TG EAPCET 2025 (Online) 3rd May Morning Shift
JEE 2025 Previous Year
3 hDuration
159Total Marks
159Questions
3Sections
Instructions
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Paper Structure
Chemistry
Chemistry
Q1.
mcq single
+1 / 0
The reagent which is used to distinguish primary, secondary and tertiary amines from the mixture is
Q2.
mcq single
+1 / 0
$E_{\mathrm{M}^{3}| \mathrm{M}^{2+}}^{\circ}($ in V$)$ is highest for
Q3.
mcq single
+1 / 0
Neoprene is the polymer of a monomer $X$. IUPAC name of $X$ is
Q4.
mcq single
+1 / 0
The sum of bond order of $\mathrm{O}_2^{+}, \mathrm{O}_2^{-}, \mathrm{O}_2$ and $\mathrm{O}_2^{2+}$ is equal to
Q5.
mcq single
+1 / 0
Observe the following statements
Statement-I Hybridisation is not same in both $\mathrm{SF}_6$ and $\mathrm{BrF}_5$.
Statement-II $\mathrm{BrF}_5$ is square pyramidal while $\mathrm{SF}_6$ is octahedral in shape.
The correct answer is
Q6.
mcq single
+1 / 0
The energy associated with electron in first orbit of hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. The frequency of the light required (in Hz ) to excite the electron to fifth orbit is ( $h=6.6 \times 10^{-34} \mathrm{Js}$ )
Q7.
mcq single
+1 / 0
In $\mathrm{Sr}(Z=38)$, the number of electrons with $l=0$ is $x$, number of electrons with $l=2$ is $y \cdot(x-y)$ is equal to ( $l=$ Azimuthal quantum number)
Q8.
mcq single
+1 / 0
200 mL of an aqueous solution of $\mathrm{HCl}(\mathrm{pH}=2)$ is mixed with 300 mL of aqueous solution of NaOH $(\mathrm{pH}=12)$ and is diluted to 1.0 L . The pH of the resulting solution is ( $\mathrm{pH}=2$ )
Q9.
mcq single
+1 / 0
In the extraction of iron using blast furnace to remove the impurity $(X)$, chemical $(Y)$ is added to the ore. $X$ and $Y$ are respectively
Q10.
mcq single
+1 / 0
For a first order decomposition of a certain reaction, rate constant is given by the equation. $\log k\left(s^{-1}\right)=7.14-\frac{1 \times 10^4 \mathrm{~K}}{T}$. The activation energy of the reaction ( in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) is
$$ \left(R=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right) $$
Q11.
mcq single
+1 / 0
What is the product ' $Z$ ' in the following reaction sequence?
$$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}_2 \mathrm{Cl} \xrightarrow[\mathrm{HCl}]{\mathrm{Cu}_2 \mathrm{Cl}_2} X \xrightarrow[\text { Na/dry ether }]{\mathrm{CH}_3 \mathrm{Cl}} Y \xrightarrow[\text { Dark }]{\mathrm{Cl}_2 / \mathrm{Fe}} Z $$
Q12.
mcq single
+1 / 0
The empirical formula of the compound ' $D$ ' formed in the given reaction sequence is
$$ \mathrm{C}_2 \mathrm{H}_4 \xrightarrow{\mathrm{Br}_2 / \mathrm{CCl}_4} A \xrightarrow[\text { (ii) } \mathrm{NaNH}_2]{\text { (i) } \mathrm{Alc} \cdot \mathrm{KOH}} B \xrightarrow[\text { polymerisation }]{\text { Cyclic }} C \xrightarrow[\text { DryAlCla }{ }_3 \text {, dark.cold }]{\mathrm{Cl}_2 \text { (excess) }} $$
Q13.
mcq single
+1 / 0
Observe the following data ( $\Delta_t H_1, \Delta_t H_2$ and $\Delta_{\mathrm{eg}} H$ represent the first, second ionisation enthalpies and electron gain enthalpy respectively)
$$
\text { Element }
$$
$$
\Delta_l H_1\left(\mathrm{kJmol}^{-1}\right)
$$
$$
\Delta_1 H_2\left(\mathrm{kJmol}^{-1}\right)
$$
$$
\Delta_{\mathrm{eg}} H\left(\mathrm{kJmol}^{-1}\right)
$$
I
520
7300
-60
II
490
3051
-48
III
1681
3374
-328
IV
2372
5251
+48
Using the data identify the most reactive metal.
Q14.
mcq single
+1 / 0
$$ \text { Match the following. } $$
$$
\text { List-I (Element) }
$$
$$
\text { List-II }\left(\Delta_{\mathrm{e}g} H\right) \text { (in } \mathrm{kJmol}^{-1} \text { ) }
$$
A.
