AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which has highest specific charge?
A \( . N a^{+}(\text {mass } n o=23) \)
В. \( M g^{2+}(\text { mass } \text {по}=24) \)
C \( . A l^{+3}(\text {mass } n o=27) \)
D. \( S i^{+4}(\text {mass } n o=28) \)
Subject: Maths
Examine the continuity of the following function at the point \( \boldsymbol{x}=-\frac{1}{2} \) \( f(x)=\left\{\begin{array}{ll}\frac{4 x^{2}-1}{2 x+1} & x \neq-\frac{1}{2} \\ -2, & x=-\frac{1}{2}\end{array}\right. \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]^{2}+\sqrt{\{\boldsymbol{x}\}} \) where \( \mathbb{D} \boldsymbol{\&} \)
Orespectively denotes the greatest integer and fractional part functions, then which of the following is
correct?
A. \( f(x) \) is continuous at all integral points
B. \( f(x) \) is not differentiable \( \forall x \in I \)
c. \( f(x) \) is discontinuous as \( x \in I-\{1\} \)
\( f(x) \) is continuous \( \& \) differentiable at \( x=0 \) 0
Subject: Chemistry
Assertion
The solutions which show large positive
deviations from Raoult's law form
maximum boiling azeotropes.
Reason
\( 95 \% \) aqueous solution of ethanol is maximum boiling azeotrope
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Let \( A \) be the area bounded by the curve
\( \boldsymbol{y}=(\tan x)^{n} \) for \( n>2 \) and the lines
\( x=0 \) and \( y=0 \) and \( x=\frac{\pi}{4} \) then the
range of \( \boldsymbol{A}_{\mathbf{1 0}} \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{20}, \frac{1}{16}\right) \)
B. \( \left(\frac{1}{18}, \frac{1}{16}\right) \)
\( ^{c \cdot}\left(\frac{1}{14}, \frac{1}{10}\right) \)
D. \( \left(\frac{1}{22}, \frac{1}{18}\right) \)
Subject: Maths
Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{y}=\mathbf{4} \boldsymbol{x}-\frac{\mathbf{5}}{\mathbf{2}} \)
A . It passes through (2.5,0) and \( m=-4 \)
B. It passes through (2.5,0) and \( m=4 \)
C. It passes through (0,2.5) and \( m=-4 \)
D. It passes through (0,-2.5) and \( m=4 \)
Subject: Physics
The Poisson's ratio of a material is \( 0.4 . \) If
a force is applied to a wire of this material, there is a decrease of cross-
sectional area by \( 2 \% . \) The percentage increase in its length is :
A . \( 3 \% \)
в. 2.5\%
c. \( 1 \% \)
D. 0.5\%
Subject: Physics
An electronic transition from \( M \) shell
\( =3 \) to \( K \) shell \( (n=1) \) takes place in a hydrogenatom. Find the wavelength of radiation emited. \( \left(R=109,677 \mathrm{cm}^{-1}\right) \)
A \( \cdot 1026 A^{\circ} \)
\( ^{\circ} \)
B . \( 1.026 \times 10^{-5} \mathrm{m} \)
c. \( 1.026 \times 10^{-3} \mathrm{cm} \)
D. none of these
Subject: Chemistry
\( _{6}^{14} \boldsymbol{C} \rightarrow_{7}^{14} \boldsymbol{N}+\boldsymbol{X} \)
The above nuclear reaction is an
example of :
A. \( \alpha \) decay
B \( \cdot \beta^{-} \) decay
\( \mathbf{c} \cdot \beta^{+} \) decay
D. Fusion
E . \( \gamma \) decay
Subject: Chemistry
Supposing the ionisation energy of hydrogen like species is 960 eV. Find out the value of principal quantum number having the energy equal to - 60
\( \mathrm{eV} \)
\( A \cdot n=2 \)
B. \( n=3 \)
\( c \cdot n=4 \)
\( D \cdot n=5 \)
Subject: Physics
Which of the following observations of \( \alpha \)
-ray scattering experiment lead to the presence of small positively charged
nucleus in the centre?
