TG EAPCET 2025 (Online) 4th May Morning Shift
JEE 2025 Previous Year
3 hDuration
160Total Marks
160Questions
3Sections
Instructions
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Paper Structure
Chemistry
Chemistry
Q1.
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What is the product ' $Z$ ' in the given sequence of reactions?
Q2.
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What is the major product ' $Z$ ' in the given reaction sequence?
Q3.
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In which of the following transition metal ion (aquated) is not correctly matched with its colour?
Q4.
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Consider the following sequence of reaction
$$ 2 \mathrm{CH}_3 \mathrm{Cl}+\mathrm{Si} \xrightarrow[573 \mathrm{~K}]{\mathrm{Cu}} X \xrightarrow{\mathrm{H}_2 \mathrm{O}} Y \xrightarrow{\text { Polymerisation }} Z $$
The repeating structural unit in Z is
Q5.
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Polymer $X$ is an example of polyester and $Y$ is an example of polyamide $X$ and $Y$ are respectively
Q6.
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In which of the following the compounds are correctly arranged in the decreasing order of boiling points?
Q7.
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Arrange the following molecules in the correct order of their bond angles
$$
\mathrm{S}_8
$$
$$
P_4
$$
$$
\mathrm{S}_6
$$
$$
\mathrm{O}_3
$$
A
B
C
D
Q8.
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In which of the following options, the molecules are correctly arranged in the increasing order of their bond angles?
Q9.
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An electromagnetic radiation of wavelength 331.5 nm is made to strike the surface of a metal. Electrons are emitted with a kinetic energy of $12 \times 10^5 \mathrm{~J} \mathrm{~mol}^{-1}$. The work function (in eV ) of the metal is $\left(h=6.63 \times 10^{-34} \mathrm{Js}, N_A=6 \times 10^{23} \mathrm{~mol}^{-1}\right)$
Q10.
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The radius of second orbit of hydrogen atom is same as that of orbit ( $n$ ) of an ion ( $x$ ), $n$ and $x$ are respectively.
Q11.
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The volume of water required to dissolve $0.1 \mathrm{~g} \mathrm{PbCl}_2$ to get a saturated solution (in mL ) is (Given $K_{s p}\left(\mathrm{PbCl}_2\right)=3.2 \times 10^{-8}$; Atomic mass of $\mathrm{Pb}=207 \mathrm{u}$ )
Q12.
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The ore of which metal is concentrated by leaching?
Q13.
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$R \rightarrow P$ is a first order reaction. For this reaction a graph of $\ln [R]$ (on $y$-axis) and time (on x -axis) gave a straight line with negative slope. The intercept on $y$-axis is equal to ( $k=$ rate constant)
Q14.
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$$ \begin{aligned} &\text { Consider the following redox reaction in basic medium. }\\ &\begin{aligned} x \mathrm{Cr}(\mathrm{OH})_3+y\left(\mathrm{IO}_3\right)^{-} & +\mathrm{z}(\mathrm{OH})^{-} \rightarrow a\left(\mathrm{CrO}_4\right)^{2-}+b(\mathrm{I})^{-}+\mathrm{c}\left(\mathrm{H}_2 \mathrm{O}\right) \end{aligned} \end{aligned} $$
The incorrect option about it is
Q15.
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What are the products formed when ammonium dichromate is thermally decomposed?
Q16.
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The correct statements about the properties of colloidal solutions are
A. Tyndall effect is used to distinguish between a colloidal solution and a true solution.
B. Zeta potential is related to movement of colloidal particles.
C. Brownian motion in colloidal solution is faster if the viscosity of the solution is very high.
D. Brownian motion stabilises the sols.
Q17.
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Identify the compound $(Z)$ in the following reaction sequence
Q18.
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Match the following$$ \begin{array}{llll} \hline & \text { List-I (Element) } & & \text { List-II (Block) } \\ \hline \text { (A) } & \mathrm{Cd} & \text { I } & f \text {-block } \\ \hline \text { (B) } & \mathrm{Eu} & \text { II } & s \text {-block } \\ \hline \text { (C) } & \mathrm{Se} & \text { III } & d \text {-block } \\ \hline \text { (D) } & \mathrm{Ba} & \text { IV } & p \text {-block } \\ \hline \end{array} $$
The correct answer is
Q19.