O
I.
-200
B.
F
II.
-349
C.
Cl
III.
-141
D.
S
IV.
-328
V.
+48
The correct answer is
Q15.
mcq single
+1 / 0
At 298 K , if the standard Gibbs energy change $\Delta_r G^{\circ}$ of a reaction is -115 kJ , the value of $\log _{10} K_p$ will be $\left(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$
Q16.
mcq single
+1 / 0
Which one of the following mixtures can be separated by steam distillation technique?
Q17.
mcq single
+1 / 0
Observe the following data given in the table ( $K_H=$ Henry's law constant)$$ \begin{aligned} &\begin{array}{ccccc} \hline \text { Gas } & \mathrm{CO}_2 & \mathrm{Ar} & \mathrm{HCHO} & \mathrm{CH}_4 \\ \hline\left(\boldsymbol{K}_{\mathrm{H}} \text { bar at } \mathbf{2 9 8 ~ K}\right) & 1.67 & 40.3 & 1.83 \times 10^{-5} & 0.413 \\ \hline \end{array}\\ &\text { The correct order of their solubility in water is } \end{aligned} $$
Q18.
mcq single
+1 / 0
Which of the following is an incorrect statement about the compounds of group 13 elements?
Q19.
mcq single
+1 / 0
Consider the following.
Assertion (A) Phosphorus can form both phosphorus (III) and phosphorus (V) chlorides but nitrogen cannot form nitrogen (V) chloride.
Reason (R) The electronegativity of nitrogen is more than that of phosphorus.
The correct answer is
Q20.
mcq single
+1 / 0
Identify the electron rich hydrides from the following
Q21.
mcq single
+1 / 0
Which one of the following statements is not correct?
Q22.
mcq single
+1 / 0
The incorrect statement about the oxidation states of group 14 elements is
Q23.
mcq single
+1 / 0
Thionyl chloride on reaction with white phosphorus gives a compound of phosphorus ' $C$ ' which on hydrolysis gives an oxo acid ' $O$ '. The correct statement about $C$ and $O$ are
I. Shape of ' $C$ ' is pyramidal
II. ' $O$ ' is a dibasic acid
III. ' $O$ ' is a monobasic acid
IV. ' $C$ ' on reaction with acetic acid given ' $O$ '
Q24.
mcq single
+1 / 0
Arrange the following complexes in the increasing order of their spin only magnetic moment (in B.M)
I. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$
II. $\left[\mathrm{MnCl}_4\right]^{2-}$
III. $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{4-}$
IV. $\left.\left[\mathrm{Cr}(\mathrm{NH})_3\right)_6\right]^{3+}$
Q25.
mcq single
+1 / 0
In drinking water, if the maximum prescribed concentration of copper is $x \mathrm{mgdm}^{-3}$, the maximum prescribed concentration of zinc will be
Q26.
mcq single
+1 / 0
$$ \text { The IUPAC name of the following compound is } $$
Q27.
mcq single
+1 / 0
$$ \text { Match the following } $$
$$
\text { List-I (Chemical) }
$$
$$
\text { List-II (Type) }
$$
A
Bithionol
I
$$
\text { Artificial sweetener }
$$
B
Saccharin
II
Antifertility drug
C
Sodium benzoate
III
Antiseptic
D
Norethindrone
IV
Food preservative
The correct answer is
Q28.
mcq single
+1 / 0
Identify the incorrect match with respect to compounds to be distinguished and reagent used
Q29.
mcq single
+1 / 0
In which of the following, intramolecular hydrogen bonding is present?
Q30.
mcq single
+1 / 0
An alkyne has the molecular formula $\mathrm{C}_6 \mathrm{H}_{10}$. The number of 1 -alkyne isomers (excluding stereoisomers) possible for it is
Q31.
mcq single
+1 / 0
At $T(\mathrm{~K})$ root mean square (rms) velocity of argon (molar mass $40 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is $20 \mathrm{~ms}^{-1}$. The average kinetic energy of the same gas at $T(\mathrm{~K})$ (in $\mathrm{J} \mathrm{mol}^{-1}$ ) is
Q32.
mcq single
+1 / 0
On prolonged heating with HI , glucose gives a compound ' $C$ ' which can be obtained by Wurtz reaction using sodium metal and compound ' $D$ ' . Identify ' $D$ '
Q33.
mcq single
+1 / 0
The source of an enzyme is malt and that enzyme converts $X$ into $Y . X$ and $Y$ respectively are
Q34.
