TG EAPCET 2024 (Online) 9th May Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \mathrm{~Hz}$ hits a metal, is $2 \times 10^{-19} \mathrm{~J}$. What is the threshold frequency of the metal (in Hz )? $\left(h=6.6 \times 10^{-34} \mathrm{Js}\right)$

In which of the following species, the ratio of $s$-electrons to $p$-electrons is same?

Identify the pair of elements in which the difference in atomic radii is maximum

Match the following.

List I (Element)	List II (Block)
A Ra	I p - block
B Uuq	II s- block
C Ds	III f - block
D Fm	IV d - block

The correct answer is

Identify the pair in which difference in bond order value is maximum.

The pair of molecules/ions with same geometry but central atoms in them are in different states of hybridisation is

If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is $0.920 \mathrm{gL}^{-1}$, what is the mole fraction of nitrogen in the mixture? ( $R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$; assume ideal gas behaviour for oxygen and nitrogen)

The incorrect rule regarding the determination of significant figures is

At 61 K , one mole of an ideal gas of 1.0 L volume expands isothermally and reversibly to a final volume of 10.0 L . What is the work done in the expansion?

At $T(\mathrm{~K}), K_C$ for the dissociation of $\mathrm{PCl}_5$ is $2 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$. The number of moles of $\mathrm{PCl}_5$ that must be taken in 1.0 L flask at the same temperature to get 0.2 mol of chlorine at equilibrium is

The dihedral angles in gaseous and solid phases of $\mathrm{H}_2 \mathrm{O}_2$ molecule respectively are

Identify the compound which gives $\mathrm{CO}_2$ more readily on heating?

The major components of cement are

Consider the following reactions (not balanced).

$$ \begin{array}{r} \mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm{~K}} X+\mathrm{NaF} \\ X+\mathrm{H}_2 \mathrm{O} \longrightarrow Y+\mathrm{H}_2 \uparrow \end{array} $$

The correct statements about $X$ and $Y$ are

I. $X$ is an electron deficient molecule.

II. in $X, B-B$ bond is present.

III. $Y$ is a weak tribasic acid.

IV. $Y$ acts as a Lewis acid.

Which of the following does not exist?

Methemoglobinemia is due to

The IUPAC name of the following compound is

The functional groups present in the product ' $X$ ' of the reaction given below are

Identify the major product $(P)$ in the following reaction sequence.

$$ \left(\mathrm{CH}_3\right)_3 \mathrm{CBr} \xrightarrow[\text { KOH, } \Delta]{\text { Alcoholic }} X \xrightarrow{\mathrm{HBr}} P $$

What is the percentage of carbon in the product ' $X$ ' formed in the given reaction?

$+\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl} \xrightarrow[\mathrm{AlCl}_3]{\text { Anhydrous }} X$

Identify the correct statement about the crystal defects in solids.

Dry air contains $79 \% \mathrm{~N}_2$ and $21 \% \mathrm{O}_2$. At $T(\mathrm{~K})$, if Henry's law constants for $\mathrm{N}_2$ and $\mathrm{O}_2$ in water are $857 \times 10^4 \mathrm{~atm}$ and $4.56 \times 10^4 \mathrm{~atm}$, the ratio of mole fraction of $\mathrm{N}_2$ and $\mathrm{O}_2$ dissolved in water at 1 atm is

If the degree of dissociation of formic acid is $11.0 \%$, the molar conductivity of 0.02 M solution of it is (Given, $\lambda^{\circ}\left(\mathrm{H}^{+}\right)=349.6 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ $\lambda^{\circ}\left(\mathrm{HCOO}^{-}\right)=54.6 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ )

Consider the gaseous reaction, $$ A_2+B_2 \longrightarrow 2 A B $$ The following data was obtained for the above reaction.

[A₂]₀	[B₂]₀	Initial rate of formation of AB (mol L⁻¹ s⁻¹)
0.1 M	0.1 M	2.5 × 10⁻⁴
0.2 M	0.1 M	5.0 × 10⁻⁴
0.2 M	0.1 M	1.0 × 10⁻³

The value of rate constant for the above reaction is

Adsorption of a gas a solid adsorbent follows. Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass ' $m$ ' of the adsorbent at pressure $p$. From the graph given extent of adsorption is proportional to

Consider the following reactions.

$$ X+\mathrm{O}_2 \rightarrow \mathrm{Cu}_2 \mathrm{O}+\mathrm{SO}_2, \mathrm{Cu}_2 \mathrm{O}+X \rightarrow \mathrm{Cu}+Y \uparrow $$