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In long form of periodic table an element ' $E$ ' has atomic number 78 . The period and group number of the element are $x$ and $y$ respectively. $(x+y)$ is equal to
Q20.
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The entropy and enthalpy changes for the reaction $\mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g})$ at 300 K and 1 atm are respectively $-42.4 \mathrm{JK}^{-1}$ and -41.2 kJ . The temperature at which the reaction will go in the reverse direction is
Q21.
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Which purification method is generally used for a high boiling organic liquid compound which decompose below its boiling point?
Q22.
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1 mL of " $x$ volume" $\mathrm{H}_2 \mathrm{O}_2$ solution on heating gives 20 mL of oxygen gas at STP. The $(w / v) \%$ corresponding to " $x$ volume" of $\mathrm{H}_2 \mathrm{O}_2$ is
Q23.
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In a mixture of liquids $A$ and $B$, if the mole fractions of component $A$ in vapour phase and liquid mixture are $x_1$ and $x_2$ respectively, then the total vapour pressure of liquid mixture is
(Where $p_{\mathrm{A}}^0$ and $p_{\mathrm{B}}^0$ are the vapour pressure of pure $A$ and $B$ )
Q24.
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Sulphur dioxide on reaction with chlorine in the presence of charcoal gives compound $(A)$. This on reaction with white phosphorus gives $\mathrm{SO}_2$ and compound $(B)$. The correct statement about ' $B$ ' is
Q25.
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Boron trifluoride on reaction with lithium aluminium hydride in ether gives $\mathrm{LiF}^{\circ} \mathrm{AlF}_3$ and $X . X$ on reaction with $\mathrm{NH}_3$ gives $Y$. $Y$ on further heating gives a compound $Z$. The number of $\sigma$-bonds and $\pi$-bonds in $Z$ are $x$ and $y$ respectively. $(x+y)$ is equal to
Q26.
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Which one of the following complex ions is diamagnetic in nature?
Q27.
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Which of the following is not the common component of photochemical smog?
Q28.
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$$ \text { The correct IUPAC name of the following compound is } $$
Q29.
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Consider the following.
Assertion (A) Aspirin is useful in the prevention of heart attacks.
Reason (R) Aspirin acts as anti-blood clotting agent The correct answer is
Q30.
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Identify the correct statement from the following
I. LiF is less soluble in water than NaF
II. Both LiCl and $\mathrm{MgCl}_2$ are insoluble in ethanol
III. Both Li and Mg form nitrides
IV. $\mathrm{Na}_2 \mathrm{CO}_3$ gives $\mathrm{CO}_2$ on heating
Q31.
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The major ingredient $(51 \%)$ in Portland cement is
Q32.
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$$ \text { The ratio of } \sigma \text { bonds to } \pi \text { bonds in } Q \text { is } $$
Q33.
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Cumene on oxidation in air gives a compound, $X$. This on reaction with dilute acid gives $Y$ and $Z . Y$ reacts with sodium metal and not $Z$. What is $Z$ ?
Q34.
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Chlorobenzene when subjected to fittig reaction gives a compound ' $X$ '. The sum of $\sigma$ and $\pi$ - bonds in $X$ is
Q35.
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$$ \text { Match the following } $$
The correct answer is
The correct answer is
Q36.
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The force $(F)$ required to maintain the flow of layers of a liquid is equal to
( $A=$ area of contact of layers
$d z=$ distance between the layers
$d u=$ change in velocity
$\eta=$ coefficient of viscosity)
Q37.
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The general structure of alpha amino acid can be represented as
Which amino acid is not correctly matched with $R$ given?
Which amino acid is not correctly matched with $R$ given?
Q38.
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Sodium metal crystallises in a body centred cubic lattice with edge length of $x \mathop {\rm{A}}\limits^{\rm{o}}$. If the radius of sodium atom is $1.86 \mathop {\rm{A}}\limits^{\rm{o}}$ the value of $x$ is
Q39.
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A current of 0.5 ampere is passed through molten $\mathrm{AlCl}_3$ for 96.5 seconds. The mass of aluminium deposited at cathode is $x \mathrm{mg}$ and volume of chlorine liberated (at STP) at anode is $y \mathrm{~mL} . x$ and $y$ are respectively.