mcq single
+1 / 0
A metal crystallises in two cubic phases, fcc and bcc with edge lengths $3.5 \mathop {\rm{A}}\limits^{\rm{o}}$ and $3 \mathop {\rm{A}}\limits^{\rm{o}}$ respectively. The ratio of densities of fcc and bcc is approximately
Q35.
mcq single
+1 / 0
The incorrect statement about Castner-kellner cell process is
Q36.
mcq single
+1 / 0
The Gibbs energy change of the reaction (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) corresponding to the following cell
$\mathrm{Cr}\left|\mathrm{Cr}^{3+}(0.1 \mathrm{M}) \| \mathrm{Fe}^{2+}(0.001 \mathrm{M})\right| \mathrm{Fe}$
(Given $E_{\mathrm{Cr}^{3+} \mid \mathrm{Cr}}^{\circ}=-0.75 \mathrm{~V} ; E_{\mathrm{Fe}^{2+} \mid \mathrm{Fe}}^{\circ}=-0.45 \mathrm{~V}$,
$\left.\mathrm{IF}=96,500 \mathrm{C} \mathrm{mol}^{-1}\right)$
Q37.
mcq single
+1 / 0
The incorrect statement about Castner-kellner cell process is
Q38.
mcq single
+1 / 0
Identify the compounds $A$ and $B$ involved in the formation of given aldol
Q39.
mcq single
+1 / 0
The products $C$ and $D$ are
Mathematics
Mathematics
Q1.
mcq single
+1 / 0
If a possion variate $X$ satisfies the relation $P(X=3)=P(X=5)$, then $P(X=4)=$
Q2.
mcq single
+1 / 0
The variance of the discrete data $3,4,5,6,7,8,10,13$ is
Q3.
mcq single
+1 / 0
If $\mathbf{a}=(x+2 y-3) \hat{\mathbf{i}}+(2 x-y+3) \hat{\mathbf{j}}$ and $\mathbf{b}=(3 x-2 y) \hat{\mathbf{i}} +(x-y+1) \hat{\mathbf{j}}$ are two vectors such that $\mathbf{a}=2 \mathbf{b}$, then $y-5 x=$
Q4.
mcq single
+1 / 0
Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+p \hat{\mathbf{k}}$ be two vectors.
If $(\mathbf{a}, \mathbf{b})=60^{\circ}$, then $p=$
Q5.
mcq single
+1 / 0
If $\mathbf{a}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-10 \hat{\mathbf{k}}$ are two vectors, then the component of $\mathbf{b}$ perpendicular to $\mathbf{a}$ is
Q6.
mcq single
+1 / 0
$7 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}, \hat{\mathbf{i}}-6 \hat{\mathbf{j}}+10 \hat{\mathbf{k}},-\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are the position vectors of the points $A, B, C$ and $D$ respectively. If $p \hat{\mathbf{i}}+q \hat{\mathbf{j}}+r \hat{\mathbf{k}}$ is the position vector of the point of intersection of the diagonals of the quadrilateral $A B C D$, then $p+q+r=$
Q7.
mcq single
+1 / 0
Number of solutions of the equation $\sin ^2 \theta+2 \cos ^2 \theta-\sqrt{3} \sin \theta \cos \theta=2$ lying in the interval ( $-\pi, \pi$ ) is
Q8.
mcq single
+1 / 0
If $\cos \alpha+\cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+\sin \gamma$, then $\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma=$
Q9.
mcq single
+1 / 0
If $X$ is a random variable with probability distribution $P(X=k)=\frac{(2 k+3) c}{3^k}, k=0,1,2, \ldots .$. to $\infty$, then $P(X=3)=$
Q10.
mcq single
+1 / 0
If a coin is tossed seven times, then the probability of getting exactly three heads such that number two heads occur consecutively is
Q11.
mcq single
+1 / 0
If a number $x$ is drawn randomly from the set of numbers $\{1,2,3, \ldots ., 50\}$, then the probability that number $x$ that is drawn satisfies the inequation $x+\frac{10}{x} \leq 11$ is
Q12.
mcq single
+1 / 0
Two cards are drawn randomly from a pack of 52 playing cards one after the other with replacement. If $A$ is the event of drawing a face card in first draw and $B$ is the event of drawing a clubs card in second draw, then $P\left(\frac{\bar{B}}{A}\right)=$
Q13.
mcq single
+1 / 0
If both roots of the equation $x^2-5 a x+6 a=0$ exceed 1 , then the range of ' $a$ ' is
Q14.
mcq single
+1 / 0
The equation having the multiple root of the equation $x^4+4 x^3-16 x-16=0$ as its roots is
Q15.
mcq single
+1 / 0
If the equations $x^2+p x+2=0$ and $x^2+x+2 p=0$ have a common root, then the sum of the roots of the equation $x^2+2 p x+8=0$ is
Q16.