This question has multiple correct options
A. Most of the \( \alpha \) -particles passed straight
B. Most of the \( \alpha \) -particles rebounded after hitting the atoms
c. only a few \( \alpha \) -particles deflected away from their path
D. Very few \( \alpha \) -particles rebounded
Subject: Physics
A body thrown vertically up reaches a maximum height of 50 m. Another body with double the mass is thrown up with
double the initial velocity will reach a maximum height of :
A . \( 100 \mathrm{m} \)
B. 200 \( \mathrm{m} \)
c. \( 400 \mathrm{m} \)
D. 50 \( m \)
Subject: Maths
The number of ordered triplets of positive integral solutions of \( \left|\begin{array}{ccc}\boldsymbol{y}^{3}+\mathbf{1} & \boldsymbol{y}^{2} \boldsymbol{z} & \boldsymbol{y}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{z}^{2} & \boldsymbol{z}^{3}+\mathbf{1} & \boldsymbol{z}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{x}^{2} & \boldsymbol{x}^{2} \boldsymbol{z} & \boldsymbol{x}^{3}+\mathbf{1}\end{array}\right|=\mathbf{1 1} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\stackrel{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3}(\operatorname{excess})+\boldsymbol{B} \boldsymbol{r}_{2} \stackrel{\boldsymbol{h} \boldsymbol{v}}{\boldsymbol{C H}_{3}} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C}}-\boldsymbol{C H}_{3}+\boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{B r} \)
The relative reactivity of \( 1^{\circ} H, 2^{\circ} H \) and
\( \mathbf{3}^{o} \boldsymbol{H} \) in bromination reaction has been
found to be 1: 82: 1600 respectively. In the reaction the percentage yields of the products \( (A) \) and \( (B) \) are expected to be
A. 99.4\%, 0.6\%
B. 50\%, 50\%
c. ०.6\%, 99.4\%
D. 80\%, 20\%
Subject: Biology
Match the nucleic acid and its model
from the given columns.
Nucleic acid
(A) DNA
(p) Double helical
(B) tRNA (two dimensional)
(q) Clover leaf
(C) tRNA (three dimensional
(r) Hair pin
(D) rRNA
(s) L Shape
A. A-p, B-q, C-s, D-r
B. A-p, B-r, C-q, D-s
c. A-p, B-s, C-q, D-r
D. A-p, B-s, C-r, D-q
Subject: Maths
If \( \frac{\pi}{4}<\alpha<\frac{\pi}{2}, \) value of
\( \int_{-\pi / 2}^{\pi / 2} \frac{\sin 2 x}{\sqrt{1+\sin 2 \alpha \sin x}} \) is
A \( \cdot-\frac{4}{3} \tan \alpha \sec \alpha \)
B. \( -\frac{4}{3} \cot \alpha \operatorname{cosec} \alpha \)
c. \( -\frac{4}{3} \tan \alpha \operatorname{cosec} \alpha \)
D. \( -\frac{4}{3} \cot \alpha \sec \alpha \)
Subject: Chemistry
Which of the following compounds contain(s) no covalent bonds?
\( \boldsymbol{K} \boldsymbol{C l}, \boldsymbol{P H}_{3}, \boldsymbol{O}_{2}, \boldsymbol{B}_{2} \boldsymbol{H}_{6}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. \( K C l \)
в. \( K C l, B_{2} H_{6} \)
c. \( K C l, B_{2} H_{6}, P H_{3} \)
D. \( K C l, H_{2} S O_{4} \)
Subject: Maths
The conjugate complex number of \( \frac{2-i}{(1-2 i)^{2}} \) is
A \( \cdot \frac{2}{25}+\frac{11}{25} i \)
в. \( \frac{2}{25}-\frac{11}{25} i \)
c. \( -\frac{2}{25}+\frac{11}{25} i \)
D. \( -\frac{2}{25}-\frac{11}{25} i \)
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction
\( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
is 1 at \( 27 C \) and 4 at 47 .