Q40.
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The reaction of benzene with CO and HCl in the presence of anhydrous $\mathrm{AlCl}_3$ gives a compound $X \cdot X$ can also be obtained from which of the following reaction?
Mathematics
Mathematics
Q1.
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$$ \text { The coefficient of variation for the following data is } $$
$$ \begin{array}{llllll} \hline \text { Class interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} $$
Q2.
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If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=|\mathbf{b}|=\sqrt{6}$ and $\mathbf{a} \cdot \mathbf{b}=-1$, then $|\mathbf{a} \times \mathbf{b}| \sin (\mathbf{a}, \mathbf{b})=$
Q3.
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Let $\mathbf{a}$ and $\mathbf{b}$ be two vectors such that $|\mathbf{a}|=|\mathbf{b}|$ and $|\mathbf{a}+2 \mathbf{b}|=|2 \mathbf{a}-\mathbf{b}|$. If $\mathbf{c}$ is a vector parallel to $\mathbf{a}$, then the angle between $\mathbf{b}$ and $\mathbf{c}$ is
Q4.
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If the volume of a tetrahedron having $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+p \hat{\mathbf{k}}$ as its coterminous edges is 2 , then the values of $\mathbf{p}$ are the roots of the equation
Q5.
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$A B C D$ is a tetrahedron, $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}},-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$, $3 \bar{i}+2 \bar{j}-\bar{k}$ are the the position vectors of the points $A, B$ and $C$ respectively. $-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ is the position vector of the centroid of the triangular face $B C D$. If G is the centroid of the tetrahedron, then $G D=$
Q6.
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If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=-4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ are three vectors, then $\sqrt{(|\mathbf{a}|+|\mathbf{b}|+|\mathbf{c}|)+|\mathbf{a}+\mathbf{b}+\mathbf{c}|}=$
Q7.
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If $0 \leq A, B \leq \frac{\pi}{4}$ and $\cot A+\cot B+\tan A+ \tan B=\cot A \cot B-\tan A \tan B$, then $\sin (A+B)=$
Q8.
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Number of solutions of the equation $\tan ^2 x+3 \cot ^2 x=2 \sec ^2 x$ lying in the interval $[0,2 \pi]$ is
Q9.
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If two smallest squares are chosen at random on a chess board, then the probability of getting these squares such that they do not have a side in common is
Q10.
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The range of a discrete random variable $X$ is $\{1,2,3\}$ and the probabilities of its elements are given by $P(X=1)=3 k^3, P(X=2)=2 k^2$ and $P(X=3)=7-19 \mathrm{k}$. Then, $P(X=3)=$
Q11.
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An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is
Q12.
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Among every 8 units of a product, one is likely to be defective. If a consumer has order 5 units of that product, then the probability that atmost one unit is defective among them is
Q13.
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Let $A$ and $B$ be two events in a random experiment . If $P(A \cap \bar{B})=0.1, P(\bar{A} \cap B)=0.2$ and $P(B)=0.5$, then $P(\bar{A} \cap \bar{B})=$
Q14.
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If $f(x)=x^2+b x+c$ and $f(1+k)=f(1-k) \forall k \in R$, for two real numbers $b$ and $c$ then
Q15.
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If $\alpha, \beta$ are the roots of the equation $x^2+3 x+k=0$ and $\alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta}$ are the roots of the equation $4 x^2+p x+18=0$, then $k$ satisfies the equation
Q16.
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If $\alpha, \beta, \gamma, \delta$ and $\varepsilon$ are the roots of the equation $x^5+x^4-13 x^3-13 x^2+36 x+36=0$ and $\alpha<\beta<\gamma<\delta<\varepsilon$ then $\frac{\varepsilon}{\alpha}+\frac{\delta}{\beta}+\frac{1}{\gamma}=$
Q17.
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If one of the roots of the equation $6 x^3-25 x^2+2 x+8=0$ is an integer and $\alpha>0, \beta<0$ are the other two roots, then $\frac{4}{\alpha}+\frac{1}{\beta}=$
Q18.
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If $f(x)$ is a second degree polynomial such that $f(x) \geq 0 \forall x \in R, f(-3)=0$ and $f(0)=18$, then $f(3)=$
Q19.