mcq single
+1 / 0
If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4-4 x^3+3 x^2+2 x-2=0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha+2 \beta+\gamma^2+\delta^2=$
Q17.
mcq single
+1 / 0
If $3 \sin \theta+4 \cos \theta=3$ and $\theta \neq(2 n+1) \frac{\pi}{2}$, then $\sin 2 \theta=$
Q18.
mcq single
+1 / 0
$16 \sin 12^{\circ} \cos 18^{\circ} \sin 48^{\circ}=$
Q19.
mcq single
+1 / 0
$$ \frac{\cos 15^{\circ} \cos ^2 22 \frac{1^{\circ}}{2}-\sin 75^{\circ} \sin ^2 \cdot 52 \frac{1^{\circ}}{2}}{\cos ^2 15^{\circ}-\cos ^2 75^{\circ}} $$
Q20.
mcq single
+1 / 0
If $\frac{1}{2 \cdot 7}+\frac{1}{7 \cdot 12}+\frac{1}{12 \cdot 17}+\frac{1}{17 \cdot 22}+\ldots$ to 10 terms $=k$, then $k=$
Q21.
mcq single
+1 / 0
If $\{x\}=x-[x]$, where $[x]$ is the greatest integer $\leq x$ and $\mathop {\lim }\limits_{x \to {0^ - }} \frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^4}=\theta$, then $\tan \theta$
Q22.
mcq single
+1 / 0
The value of $x$ at which the real valued function $f(x)=7|2 x+1|-19|3 x-5|$ is not differentiable is
Q23.
mcq single
+1 / 0
For $a \neq 0$ and $b \neq 0$, if the real valued function $f(x)=\frac{\sqrt[5]{a(625+x)}-5}{\sqrt[4]{625+b x}-5}$ is continuous at $x=0$, then $f(0)=$
Q24.
mcq single
+1 / 0
If the normal drawn at the point $P$ on the curve $y^2=x^3-x+1$ makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at $P$ is
Q25.
mcq single
+1 / 0
The approximate value of $\sqrt{6560}$ is
Q26.
mcq single
+1 / 0
If a balloon lying at an altitude of 30 m from an observed at a particular instant is moving horizontally. At the rate of $1 \mathrm{~m} / \mathrm{s}$ away from him, then the rate at which the balloon is moving away directly from the observer at the 40 th second is (in m/s) .
Q27.
mcq single
+1 / 0
The system of linear equation $(\sin \theta) x+y-2 z=0$, $2 x-y+(\cos \theta) z=0$ and $-3 x+(\sec \theta) y+3 z=0$, where $\theta \neq(2 n+1) \frac{\pi}{2}$, has non-trivial solution for
Q28.
mcq single
+1 / 0
If the system of simultaneous linear equations $x+\lambda y-2 z=1, x-y+\lambda z=2$ and $x-2 y+3 z=3$ is inconsistent for $\lambda=\lambda_1$ and $\lambda_2$, then $\lambda_1+\lambda_2=$
Q29.
mcq single
+1 / 0
If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$, then $\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))$
Q30.
mcq single
+1 / 0
The sum of all the roots of the equation
$\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0$ is
Q31.
mcq single
+1 / 0
If $m: n$ is the ratio in which the point $\left(\frac{8}{5},-\frac{1}{5}, \frac{8}{5}\right)$ divides the segment joining the points $(2, p, 2)$ and $(p,-2, p)$, where $p$ is an integer than $\frac{3 m+n}{3 n}=$
Q32.
mcq single
+1 / 0
Let $\pi_1$ be the plane determined by the vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}$. $\hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\pi_2$ be the plane determined by the vectors $\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{k}}-\hat{\mathbf{i}}$. Let $\mathbf{a}$ be a non-zero vector parallel to the line of intersection of the planes $\pi_1$ and $\pi_2$. If $\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$, then the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is
Q33.
mcq single
+1 / 0
If $A(2,1,-1), B(6,-3,2), C(-3,12,4)$ are the vertices of a $\triangle A B C$ and the equation of the plane containing the $\triangle A B C$ is $53 x+b y+c z+d=0$, then $\frac{d}{b+c}=$
Q34.
mcq single
+1 / 0
If $(\alpha, \beta \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and ( $1,1-2$ ), then $\alpha+\beta+\gamma=$
Q35.
mcq single
+1 / 0
If the normals drawn at the points $P\left(\frac{3}{4}, \frac{3}{2}\right)$ and $Q(3,3)$ on the parabola $y^2=3 x$ intersect again on $y^2=3 x$ at $R$, then $R=$
Q36.
mcq single
+1 / 0
If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9 x$, then
Q37.