For the reaction calculate enthalpy
change for the
\( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g}) \)
\( (\text {Given }: \boldsymbol{R}=\mathbf{2 c a l} / \boldsymbol{m o l}-\boldsymbol{K}) \)
\( \mathbf{A} \cdot 13.31 \mathrm{kcal} / \mathrm{mol} \)
в. \( 14.31 \mathrm{kcal} / \mathrm{mol} \)
c. \( 19.2 \mathrm{kcal} / \mathrm{mol} \)
D. 55.63 kcal/mol
Subject: Physics
A shell of mass \( 10 \mathrm{kg} \) is moving with a velocity of \( 10 m s^{-1} \) when it blasts and
forms two parts of mass \( 9 \mathrm{kg} \) and \( 1 \mathrm{kg} \) respectively. If the 1 st mass is stationary, the velocity of the 2 nd is:
\( \mathbf{A} \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 10 \( \mathrm{m} / \mathrm{s} \)
c. \( 100 \mathrm{m} / \mathrm{s} \)
D. \( 1000 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
\( 0.23 \mathrm{g} \) of an organic compound gave 0.332 g of \( B a S O_{4} . \) Determine the \( \% \) of sulphur in the compound.
A . \( 32.61 \% \)
в. \( 8.5 \% \)
c. \( 19.77 \% \)
D. None of these
Subject: Maths
In figure, lines \( X Y \) and \( M N \) intersect at 0
If \( \angle P O Y=90^{\circ} \) and \( a: b=2: 3, \) find \( c \)
\( 4 \cdot 106 \)
B. \( 156^{\circ} \)
\( c \cdot 126^{\circ} \)
D. 136
Subject: Physics
Choose the alternative which closely resembles the mirror image of the given
combination.
\( \mathbf{1 9 6 5} \) I NDOPAK
(1) \( \mathrm{XAGOG} \) И I ट9 96 .
(3) XAGOG I I ¿Q dI
(4) XAGOG I I èdel
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\mathbf{1}}{\mathbf{2}}[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})] \) for
real \( x \) and \( y . \) If \( f^{\prime}(0) \) exists and equals
-1 and \( f(0)=1 \) then the value of \( f(2) \)
is
A . 1
B. -
c. \( 1 / 2 \)
D. 2
Subject: Physics
A particle of mass \( 10 g \) lies in a
potential field \( v=50 x^{2}+100 . \) The
value of frequency of oscillations in \( \mathrm{Hz} \)
is:
\( A .5 H z \)
в. \( 50 / \pi H z \)
\( \mathbf{c} \cdot 10 \pi / 3 H z \)
D. none of these
Subject: Maths
\( \frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{x}}= \)
A. \( \frac{1}{2(x+1)}+\frac{3}{2(x-1)}-\frac{2}{x} \)
B. \( \frac{1}{2(x+1)}-\frac{3}{2(x-1)}-\frac{2}{x} \)
c. \( \frac{1}{2(x+1)}-\frac{3}{2(x-1)}+\frac{2}{x} \)
D. \( \frac{1}{2(x+1)}+\frac{3}{2(x-1)}+\frac{2}{x} \)
Subject: Maths
The solution of the differential equation \( y \frac{d y}{d x}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right] \) is (where, \( c \)
is a constant)
\( ^{\mathrm{A}} \cdot \phi\left(\frac{y^{2}}{x^{2}}\right)=c x \)
в. \( _{x \phi}\left(\frac{y^{2}}{x^{2}}\right)=c \)
\( ^{\mathrm{c}} \cdot \phi\left(\frac{y^{2}}{x^{2}}\right)=c x^{2} \)
D. \( x^{2} \phi\left(\frac{y^{2}}{x^{2}}\right)=c \)
Subject: Chemistry
A student performs a titration with different burettes and finds titre values
of \( 25.2 \mathrm{ml}, 25.25 \mathrm{ml} \) and \( 25.0 \mathrm{ml} \). The