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If $x=\log _e 3$, then $\tanh 2 x+\operatorname{sech} 2 x=$
Q20.
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If $\cos \theta+\sin \theta=\sqrt{2} \cos \theta$ and $0<\theta<\frac{\pi}{2}$, then $\sec 2 \theta+\tan 2 \theta=$
Q21.
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$K=\left|\begin{array}{cc}3 & 4 \\ 5 & 4\end{array}\right|+\left|\begin{array}{cc}1 & -1 \\ 5 & 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{3} & \frac{1}{4} \\ 5 & 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{9} & -\frac{1}{16} \\ 5 & 4\end{array}\right|+\ldots$ to $\infty$, then $K=$
Q22.
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$t_1, t_2, t_3, \ldots, t_n$ are positive integers, $S_n=t_1+t_2+t_3+\ldots+t_n$, $S_1=1^2, S_2=3^2, S_3=6^2, S_4=10^2, S_5=15^2$ and similarly other terms are there. Following this pattern, if $S_{10}=k^2$ then $k=$
Q23.
mcq single
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If $[x]$ is the greatest integer function and
$$ f(x)=\left\{\begin{array}{cc} 2[x]-\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0 \end{array}\right. $$
is a real valued function, then $f$ is
Q24.
mcq single
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If $\mathop {\lim }\limits_{x \to 0} \frac{3^{x^3}-\left(1-x^3\right)^{\frac{2}{3}}}{x^2 \sin x}=p+\log q$, then $p q=$
Q25.
mcq single
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The real valued function $f(x)=\frac{x^2}{2}-\log \left(x^2+x+1\right)$ is
Q26.
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If $x=2 \sqrt{2} \sqrt{\cos 2 \theta}$ and $y=2 \sqrt{2} \sqrt{\sin 2 \theta}, 0<\theta<\frac{\pi}{4}$, then the value of $\frac{d y}{d x}$ at $\theta=22 \frac{1}{2}^{\circ}$ is
Q27.
mcq single
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A rod of length 41 m with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \mathrm{fit} / \mathrm{min}$. When the end $B$ is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in $\mathrm{ft} / \mathrm{min}$ )
Q28.
mcq single
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If the extreme values of the function $f(x)=(2 \sqrt{6}+1) \cos x+(2 \sqrt{2}-\sqrt{3}) \sin x-6$ are $m$ and $M$ then $\sqrt{\left|M^2-m^2\right|}=$
Q29.
mcq single
+1 / 0
There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm . If the semi-vertical angle of the cone is $45^{\circ}$, then the approximate error in its volume is (in $\mathrm{cu} . \mathrm{cm}$ )
Q30.
mcq single
+1 / 0
If $x$ and $y$ are two positive real numbers such that $x y=4$, then the minimum value of $\left(\sqrt{x}+\frac{y^2}{2}\right)$ is
Q31.
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If the curves $y^2=12 x-3$ and $y^2=12-k x$ cut each other orthogonally, then the length of the sub-tangent at $(1, b)$ on the curve $y^2=12-k x$ is
Q32.
mcq single
+1 / 0
If $x=\alpha, y=\beta, z=\gamma$ is the solution of the system of equations $2 x+3 y+z=-1,3 x+y+z=4$, $x-3 y-2 z=1$, then the value of $\beta$ is
Q33.
mcq single
+1 / 0
If $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1\end{array}\right]$ then $|\operatorname{adj}|\left(A^2\right) \mid=$
Q34.
mcq single
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The positive value of ' $a$ ' for which the system of linear homogeneous equations $x+a y+z=0, a x+2 y-z=0$, $2 x+3 y+z=0$ has non-trivial solution is
Q35.
mcq single
+1 / 0
The equation of the locus of a point whose distance from $X Y$-plane is twice its distance from $Z$-axis is
Q36.
mcq single
+1 / 0
If the angle between the planes $a x-y+3 z=2 a$ and $3 x+a y+z=3 a$ is $\frac{\pi}{3}$, then the direction ratio of the line perpendicular to the plane $(a+2) x+(a-4) y+2 a z=a$ are
Q37.
