\overrightarrow{F_2}$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta=2 \mu$, then the ratio $F_1 / F_2$ is
Q37.
mcq multi
+2 / 0
Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially $S_1$ is at rest and $S_2$ is moving with velocity $v$ along $x$-axis. After collision $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after collision
Q38.
mcq single
+1 / 0.25
A force $\vec{F}=a \hat{i}+b \hat{j}+c \hat{k}$ is acting on a body of mass $m$. The body was initially at rest at the origin. The co-ordinates of the body after time ' $t$ ' will be
Q39.
mcq single
+1 / 0.25
A particle of charge ' $q$ ' and mass ' $m$ ' moves in a circular orbit of radius ' $r$ ' with angular speed ' $\omega$ '. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on
Q40.
mcq single
+1 / 0.25
For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by