number of significant figures in the average titre value is:
A . 3
B. 4
\( c \cdot 6 \)
D. 8
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{4} & \mathbf{2} \\ \mathbf{3} & \mathbf{3}\end{array}\right], \) then adj \( (\operatorname{adj} \boldsymbol{A}) \) is equal
to
\( \mathbf{A} \cdot\left[\begin{array}{cc}3 & -2 \\ -3 & 4\end{array}\right] \)
в. \( \left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right] \)
D. None of these
Subject: Chemistry
A solution contains \( 10 \mathrm{mL} \) of \( 0.1 \mathrm{N} \) NaOH
and \( 10 \mathrm{mL} \) of \( 0.05 \mathrm{Na}_{2} \mathrm{SO}_{4} . \) pH of this
solution is
A. equal to 7
B. less than 7
c. greater than 7
D. zero
Subject: Chemistry
Why \( H F \) is a weak acid while \( H C l \) is a
strong acid?
A \( . H F \) produces very few \( H^{+} \) ions in water
B. \( H C l \) dissociates completely to produce many \( H^{+} \) ions in water
\( c . \) Both \( A \) and \( B \)
D. None of the above
Subject: Physics
The velocity of sound in air is \( V \) and the
root mean square velocity of the molecules is \( c \). The \( V / c= \)
A \( \cdot \frac{\gamma}{3} \)
в. \( \quad\left[\frac{\gamma}{3}\right]^{\frac{1}{2}} \)
c. \( \frac{\gamma}{\sqrt{3}} \)
D. \( \frac{\sqrt{\gamma}}{3} \)
Subject: Chemistry
In which of the following reaction, the
value of \( \boldsymbol{K}_{\boldsymbol{p}} \) will be equal to \( \boldsymbol{K}_{c} \) ?
A \( \cdot H_{2}+I_{2} \rightleftharpoons 2 H I \)
в. \( P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
\( \mathrm{c} \cdot 2 N H_{3} \rightleftharpoons N_{2}+3 H_{2} \)
D. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
Subject: Physics
A point source of light is placed in front
of a plane mirror as shown in the fig.
Determine the length of reflected path
of light on the screen \( \left(\sum\right) \)
\( A . L \)
В. \( 2 L \)
\( c \cdot \frac{3 L}{2} \)
D. \( \frac{L}{2} \)
Subject: Chemistry
\( \boldsymbol{S}+\frac{\mathbf{3}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}+\mathbf{2} \boldsymbol{x} \) kcal
\( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{y} \) kcal
The heat of formation of \( S O_{2} \) is:
A . \( y-2 x \)
B. \( 2 x+y \)
c. \( x+y \)
D. \( 2 x / y \)
Subject: Maths
Let \( P(n) \) denote the statement that
\( \boldsymbol{n}^{2}+\boldsymbol{n} \) is odd. It is seen that \( \boldsymbol{P}(\boldsymbol{n}) \Rightarrow \)
\( P(n+1), P(n) \) is true for all
\( \mathbf{A} \cdot n>1 \)
B.
c \( . n>2 \)
D. None of these
Subject: Maths
The length of each side of the cubical
box is \( 2.4 m . \) Its volume is:
A . 13.824 cu. \( m \)
в. 13.824 си. ст
c. \( 13.824 \mathrm{m}^{2} \)
D. 13.824 sq. \( \mathrm{cm} \)
Subject: Physics
Copper of fixed volume 'V' is drawn into
wire of length 'I'. When this wire is
subjected to a constant force 'F', the
extension produced in the wire is \( ^{\prime} \Delta l^{\prime} \) Which of the following graph is a straight line?