mcq single
+1 / 0
If $\alpha$ is the angle between any two diagonals of a cube and $\beta$ is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube, then $\cos \alpha+\cos ^2 \beta=$
Q38.
mcq single
+1 / 0
If $L(p, q), q>3$ is one end of the latus rectum of the parabola $(y-2)^2=3(x-1)$, then the equation of the tangent at $L$ to this parabola is
Q39.
mcq single
+1 / 0
A normal chord $P Q$ drawn at a point $P$ on the parabola $y^2=5 x$ subtends a right angle at the vertex. If $P$ lies in the first quadrant, then the other end $Q$ of the normal chord is
Q40.
mcq single
+1 / 0
$$ \sin ^{-1}(-\cos 2)+\cos ^{-1}(\sin 3)+\tan ^{-1}(\cot 5)= $$
Q41.
mcq single
+1 / 0
The domain of the derivative of the function $f(x)=\cos ^{-1}(2 x-5)-\sin ^{-1}(x-2)$ is
Q42.
mcq single
+1 / 0
If $C_0, C_1, C_2, \ldots, C_{10}$ represent the binomial coefficients in the expansion of $(1+x)^{10}$, then
$$ C_0 C_6+C_1 C_7+C_2 C_8+C_3 C_9+C_4 C_{10}= $$
Q43.
mcq single
+1 / 0
When $|x|<\frac{1}{2}$ the coefficient of $x^6$ in the expansion of $\left(\frac{2-x}{1+2 x}\right)^2$ is
Q44.
mcq single
+1 / 0
If $(-1,-1)$ is the point of intersection of the pair of lines $2 x^2+5 x y-3 y^2+2 g x+2 f y+c=0$. Then $g+f$
Q45.
mcq single
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$(a, b)$ are the new coordinates of the point $(2,3)$ after shifting the origin to the point $(3,2)$ by translation of axes. If $(c, d)$ are the new coordinates of the point $(a, b)$ after rotating the axes through an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction, then $d-c=$
Q46.
mcq single
+1 / 0
The area of the quadrilateral formed by the lines $x+2 y+3=0,2 x+4 y+9=0, x-2 y+3=0$ and $3 x-6 y+11=0$
Q47.
mcq single
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The lines $x+y+4=0, x-2 y-4=0$ and $3 x+4 y-2=0$
Q48.
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The area of the triangle formed by the line $L$ with the coordinate axes is 12 sq. units. If $L$ passes through the point $(12,4)$ and the product $P$ of $X$ - intercept of $L$ and square of the $Y$-intercept of $L$ is negative, then $P=$
Q49.
mcq single
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$$ (1-i \sqrt{3})^{2025}= $$
Q50.
mcq single
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One of the roots of the equation $(x+1)^4+81=0$ is
Q51.
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Let $z=x+i y$ represent a point of $P(x, y)$ in the argand plane. If $z$ satisfies the condition that amplitude of $\frac{z-3}{z-2 i}=-\frac{\pi}{2}$ then the locus of $P$ is
Q52.
mcq single
+1 / 0
$$ \left(\frac{1+i}{1-i}\right)^{228}= $$
Q53.
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+1 / 0
If $A=(0,1), B=(1,2), C=(-2,1)$, then the equation of the locus of a point $P$ such that area of $\triangle P A B=$ area of $\triangle P A C$ is
Q54.
mcq single
+1 / 0
If the latus rectum through one of the foci of a hyperbola $\frac{x^2}{9}-\frac{y^2}{b^2}=1$ subtends a right angle at the farther vertex of the hyperbola, then $b^2=$
Q55.
mcq single
+1 / 0
If $\frac{x+1}{x^3(x-1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3}+\frac{d}{x-1}$, then
Q56.
mcq single
+1 / 0
The domain of the real valued function $f(x)=\log _{\sqrt{2}}\left(\sqrt{x^2+x}+\sqrt{x^2-x}\right)$ is
Q57.
mcq single
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The differential equation corresponding to the family of ellipses $\frac{x^2}{a^2}+\frac{y^2}{4}=1$, where ' $a$ ' is an arbitrary constant is
Q58.