mcq single
+1 / 0
If $\sinh ^{-1} x=\cosh ^{-1} y=\log (1+\sqrt{2})$, then $\tan ^{-1}(x+y)$
Q38.
mcq single
+1 / 0
If $0 \leq x<\frac{3}{4}$, then the number of values of $x$ satisfying the equation $\tan ^{-1}(2 x-1)+\tan ^{-1} 2 x= \tan ^{-1} 4 x-\tan ^{-1}(2 x+1)$ is
Q39.
mcq single
+1 / 0
Numerically greatest term in the expansion of $(2 x-3 y)^n$ when $x=\frac{7}{2}, y=\frac{3}{7}$ and $n=13$ is
Q40.
mcq single
+1 / 0
If $C_0, C_1, C_2, \ldots, C_8$ are the binomial coefficients in the expansion of $(1+x)^8$, then $\sum\limits_{r = 1}^8 {} r^3 \frac{C_r}{C_{r-1}}=$
Q41.
mcq single
+1 / 0
The line $L \equiv 6 x+3 y+k=0$ divides the line segment joining the points $(3,5)$ and $(4,6)$ in the ratio $-5: 4$. If the point of intersection of the lines $L=0$ and $x-y+1=0$ is $P(g, h)$, then $h=$
Q42.
mcq single
+1 / 0
The lines $x-2 y+1=0,2 x-3 y-1=0$ and $3 x-y+k=0$ are concurrent. The angle between the lines $3 x-y+k=0$ and $m x-3 y+6=0$ is $45^{\circ}$. If $m$ is an integer, then $m-k=$
Q43.
mcq single
+1 / 0
If $\tan ^{-1}(2 \sqrt{10})$ is the angle between the lines $a x^2+4 x y-2 y^2=0$ and $a \in Z$, then the product of the slopes of given lines is
Q44.
mcq single
+1 / 0
A straight line through the point $P(1,2)$ makes an angle $\theta$ with positive X -axis in anticlockwise direction and meets the line $x+\sqrt{3 y}-2 \sqrt{3}=0$ at $Q$. If $P Q=\frac{1}{2}$, then $\theta=$
Q45.
mcq single
+1 / 0
If $2 x^2+x y-6 y^2+k=0$ is the transformed equation of $2 x^2+x y-6 y^2-13 x+9 y+15=0$ when the origin is shifted to the point $(a, b)$ by translation of axes, then $k=$
Q46.
mcq single
+1 / 0
One of the values of $\sqrt{24-70 i}+\sqrt{-24+70 i}$ is
Q47.
mcq single
+1 / 0
The set of all values of $\theta$ such that $\frac{1-i \cos \theta}{1+2 i \sin \theta}$ is purely imaginary is
Q48.
mcq single
+1 / 0
If $\alpha$ is a root of the equation $x^2-x+1=0$, then
$\left(\alpha+\frac{1}{\alpha}\right)^3+\left(\alpha^2+\frac{1}{\alpha^2}\right)^3+\left(\alpha^3+\frac{1}{\alpha^3}\right)^3+\left(\alpha^4+\frac{1}{\alpha^4}\right)^3+\ldots$ to 12 terms $=$
Q49.
mcq single
+1 / 0
If the tangent drawn at the point $P(3 \sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in fourth quadrant, then $\beta=$
Q50.
mcq single
+1 / 0
If $D \subseteq R$ and $f: D \rightarrow R$ defined by $f(x)=\frac{x^2+x+a}{x^2-x+a}$ is a surjection, then ' $a$ ' lies in the interval.
Q51.
mcq single
+1 / 0
A real valued function $f:[4, \infty) \rightarrow R$ is defined as $f(x)=\left(x^2+x+1\right)^{\left(x^2-3 x-4\right)}$, then $f$ is
Q52.
mcq single
+1 / 0
If the domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$, then $2 b=$
Q53.
mcq single
+1 / 0
The general solution of the differential equation $\left(x^3-y^3\right) d x=\left(x^2 y-x y^2\right) d y$ is
Q54.
mcq single
+1 / 0
The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2 x$ and eccentricity is $\sqrt{3}$ is
Q55.
mcq single
+1 / 0
If the centre $(\alpha, \beta)$ of a circle cutting the circles $x^2+y^2-2 y-3=0$ and $x^2+y^2+4 x+3=0$ orthogonally lies on the line $2 x-3 y+4=0$, then $2 \alpha+\beta=$
Q56.