A \( \cdot \Delta l v s \frac{1}{l} \)
B. \( \Delta l v s l^{2} \)
c. \( \Delta l v s \frac{1}{l^{2}} \)
D. \( \Delta l \) vs \( l \)
Subject: Physics
A particle executes \( \boldsymbol{S} \boldsymbol{H} \boldsymbol{M} \) of
amplitude \( 25 c m \) and time period \( 3 s \)
What is the minimum time required for the particle to move between two points
\( 12.5 \mathrm{cm} \) on either side of the mean
position?
A . \( 0.5 s \)
B. \( 1.0 s \)
c. \( 1.5 s \)
D. 2.0
Subject: Chemistry
\( \boldsymbol{P h C H}_{2} \boldsymbol{C H}_{3} \frac{(i) C r O_{2} C l_{2} / C C l_{4}}{(i i) H_{3} O^{+}} \)
\( \boldsymbol{P h C H}_{2} \boldsymbol{C H O} \)
The above reaction is an example of which name reaction?
A. Rossenmund reduction
B. Birch reduction
c. Mendius reduction
D. Etard reduction
Subject: Chemistry
toppr LoGıN
Q Type your question
the combustion reaction is
\( \boldsymbol{C}_{8} \boldsymbol{H}_{18}+\mathbf{1 2 . 1} \boldsymbol{O}_{2} \rightarrow \mathbf{0 . 8} \boldsymbol{C O}+ \)
\[
\mathbf{7} . \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{\mathbf{2}}+\mathbf{9} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}
\]
Calculate the temperatures of the Gases just at the time of maximum compression and Write sum of these two temperatures. Exhaust gases leaving the cylinder if
the final pressure in the cylinder is
\( 200 k p a \)
Relevant data neede for one burn cycle
is given below:
Compound \( \boldsymbol{\Delta} \boldsymbol{H}_{f}\left(\boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1}\right) \) mol
\( N_{2}(g) \) 0.0
\( O_{2}(g) \) 0.0
\( \mathcal{P}(g) \) -110.53
\( \mathcal{P} O_{2}(g) \)
-395.51
-241.82 \( H_{2} O(g) \)
sooctane -187.82
Subject: Physics
The pendulum of a bob undergoes SHM with an amplitude A is given by the equation \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{s} \boldsymbol{i n} \boldsymbol{\omega} \boldsymbol{t} . \) The
corresponding angular SHM equation can be written as
A \( \cdot \theta=\phi \cos (\omega t) \)
в. \( \theta=\phi \sin (\omega t) \)
c. \( \theta=\phi \tan (\omega t) \)
D. \( \theta=\phi(\omega t) \)
Subject: Physics
A structure steel rod has a radius of
\( 10 m m \) and a length of \( 1.0 m . A 100 k N \)
force stretches it along its length.
(b) elongation. and Calculate ( \( a \) ) stress.
(c) strain on the rod. Young's modulus, of stricture steel is \( 2.0 \times 10^{11} N m^{-2} \)
Subject: Chemistry
Assertion
In the formation of water molecule, both hydrogen and oxygen atoms attain octet of electrons.