The shape of the molecule $Y$ is

$Y$ in the given sequence of reactions is

$$ \begin{gathered} \mathrm{P}_4+x \mathrm{NaOH}+y \mathrm{H}_2 \mathrm{O} \xrightarrow{\mathrm{CO}_2} X+z \mathrm{NaH}_2 \mathrm{PO}_2 \\ X+\mathrm{CuSO}_4 \longrightarrow Y+\mathrm{H}_2 \mathrm{SO}_4 \end{gathered} $$

In contact process of manufacture of $\mathrm{H}_2 \mathrm{SO}_4$, the arsenic purifier used in the industrial plant contains

$\mathrm{Pt}+3: 1$ mixture of $\left(\right.$ Conc. $\mathrm{HCl}+$ conc. $\left.\mathrm{HNO}_3\right) \rightarrow[\mathrm{X}]^{2-}$

What is the oxidation state of Pt in $[\mathrm{X}]^{2-}$ complex ion ?

In which of the following, ions are correctly arranged in the increasing order of oxidising power?

Which of the following will have a spin only magnetic moment of 2.86 BM ?

The monomer which is present in both bakelite and melamine polymers is

Cellulose is a polysaccharide and is made of

Match the following.

List I (Type of drug)	List II (Examaple)
A Antacid	I Serotonin
B Antihistamine	II Seldane
C Tranquiliser	III Ranitidine
D Antibiotic	IV Chloramphenicol

The correct answer is

Which of the following is an example of allylic halide?

Identify the correct statements about $Z$.

$$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2 \xrightarrow[0^{\circ} \mathrm{C}]{\mathrm{NaNO}_2 / \mathrm{HCl}} X \xrightarrow{\mathrm{H}_2 \mathrm{O}} Y \xrightarrow{\mathrm{Cu} / 573 \mathrm{~K}} Z $$

I. $Z$ is an aldehyde.

II. $Z$ undergòes Cannizzaro reaction.

III. $Z$ gives iodoform test.

IV. $Z$ does not give, test with Tollens' reagent.

Assertion (A) : Aldehydes are more reactive than ketones towards nucleophilic addition reactions

Reason (R) : In aldehydes, carbonyl carbon is less electrophilic compared to ketones.

The correct answer is

Arrange the following in the correct order of their boiling points.

What is the major product $Z$ in the given reaction sequence?

$$ \left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{O} \xrightarrow[\text { (ii) } 2 \mathrm{H}_2 \mathrm{O}^{+}]{(\mathrm{i}) \mathrm{C}_2 \mathrm{H}_5 \mathrm{MgBr}} \xrightarrow[\Delta]{\substack{\text { (i) } \mathrm{OOCl}_2 \\ \text { (ii) } \mathrm{CH}_3 \mathrm{ONa}}} Y \xrightarrow[\text { Peroxide }]{\mathrm{HBr}} Z $$

Match the following.

List -I (Amine)	List -II (pKb value)
A. N,N-dimethyl aniline	I. 9.30
B. Aniline	II. 8.92
C. N-ethylethanamine	III. 9.38
D. N-methylaniline	IV. 3.00

The correct answer is

Mathematics

The domain of the real valued function $f(x)=\sqrt[3]{\frac{x-2}{2 x^2-7 x+5}}+\log \left(x^2-x-2\right)$ is

$f$ is a real valued function satisfying the relation $f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}$. If $f\left(x+\frac{1}{x}\right)=1$, then $x$ is equal to

$\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & x\end{array}\right|=0$ and $\min (\alpha, \beta, \gamma)=\alpha$, then $2 \alpha+3 \beta+4 \gamma$ is equal to

If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$

If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then

If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+7=0$, $2 x+3 y-z=10$ and $x-2 y-3 z=3$, then $\alpha=$

If $\frac{(2-i) x+(1+i)}{2+i}+\frac{(1-2 i) y+(1-i)}{1+2 i}=1-2 i$, then $2 x+4 y=$

If $z=1-\sqrt{3} i$, then $z^3-3 z^2+3 z=$

The product of all the values of $(\sqrt{3}-i)^{\frac{2}{5}}$ is

The number of common roots among the 12 th and 30th roots of unity is

$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2}<\alpha<0$, then $\alpha$ is equal to

If $4+3 x-7 x^2$ attains its maximum value $M$ at $x=\alpha$ and $5 x^2-2 x+1$ attains its minimum value $m$ at $x=\beta$, then $\frac{28(M-a)}{5(m+\beta)}=$

If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3-5 x^2+4 x-3=0$, then $\Sigma \alpha \beta(\alpha+\beta)=$

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation

$$ \begin{aligned} & \alpha, \beta, \gamma+4 x^4-13 x^3-52 x^2+36 x+144=0 . \text { If } \\ & \alpha<\beta<\gamma<2<\varepsilon \text {, then } \alpha+2 \beta+3 \gamma+5 \varepsilon= \end{aligned} $$