mcq single
+1 / 0
If the equation of the circumcircle of the triangle formed by the lines $L_1 \equiv x+y=0$,
$L_2 \equiv 2 x+y-1=0, L_3 \equiv x-3 y+2=0$ is $\lambda_1 L_1 L_2+\lambda_2 L_2 L_3+\lambda_3 L_3 L_1=0$, then $\frac{7 \lambda_1}{\lambda_2}+\frac{\lambda_3}{\lambda_1}=$
Q57.
mcq single
+1 / 0
The equation of the locus of a point, which is at a distance of 5 units from a fixed point $(1,4)$ and also from a fixed line $2 x+3 y-1=0$ is
Q58.
mcq single
+1 / 0
If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1,-2)$ to the circle $(x-3)^2+(y-4)^2=4$, then $\sqrt{3}\left|m_1-m_2\right|=$
Q59.
mcq single
+1 / 0
A line meets the circle $x^2+y^2-4 x-4 y-8=0$ in two points $A$ and $B$. If $P(2,-2)$ is a point on the circle such that $P A=P B=2$, then the equation of the line $A B$ is
Q60.
mcq single
+1 / 0
A circle $C$ touches $X$-axis and makes an intercept of length 2 units on $Y$-axis. If the centre of this circle lies on the line $y=x+1$, then a circle passing through the centre of the circle $C$ is
Q61.
mcq single
+1 / 0
The radius of a circle $C_1$ is thrice the radius of another circle $C_2$ and the centres of $C_1$ and $C_2$ are $(1,2)$ and $(3,-2)$ respectively. If they cut each other orthogonally and the radius of the circle $C_1$ is $3 r$, then the equation of the circle with $r$ as radius and $(1,-2)$ as centre is
Q62.
mcq single
+1 / 0
If a normal is drawn at a variable point $P(x, y)$ on the curve $9 x^2+16 y^2-144=0$, then the maximum distance from the centre of the curve to the normal is
Q63.
mcq single
+1 / 0
The mid-point of the chord of the ellipse $x^2+\frac{y^2}{4}=1$ formed on the line $y=x+1$ is
Q64.
mcq single
+1 / 0
Let $P$ be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and let the perpendicular drawn through $P$ to the major axis meet its auxiliary circle at $Q$. If the normals drawn at $P$ and $Q$ to the ellipse and the auxiliary circle respectively meet in $R$, then the equation of the locus of $R$ is
Q65.
mcq single
+1 / 0
If $f(x)=\log _{\left(x^2-2 x+1\right)}\left(x^2-3 x+2\right), x \in R-[1,2]$ and $x \neq 0$, then $f^{\prime}(3)=$
Q66.
mcq single
+1 / 0
If $y=\left(1-x^2\right) \tanh ^{-1} x$, then $\frac{d^2 y}{d x^2}=$
Q67.
mcq single
+1 / 0
If $3^x y^x=x^{3 y}$, then the value of $\frac{d y}{d x}$ at $x=1$ is
Q68.
mcq single
+1 / 0
Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is
Q69.
mcq single
+1 / 0
There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at atleast two consecutive stations, then the number of ways in which the train can be stopped is
Q70.
mcq single
+1 / 0
Number of all possible ways of distributing eight identical apples among three persons is
Q71.
mcq single
+1 / 0
$$ \int_8^{18} \frac{1}{(x+2) \sqrt{x-3}} d x= $$
Q72.
mcq single
+1 / 0
$$ \int_0^{\pi / 4} \frac{1}{5 \cos ^2 x+16 \sin ^2 x+8 \sin x \cos x} d x= $$
Q73.
mcq single
+1 / 0
If [.] denotes the greatest integer function, then $\int_1^2\left[x^2\right] d x=$
Q74.
mcq single
+1 / 0
In a $\triangle A B C$, if $c^2-a^2=b(\sqrt{3} c-b)$ and $b^2-a^2=c(c-a)$ then, $\angle A B C$
Q75.
mcq single
+1 / 0
Let $A B C$ be a triangle right angled at $B$. If $a=13$ and $c=84$, then $r+R=$
Q76.
mcq single
+1 / 0
If $\frac{x+3}{(x+1)\left(x^2+2\right)}=\frac{a}{x+1}+\frac{b x+c}{x^2+2}$, then $a-b+c=$
Q77.
mcq single
+1 / 0
$$ \int \frac{\log x}{(1+x)^3} d x= $$
Q78.
mcq single
+1 / 0
$$ \int e^{-x}\left(x^3-2 x^2+3 x-4\right) d x= $$
Q79.
mcq single
+1 / 0
$$ \int \frac{x^2 \tan ^{-1} x}{\left(1+x^2\right)^2} d x= $$
Q80.
mcq single
+1 / 0
$$ \int\left(1+\tan ^2 x\right)(1+2 x \tan x) d x= $$
Physics
Physics
Q1.