mcq single
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If $y=f(x)$ is the solution of the differential equation $\left(1+\cos ^2 x\right) f^{\prime}(x)-4 \sin 2 x-f(x) \sin 2 x=0$ when $f(0)=0$, then $f\left(\frac{\pi}{3}\right)=$
Q59.
mcq single
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The power of a point $(2,-1)$ with respect to a circle $C$ of radius 4 is 9 . The centre of the circle $C$ lies on the lines $x+y=0$ and in the 2nd quadrant. If ( $\alpha, \beta$ ) is the centre of the circle $C$ then $\beta-\alpha=$
Q60.
mcq single
+1 / 0
If the line $x+y=2$ cuts the circle $x^2+y^2+2 x-4 y+4=0$ at two points $A$ and $B$, then the radius of the circle passing through $A, B$ and orthogonal to $x^2+y^2-2 x-4 y-4=0$ is
Q61.
mcq single
+1 / 0
The angle between the tangents drawn from the point $P(k, 6 k)$ to the circle $x^2+y^2+6 x-6 y+2=0$ is $2 \tan ^{-1}\left(\frac{4}{3}\right)$. If the coordinates of $P$ are integers, then $k=$
Q62.
mcq single
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If the length of the chord $2 x+3 y+k=0$ of the circle $x^2+y^2-2 x+4 y-11=0$ is $2 \sqrt{3}$, then the sum of all possible values of $k$ is
Q63.
mcq single
+1 / 0
The tangents drawn from a point $(2,-1)$ touch the circle $x^2+y^2+4 x-2 y+1=0$ at the points $A$ and $B$. If $C$ is the centre of the circle, then the area (in sq. units) of the $\triangle A B C$ is
Q64.
mcq single
+1 / 0
If $\theta$ is the angle between the circles $x^2+y^2-4 x+2 y-4=0$ and $x^2+y^2-2 x+4 y-11=0$ then $\sin \theta=$
Q65.
mcq single
+1 / 0
Let $e$ be the eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.
If $a=5, b=4$ and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is $l x+m y=27$ then $l+m=$
Q66.
mcq single
+1 / 0
If $P$ is any point on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $S, S^{\prime}$ are its foci, then the maximum area (in sq. units) of $\triangle S P S^{\prime}=$
Q67.
mcq single
+1 / 0
If $y=x^{\log x}+(\log x)^x, x>1$, then $\left(\frac{d y}{d x}\right)_{x=e}=$
Q68.
mcq single
+1 / 0
If $y=\tan ^2\left(\cos ^{-1} \sqrt{\frac{1+x^2}{2}}\right)$, then $\frac{d y}{d x}=$
Q69.
mcq single
+1 / 0
$$ { }^{20} P_5-{ }^{19} P_5= $$
Q70.
mcq single
+1 / 0
5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is
Q71.
mcq single
+1 / 0
All possible words (with or without meaning) the contain the word 'GENTLE' are formed using all the letters of the word 'INTELLIGENCE'. Then, the number of words in which the word 'GENTLE' appears among the first nine positions only is
Q72.
mcq single
+1 / 0
$$ \int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}= $$
Q73.
mcq single
+1 / 0
$$ \int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x= $$
Q74.
mcq single
+1 / 0
$$ \int_0^{\frac{\pi}{2}} \sqrt{\tan x d x}= $$
Q75.
mcq single
+1 / 0
Let $p_1, p_2$ and $p_3$ be the altitudes of a $\triangle A B C$ drawn through the vertices $A, B$ and $C$ respectively. If $r_1=4$, $r_2=6, r_3=12$ are the ex-radii of $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$
Q76.
mcq single
+1 / 0
If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then $\cot A+\cot B+\cot C=$
Q77.
mcq single
+1 / 0
$$ \int \frac{x+\cos x}{1-\sin x} d x= $$
Q78.
mcq single
+1 / 0
If $I_1=\int \sin ^6 x d x$ and $I_2=\int \cos ^6 x d x$, then $I_1+I_2=$
Q79.
mcq single
+1 / 0
If $\int \frac{1}{(x+2) \sqrt{x^2+x+2}} d x=$
Q80.
mcq single
+1 / 0
If $\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+C$, then $f(\mathrm{l})+g(\mathrm{l})=$
Physics
Physics
Q1.