Among the 4 -digit numbers that can be formed using the digits $1,2,3,4,5$ and 6 without repeating any digit, the number of numbers which are divisible by 6 is

If the number of circular permutations of 9 distinct things taken 5 at a time is $n_1$ and the number of linear permutation of 8 distinct things taken 4 at a time is $n_2$, then $\frac{n_1}{n_2}=$

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is

If the coefficients of 3 consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression, then those terms are

The numerically greatest term in the expansion of $(3 x-16 y)^{15}$, when $x=\frac{2}{3}$ and $y=\frac{3}{2}$, is

If $\frac{3 x^4-2 x^2+1}{(x-2)^4}=A+\frac{B}{x-2}+\frac{C}{(x-2)^2}$ $+\frac{D}{(x-2)^3}+\frac{E}{(x-2)^4}$, then $2 A+3 B-C-D+E=$

The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

If $A+B+C=2 S$, then $\sin (S-A) \cos (S-B)-\sin (S-C) \cos S=$

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i

If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$

Match the functions given in List I with their relevant characteristics from List II.

List I	List II
(A) sinh x	(I) Domains is (-1,1), even function
(B) sec hx	(II) Domain is [1,∞), neither even nor odd function
(C) tan hx	(III) Even function
(D) cosec h⁻¹x	(IV) Range is R, odd function
	(V) Range is (-1,1), odd function

The correct answer is

In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$

In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \mathbf{c}$ and $4 \mathbf{a}+7 \mathbf{b}-8 \mathbf{c}$ are collinear, then $\lambda=$

If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are the position vectors of the points $A, B, C, D, E$ respectively, then the point of intersection of the line $A B$ and the plane passing through $C, D, E$ is.

If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{37},|\mathbf{a}-\mathbf{b}|=k$ and $(\mathbf{a}, \mathbf{b})=\theta$, then $\frac{4}{13}(k \sin \theta)^2=$

$r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, If the magnitude of the projection of $\mathbf{r}$ on the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is l , then $|\mathbf{r}|=$

$\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors and $\mathbf{a}$ is a vector such that $\cos (\mathbf{a}, \mathbf{b} \times \mathbf{c})=\sqrt{\frac{2}{3}}$. If $\mathbf{a}$ is a unit vector, then $|\mathbf{a} \times(\mathbf{b} \times \mathbf{c})|=$

The variance of the following continuous frequency distribution is

Classinterval	0-4	4-8	8-12	12-16
Frequency	2	3	2	1

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

If a random variable X has the following probability distribution, then the mean of $X$ is $$ \begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2 \end{array} $$

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, then the equation of the locus of $P$ is

If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equation of $2 x^2+4 x y+y^2+2 x-2 y+1=0$ is

$L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\alpha$ lies in the fourth quadrant and perpendicular distance from $(\sqrt{2}, \sqrt{2})$ to the line, $L=0$ is 5 units, then $p=$

$(-2,-1),(2,5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the third vertex of that triangle, then $m+n$ is equal to.

$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=$ 0 , then $\frac{b^2}{|a c|}=$

The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

If $P\left(\frac{\pi}{4}\right), Q\left(\frac{\pi}{3}\right)$ are two points on the circle $x^2+y^2-2 x-2 y-1=0$, then the slope of the tangent to this circle which is parallel to the chord $P Q$ is

The power of a point $(2,0)$ with respect to a circle $S$ is -4 and the length of the tangent drawn from the point $(1,1)$ to $S$ is 2 . If the circle $S$ passes through the point $(-1,-1)$, then the radius of the circle $S$ is

The pole of the line $x-5 y-7=0$ with respect to the circle $S \equiv x^2+y^2-2 x+4 y+1=0$ is $P(a, b)$. If $C$ is the centre of the circle $S=0$, then $P C=$

The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1=0$ is

If a circle passing through the point $(1,1)$ cuts the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-4 y+3=0$ orthogonally, then the centre of that circle is

Length of the common chord of the circles $x^2+y^2-6 x+5=0$ and $x^2+y^2+4 y-5=0$ is

$P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4 a x$. If $P=(9,9)$ and $Q=(p, q)$, then $p-q=$

The number of normals that can be drawn through the point $(9,6)$ to the parabola $y^2=4 x$ is

The equations of the directrices of the elmpse $9 x^2+4 y^2-18 x-16 y-11=0$ are

$L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which is lying in the third quadrant. If the normal drawn at $L_1^{\prime}$ to this ellipse intersects the ellipse again at the point $P(a, b)$, then $a=$

$(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9 x^2-16 y^2=144$. If $p>0$ and $q>0$, then $q=$

$A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the side $B C$ at $D(p, q, r)$, then $\sqrt{2 p+q+r}=$