mcq single
+1 / 0
A metal rod of area of cross-section $3 \mathrm{~cm}^2$ is stretched along its length by applying a force of $9 \times 10^4 \mathrm{~N}$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \mathrm{Nm}^{-2}$, the energy stored per unit volume in the stretched rod is
Q2.
mcq single
+1 / 0
In Young's double slit experiment, if the distance between 5th bright and 7th dark fringes is 3 mm , then the distance between 5th dark and 7th bright fringes is
Q3.
mcq single
+1 / 0
If the amplitude of a damped harmonic oscillator becomes half of its initial amplitude in a time of 10 s , then the time taken for the mechanical energy of the oscillator to become half of its initial mechanical energy is
Q4.
mcq single
+1 / 0
A thin uniform circular disc of mass $\frac{10}{\pi^2} \mathrm{~kg}$ and radius 2 m is rotating about an axis passing through its centre and perpendicular to its plane. The work done to increase the angular speed of the disc from $90 \mathrm{rev} / \mathrm{min}$ to $120 \mathrm{rev} / \mathrm{min}$ is
Q5.
mcq single
+1 / 0
A body of mass ' $m$ ' moving with a velocity of ' $v$ ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' $~ e$ ', then the ratio of the velocities of the two bodies after collision is
Q6.
mcq single
+1 / 0
A solid cylinder of mass 2 kg , length 40 cm and radius 10 cm is placed in contact with a solid sphere of mass 0.5 kg and radius 10 cm such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is
Q7.
mcq single
+1 / 0
A circular coil of area $3 \times 10^{-2} \mathrm{~m}^2, 900$ turns and a resistance of $1.8 \Omega$ is placed with its plane perpendicular to a uniform magnetic field of $3.5 \times 10^{-5} \mathrm{~T}$. The current induced in the coil when it is rotated through $180^{\circ}$ in half a second is
Q8.
mcq single
+1 / 0
The pressure of a mixture of 64 g of oxygen, 28 g of nitrogen and 132 g of carbon dioxide gases in a closed vessel is $p$. Under isothermal conditions if entire oxygen is removed from the vessel, the pressure of the mixture of remaining two gases is
Q9.
mcq single
+1 / 0
To increase the length of a metal rod by $0.4 \%$ the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $\left.=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)$
Q10.
mcq single
+1 / 0
The power of a refrigerator that can make 15 kg of ice at $0^{\circ} \mathrm{C}$ from water at $30^{\circ} \mathrm{C}$ in one hour is
Q11.
mcq single
+1 / 0
Three moles of an ideal gas undergoes a cyclic process $A B C A$ as shown in the figure. The pressure, volume and absolute temperature at points $A, B$ and $C$ are respectively $\left(p_1, V_1, T_1\right),\left(p_2, 3 V_1, T_1\right)$ and $\left(p_2, V_1, T_2\right)$. Then, the total work done in the cycle $A B C A$ is ( $R=$ Universal gas constant).
Q12.
mcq single
+1 / 0
20 kV electrons can produce X- rays with a minimum wavelength of
Q13.
mcq single
+1 / 0
If a particle of mass 10 mg and charge $2 \mu \mathrm{C}$ at rest is subjected to a uniform electric field of potential difference 160 V , then the velocity acquired by the particle is
Q14.
mcq single
+1 / 0
Four electric charges $2 \mu \mathrm{C}, Q, 4 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed on $X$-axis at distance $x=0,1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 4 cm respectively. If the net force acting on the charge at origin is zero, then $Q=$
Q15.
mcq single
+1 / 0
A body is projected from the Earth's surface with a speed $\sqrt{5}$ times the escape speed $\left(V_e\right)$. The speed of the body when it escapes from the gravitational influence of the Earth is
Q16.
mcq single
+1 / 0
If the rate of change in electric flux between the plates of a capacitor is $9 \pi \times 10^3 \mathrm{Vms}^{-1}$, then the displacement current inside the capacitor is
Q17.
mcq single
+1 / 0
Monochromatic light of wavelength $6000 \mathop {\rm{A}}\limits^{\rm{o}} $ incidents on a small angled prism. If the angle of the prism is $6^{\circ}$, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48 , then the angle of dispersion produced for this incident light is
Q18.
mcq single
+1 / 0
An object of height 3.6 cm is placed normally on the principal axis of a concave mirror of radius of curvature 30 cm . If the object is at a distance of 10 cm from the principal focus of the mirror, then the height of the real image formed due to the mirror is
Q19.
mcq single
+1 / 0
A square coil of side 10 cm having 200 turns is placed in a uniform magnetic field of 2 T such that the plane of the coil is in the direction of magnetic field. If the current through the coil is 3 mA , then the torque acting on the coil is
Q20.