Reason
Oxygen atom forms two ionic or electrovalent bonds with two hydrogen
atoms.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \vec{a}=x \hat{i}+y \hat{j}+z \hat{k} \) makes equal angles with \( \vec{b}=y \hat{i}-2 z \hat{j}+3 x \hat{k} \) and \( \vec{c}=2 z \hat{i}+3 x \hat{j}-y \hat{k} \) and \( \vec{a} \perp \vec{d}, \) where
\( \vec{d}=\hat{i}-\hat{j}+2 \hat{k} . \) If \( |\vec{a}|=2 \sqrt{3}, \) then
\( \vec{a} \cdot \vec{b}= \)
A . 12
B. -12
\( c \cdot 24 \)
D. -24
Subject: Physics
A certain charge \( Q \) is divide at first into
two parts \( (q) \) and \( (Q-q) . \) Later on the
charges are placed at a certain
distance. If the force of interaction
between the two charges is maximum
then:
A \( \cdot(Q / q)=(4 / 1) \)
B \cdot \( (Q / q)=(2 / 1) \)
c. \( (Q / q)=(3 / 1) \)
D・ \( (Q / q)=(5 / 1) \)
Subject: Chemistry
The molecular mass of \( C u S O_{4} .5 H_{2} O \)
is:
(Atomic mass of \( C u=63.5, H=1, O= \)
\( 16, S=32) \)
A. 233.5 gm/mole
B. 249.5 gm/mole
c. \( 251.5 \mathrm{gm} / \mathrm{mole} \)
D. 247.5 gm/mole
Subject: Chemistry
Which of the following is the correct order of the magnitude of \( -I \) effect
among the groups given?
\( A \cdot-F>-N O_{2}>-C O O H>-O C H_{3} \)
B. - \( \mathrm{NO}_{2}>-\mathrm{F}>-\mathrm{COOH}>-\mathrm{OCH}_{3} \)
c. \( -\mathrm{NO}_{2}>-\mathrm{COOH}>-\mathrm{F}>-\mathrm{OCH}_{3} \)
D. - COOH > - NO \( _{2}>-\mathrm{OCH}_{3}>-\mathrm{F} \)
Subject: Maths
If \( f(x)=\left\{\begin{array}{ll}\frac{x}{1+e^{1 / x}} & x \neq 0 \\ 0 & x=0\end{array} \), then the \right.
function \( f(x) \) is differentiable for:
\( \mathbf{A} \cdot x \in R^{+} \)
B. \( x \in R \)
c. \( x \in R-\{0\} \)
D. \( x \in R-\{0,1\} \)
Subject: Physics
A cyclotron is used to accelerate
protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the
cyclotron is \( 2 T, \) find the radius and the frequency needed for the applied alternating voltage of the cyclotron.
(Given: Velocity of proton \( =3 x \)
\( \left.10^{7} m / s\right) \)
Subject: Maths
\( \boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x} \neq \mathbf{0},-\boldsymbol{4} \leq \boldsymbol{x} \leq \mathbf{4}\} \boldsymbol{f} \)
\( A \rightarrow R \) is defined as \( f(x)=\frac{|x|}{x} \) then
the range of \( \boldsymbol{f} \) is
A \( \cdot\{1,-1\} \)
B . \( \{x: 0 \leq x \leq 4\} \)
c. \{1\}
D \cdot \( \{x:-4 \leq x \leq 0\} \)
Subject: Physics
A ball is projected on smooth inclined
plane in direction perpendicular to line of greatest slope with velocity of \( 8 \boldsymbol{m} / \boldsymbol{s} \)
t's speed after \( \left.1 s \text { is (take } g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 12 m / s \)
\( D \cdot 16 \mathrm{m} / \mathrm{s} \)
Subject: Maths
The equation of a parabola which passes through the intersection of a straight line \( x+y=0 \) and the circle \( x^{2}+y^{2}+4 y=0 \) is.
A \( \cdot y^{2}=4 x \)
В. \( y^{2}=x \)
c. \( y^{2}=2 x \)
D. None of these
Subject: Physics
Let L be the length and d be the
diameter of cross-section of a wire.
Wires of the same material with
different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
A. \( L=200 \mathrm{cm}, d=0.5 \mathrm{mm} \)
в. \( L=300 \mathrm{cm}, d=1.0 \mathrm{mm} \)
c. \( L=50 \mathrm{cm}, d=0.05 \mathrm{mm} \)
D. \( L=100 \mathrm{cm}, d=0.2 \mathrm{mm} \)
Subject: Maths
A piece of elastic was stretched by \( 24 \% \)
to a length of \( 31 \mathrm{cm} \). Find its unstretched original length.