mcq single
+1 / 0
The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass 2.96 kg and density $7.4 \mathrm{~g} \mathrm{~cm}^{-3}$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )
Q2.
mcq single
+1 / 0
When two light waves of equal intensity superimpose, the maximum intensity obtained is $I$. If the intensity of one of the waves is quadrupled, then the maximum intensity obtained is
Q3.
mcq single
+1 / 0
Match the "Technology" given in List-I with the "Principle of physics" given in List-II.
$$ \begin{array}{l|l|l|l} \hline & \text { List-I (Technology) } & & \text { List-II (Principle of physics) } \\ \hline \text { (A) } & \text { Steam engine } & \text { I } & \begin{array}{l} \text { Magnetic confinement of } \\ \text { plasma } \end{array} \\ \hline \text { (B) } & \text { Electron microscope } & \text { II } & \text { Laws of thermodynamics } \\ \hline \text { (C) } & \text { Non-reflecting coatings } & \text { III } & \text { Wave nature of electrons } \\ \hline \text { (D) } & \text { Tokamak } & \text { IV } & \text { Interference of light } \\ \hline \end{array} $$
Q4.
mcq single
+1 / 0
If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0, A_1$ and $A_2$ respectively, then the amplitude of the oscillator at a time of $\left(t_1+t_2\right)$ is
Q5.
mcq single
+1 / 0
A thin uniform wire of mass ' $m$ ' and linear density ' $\rho$ ' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is ' $m$ '
Q6.
mcq single
+1 / 0
A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is $3 \mathrm{~ms}^{-2}$, then the acceleration of the disc is
Q7.
mcq single
+1 / 0
A ball is allowed to fall freely from a height of 42 m form the ground. If the coefficient of restitution between the ball and the ground is 0.4 , then the total distance travelled by the ball before it comes to rest is
Q8.
mcq single
+1 / 0
The radius of a coil of $N$ turns is $R$. If the plane of the coil is placed parallel to a uniform magnetic field $B$, then the flux linked with the coil is
Q9.
mcq single
+1 / 0
A circular path of radius 75 m is banked at an angle of $\tan ^{-1}(0.2)$. If the coefficient of static friction between the tyres of the car and the circular path is 0.1 , then the maximum permissible speed of the car to avoid slipping is
Q10.
mcq single
+1 / 0
If the temperature of a gas is increased from $127^{\circ} \mathrm{C}$ to $527^{\circ} \mathrm{C}$, then the rms speed of the gas molecules
Q11.
mcq single
+1 / 0
The temperature of a body shown by a faulty Celsius thermometer is $49^{\circ} \mathrm{C}$ and by a correct Fahrenheit thermometer is $122^{\circ} \mathrm{F}$. The correction to be applied to the faulty thermometer is
Q12.
mcq single
+1 / 0
The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is
Q13.
mcq single
+1 / 0
If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 \mathop {\rm{A}}\limits^{\rm{o}}$, the intensity of radiation emitted by it is
(Stefan-Boltzmann's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$ and Wein's constant $=2.9 \times 10^{-3} \mathrm{mK}$ )
Q14.
mcq single
+1 / 0
When ' $n$ ' identical mercury drops combine to form a single big drop
Q15.
mcq single
+1 / 0
The work done to accelerate an electron from rest so that it can have a de-Broglie wavelength of $6600 \mathop {\rm{A}}\limits^{\rm{o}}$ is nearly
(Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ and mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ )
Q16.
mcq single
+1 / 0
The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{-7} \mathrm{~cm}^{-1}$ at a radial distance of $x$ from the wire is $7.5 \times 10^4 \mathrm{NC}^{-1}$. Then, $x=$
Q17.
mcq single
+1 / 0
A meteor of mass ' $m$ ' having a speed ' $V$ ' at infinity reaches the surface of the Earth with a speed of ( $v_c$ is escape speed from the Earth's surface)
Q18.
mcq single
+1 / 0
A parallel plate capacitor of capacitance $10 \mu \mathrm{~F}$ is charged by a 220 V supply. The capacitor is then disconnected from the supply and is connected to another uncharged parallel plate capacitor of capacitance $12 \mu \mathrm{~F}$. The loss of electrostatic energy in this process is
Q19.