mcq single
+1 / 0
The magnetic field due to a current carrying circular coil on its axis at a distance of $\sqrt{2} \mathrm{~d}$ from the centre of the coil is $B$. If $d$ is the diameter of the coil, then the magnetic field at the centre of the coil is
Q21.
mcq single
+1 / 0
When the receiving antenna is on the ground, the range of a transmitting antenna of height 980 m is (Radius of the Earth $=6400 \mathrm{~km}$ )
Q22.
mcq single
+1 / 0
If $W_1$ is the work done in increasing the radius of a soap bubble from ' $r$ ' to ' $2 r$ ' and $W_2$ is the work done in increasing the radius of the soap bubble from ' $2 r$ ' to ' $3 r$ ', then $W_1: W_2=$
Q23.
mcq single
+1 / 0
An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is $125 \%$ more than its surface area at the bottom of the tank. If the atmospheric pressure is equal to the pressure of 10 m water column, then the depth of water in the tank is
Q24.
mcq single
+1 / 0
A particle initially at rest is moving along a straight line with an acceleration of $2 \mathrm{~ms}^{-2}$. At a time of 3 s after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion in which the particle returns to its initial position is
Q25.
mcq single
+1 / 0
The ratio of wavelengths of second line in Balmer series and the first line in Lyman series of hydrogen atom is
Q26.
mcq single
+1 / 0
If the number of uranium nuclei required per hour to produce a power of 64 kW is $7.2 \times 10^{18}$, then the energy released per fission is
Q27.
mcq single
+1 / 0
A radioactive material of half-life 2.5 hours emits radiation that is 32 times the safe maximum level. The time (in hours) after which the material can be handled safely is
Q28.
mcq single
+1 / 0
The phenomenon of physics that deals with the constitution and structure of matter at the minute scales of atoms and nuclei is
Q29.
mcq single
+1 / 0
If a body projected with a velocity of $19.6 \mathrm{~ms}^{-1}$ reaches a maximum height of 9.8 m , then the range of the projectile is
(Neglect air resistance)
Q30.
mcq single
+1 / 0
A sound wave of frequency 210 Hz travels with a speed of $330 \mathrm{~ms}^{-1}$ along the positive $X$-axis. Each particle of the wave moves a distance of 10 cm between the two extreme points. The equation of the displacement function ( s ) of this wave is ( $x$ in metre, $t$ in second)
Q31.
mcq single
+1 / 0
A string vibrates in its fundamental mode when a tension $T_1$ is applied to it. If the length of the string is decreased by $25 \%$ and the tension applied is changed to $T_2$, the fundamental frequency of the string increases by $100 \%$, then $\frac{T_2}{T_1}=$
(Linear density of the string is constant)
Q32.
mcq single
+1 / 0
A force separately produces accelerations of $18 \mathrm{~ms}^{-2}$, $9 \mathrm{~ms}^{-2}$ and $6 \mathrm{~ms}^{-2}$ in three bodies of masses $P, Q$ and $R$ respectively. If the same force is applied on a body of mass $P+Q+R$, then the acceleration of that body is
Q33.
mcq single
+1 / 0
The magnetic field at a point $P$ on the axis of a short bar magnet of magnetic moment $M$ is $B$. If another short bar magnet of magnetic moment 2 M is placed on the first magnet such that their axes are perpendicular and their centres coincide. The resultant magnetic field at the point $P$ due to both the magnets is
Q34.
mcq single
+1 / 0
A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of $6 \mathrm{~ms}^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
Q35.
mcq single
+1 / 0
The potential difference between points $C$ and $D$ of the electrical circuit shown in the figure is
Q36.
mcq single
+1 / 0
The length of a potentiometer wire is 2.5 m and its resistance is $8 \Omega$. A cell of negligible internal resistance and emf of 2.5 V is connected in series with a resistance of $242 \Omega$ in the primary circuit. The potential difference between two points separated by a distance of 20 cm on the potentiometer wire is
Q37.
mcq single
+1 / 0
If the length of a rod is measured as 830600 mm , then the number of significant figures in the measurement is
Q38.
mcq single
+1 / 0
If the energy gap of a semiconductor used for the fabrication of an LED is nearly 1.9 eV , then the color of the light emitted by the LED is
Q39.
mcq single
+1 / 0
According to a graph drawn between the input and output voltages of a transistor connected in common emitter configuration, the region in which transistor acts as a switch is
Q40.
mcq single
+1 / 0
An electric bulb, an open coil inductor, an AC source and a key are all connected in series to form a closed circuit. They key is closed and after some time an iron rod is inserted into the interior of the inductor, then