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|=\frac{6}{13}$, then $k=$

A plane $(\pi)$ passing through the point $(1,2,-3)$ is perpendicular to the planes $x+y-z+4=0$ and $2 x-y+z+1=0$. If the equation of the plane $(\pi)$ is $a x+b y+c z+1=0$, then $a^2+b^2+c^2=$

$\lim _{\theta \rightarrow \frac{\pi^{-}}{2}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4}=$

Define $ f: R \rightarrow R $ by $ f(x)=\left\{\begin{array}{cl}\frac{1-\cos 4 x}{x^{2}}, & x < 0 \\ a, & x=0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & x > 0\end{array}\right. $

Then, the value of $ a $ so that $ f $ is continuous at $ x=0 $ is

If $y=\frac{\tan x \cos ^{-1} x}{\sqrt{1-x^2}}$, then the value of $\frac{d y}{d x}$, when $x=0$ is

If $y(\cos x)^{\sin x}=(\sin x)^{\sin x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

If $x=\cos 2 t+\log (\tan t)$ and $y=2 t+\cot 2 t$, then $\frac{d y}{d x}=$

If $y=44 x^{45}+45 x^{-44}$, then $y^n=$

The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is

If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2$, then $\tan \theta=$

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured in to the cone at the rate of $\frac{1}{\sqrt{3}} \mathrm{~m}^3 / \mathrm{min}$, then the rate ( $\mathrm{m} / \mathrm{min}$ ) at which the radius of the water level is increasing when the height of the water level is 3 m is

A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi-vertical angle of the cone is

If $f(x)=k x^3-3 x^2-12 x+8$ is strictly decreasing for all $x \in R$, then

$\int e^{-2 x}\left(\tan 2 x-2 \sec ^2 2 x \tan 2 x\right) d x=$

If $\int x^3 \sin 3 x d x=f(x) \cos 3 x+g(x) \sin 3 x+C$, then 27 $(f(x)+x g(x))=$

$\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$

$\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=$

$ \int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x= $

$\int_0^{16} \frac{\sqrt{x}}{1+\sqrt{x}} d x=$

$\int_0^{32 \pi} \sqrt{1-\cos 4 x} d x=$

The general solution of the differential equation $(9 x-3 y+5) d y=(3 x-y+1) d x$ is

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 y^2+1}{2 y^3-4 x y+y}$ is

Physics

The error in the measurement of resistance, when $(10 \pm 05)$ A current passing through it produces a potential difference of $(100 \pm 6) \mathrm{V}$ across it is

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. The time taken by the stone to cross the window during its downward journey is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of $100 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the ground is 2 m and the distance between its wheels is 1.5 m , the maximum speed of the truck with which it can travel without toppling over is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A block of mass $m$ with an initial kinetic energy $E$ moves up an inclined plane of inclination $\theta$. If $\mu$ is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the stopping distance is $s_1$. The man returns home on the same scooter, with the same speed with a 60 kg bag of rice. If $s_2$ is the new stopping distance when the brakes are applied with the same force, then

A thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \mathrm{~ms}^{-1}$. $12 \mathrm{~ms}^{-1}$ and $8 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of particles is

A particle of mass 4 mg is executing simple harmonic motion along $X$-axis with an angular frequency of $40 \mathrm{rad} \mathrm{s}^{-1}$. If the potential energy of the particle is $V(x)=a+b x^2$, where $V(x)$ is in joule and $x$ is in metre, then the value of $b$ is

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is (Radius of the earth $=6400 \mathrm{~km}$ )

If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the string is

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is $900 \mathrm{~kg} \mathrm{~m}^{-3}$, then the surface tension of the soap solution is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mixture at thermal equilibrium contains

A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then $d W: d U: d Q$ is

If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms speed of the gas molecules is

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of 108 kmph is (speed of sound in air $=330 \mathrm{~ms}^{-1}$ )

If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and heard per second respectively are

A small angled prism is made of a material of refractive index $\frac{3}{2}$. The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index $\frac{4}{3}$ is

If you are using eye glasses of power 2 D, your near point is

The diameter of the objective of a telescope is 3.6 m . The limit of resolution of the telescope for a light of wavelength 540 nm is

Two point charges of magnitudes $-8 \mu \mathrm{C}$ and $+32 \mu \mathrm{C}$ are separated by a distance of 15 cm in air. The position of the point from $-8 \mu \mathrm{C}$ charge at which the resultant electric field becomes zero is

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is $C_1$. If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is $C_2$. If in both cases, the dielectric is placed parallel to the plated of the capacitor, then $C_1: C_2=$

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the electrons is $2.4 \times 10^{-4} \mathrm{~ms}^{-1}$, the electron mobility in $\mathrm{m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ is

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$, where $i$ is the current in ampere through the filament of the bulb. The emf of the battery $V_a$, so that the bridge become balanced is