mcq single
+1 / 0
If the rate of change of electric field across the plates of a parallel plate capacitor is $E$ and the displacement current is $I$, then the area of one plate of the capacitor is ( $\varepsilon_0$ is permittivity of free space)
Q20.
mcq single
+1 / 0
If the distances of the object and its real image from the principal focus of a concave mirror are 16 cm and 9 cm respectively, then the focal length of the mirror is
Q21.
mcq single
+1 / 0
If the angle of minimum deviation produced by an equilateral prism is equal to the angle of the prism, then the refractive index of the material of the prism is nearly
Q22.
mcq single
+1 / 0
The number of turns of two circular coils $A$ and $B$ are 300 and 200 respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1: 2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is
Q23.
mcq single
+1 / 0
Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm , then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current is
Q24.
mcq single
+1 / 0
The radio horizon of a transmitting antenna of height 39.2 m is (Radius of the Earth $=6400 \mathrm{~km}$ )
Q25.
mcq single
+1 / 0
A wooden block of outer volume 1 litre and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then, the volume of the cavity is
Q26.
mcq single
+1 / 0
The relation between the displacement ' $x$ ' (in metre) and the time ' $t$ ' (in second) of a particle is $t=2 x^2+3 x$. If the displacement of the particle is 25 cm from the origin $(x=0)$, then the acceleration of the particle is
Q27.
mcq single
+1 / 0
If the ratio of the mass numbers of two nuclei is $27: 125$, then the ratio of their surface areas is
Q28.
mcq single
+1 / 0
If $87.5 \%$ of atoms of a radioactive element decay in 6 days, then the fraction of atoms of the element that decay in 8 days is
Q29.
mcq single
+1 / 0
If the total energy of an electron in an orbit is positive, then
Q30.
mcq single
+1 / 0
A body projected at certain angle $\left(\neq 90^{\circ}\right)$ from the ground crosses a point in its path at a time of 2.3 s and from there it reaches the ground after a time of 5.7 s . The maximum heigh reached by the body is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
Q31.
mcq single
+1 / 0
An air column in a tube of length 50 cm , closed at one end is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at 42 cm from the open end is
Q32.
mcq single
+1 / 0
A metal rod of length 125 cm is clamped at its midpoint. If the speed of the sound in the metal is $5000 \mathrm{~ms}^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is
Q33.
mcq single
+1 / 0
A horizontal force of 10 N is applied on a block of mass 1.5 kg which is initially at rest on a rough horizontal surface. The work done by the applied force in a time of 6 s from the beginning of the motion is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$; the coefficient of kinetic friction between the block and the surface is 0.2)
Q34.
mcq single
+1 / 0
A short bar magnet of magnetic moment $2.5 \mathrm{Am}^2$ is kept in a uniform magnetic field of $4 \times 10^{-5} \mathrm{~T}$. The work done in moving the magnet from its most stable position to most unstable position is
Q35.
mcq single
+1 / 0
The lengths of two wires made of the same material are in the ratio $2: 3$ and their radii are in the ratio $1: 2$. If the two wires are connected in parallel to a battery, then the ratio of the drift velocities of free electrons in the two wires is
Q36.
mcq single
+1 / 0
In a potentiometer experiment for the determination of the internal resistance of a cell, when an external resistance of $R$ is connected parallel to the cell, the balancing length decreases by $10 \%$. The internal resistance of the cell is
Q37.
mcq single
+1 / 0
In an experiment, the coefficient of viscosity (in $\mathrm{mPa} . \mathrm{s})$ of a liquid was determined as $2.62,2.68,2.58$, $2.57,2.54$ and 2.55 . The mean absolute error in the determination of the coefficient of viscosity of the liquid is
Q38.
mcq single
+1 / 0
Three logic gates are connected as shown in the figure. If the inputs are $A=1, B=0$ and $C=1$, then the values of $y_1, y_2$ and $y_3$ respectively are
Q39.
mcq single
+1 / 0
At absolute zero temperature, a semiconductor behaves like
Q40.
mcq single
+1 / 0
The inductance $L$, capacitance $C$ and resistance $R$ are the values of the components connected in series to an AC source of angular frequency $\omega$. The inductive and capacitive reactances are $X_L$ and $X_C$ respectively. If the circuit is purely resistive, then