\( A \cdot 24 \mathrm{cm} \)
B . \( 26 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a} \) \( \overrightarrow{\boldsymbol{b}}=\mathbf{0},(\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{c}}) \cdot(\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}})=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{c}}= \)
\( \lambda \vec{a}+\mu \vec{b}+\omega(\vec{a} \times \vec{b}), \) where \( \lambda, \mu, \omega \) are
scalars then?
A \( \cdot \mu^{2}+\omega^{2}=1 \)
в. \( \lambda-\mu=1 \)
C \( \cdot(\mu+1)^{2}+\mu^{2}+\omega^{2}=1 \)
D. \( \lambda^{2}+\mu^{2}=1 \)
Subject: Maths
The sequence \( \boldsymbol{S}=\boldsymbol{i}+\boldsymbol{2} \boldsymbol{i}^{2}+\boldsymbol{3} \boldsymbol{i}^{3}+\ldots \ldots \)
upto 100 times simplifies to where \( i= \) \( \sqrt{-1} \)
A. \( 50(1-i) \)
B . 25
c. \( 25(1+i) \)
D. \( 100(1-i) \)
Subject: Maths
ff \( y=f\left(x^{2}+2\right) \) and \( f^{\prime}(3)=5, \) then \( \frac{d y}{d x} \)
at \( x=1 \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. 15
D. 10
Subject: Physics
A metal ring kept (supported by a card
board) on the top of a fixed solenoid
carry a current I as shown in figure. The centre of the ring coincides with the axis of the solenoid. If the current in the
solenoid is switched off, then
A. magnetic flux linked with the metal ring increases.
B. current induced in the metal ring in clockwise direction
c. metal ring will not remain on the cardboard
D. both
(a) and
(b) are correct
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \frac{50^{0}-\boldsymbol{6} \boldsymbol{0}^{0}}{\longrightarrow} \)
\( \boldsymbol{A} \stackrel{\boldsymbol{S n}+\boldsymbol{H} C l}{\longrightarrow} \boldsymbol{B} \frac{\boldsymbol{C H}_{3} \boldsymbol{C O C l}}{\boldsymbol{N}} \boldsymbol{C} \). Then \( \boldsymbol{C} \) is:
A . aniline
B. nitro benzene
c. acetanilide
D. benzedine aniline
Subject: Physics
Block A mass 2 kg is placed over a block
B mass 8 kg. The combination is placed on a rough horizontal surface. If \( \mathrm{g}=10 \mathrm{ms}^{-2} \)
coefficient offiction between \( \mathbf{B} \) and
floor \( =0.5, \) coefficient offfiction
betweenA and \( \mathrm{B}=0.4 \) and a horizontal
force on \( 10 \mathrm{N} \) is placed of8 \( \mathrm{kg} \) block, then the force friction between \( A \)
and B is:
A. \( 100 N \)
B. 50N
c. \( 40 \mathrm{N} \)
D. None of these
Subject: Chemistry
\( \beta \) sulphur is stable between:
A \( \cdot 114^{\circ} \mathrm{C} \) to \( 160^{\circ} \mathrm{C} \)
B . \( 95.6^{\circ} \mathrm{C} \) to \( 119^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 160^{\circ} C \) to \( 230^{\circ} C \)
D. \( 112.8^{\circ} \mathrm{C} \) to \( 140^{\circ} \mathrm{C} \)
Subject: Chemistry
The compound of the formula
\( \boldsymbol{C H}_{3} \boldsymbol{C O}\left(\boldsymbol{C H}_{2}\right)_{5} \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C O O H} \)
would be expected to:
I rotate the plane polarised light
II : contain chiral centre
III : contain three stereocentres
IV: show geometrical isomerism
A. Only I, II, II are correct.
B. Only II, IV are correct.
c. ।, ॥, ॥I, IV are correct.
D. only IV is correct.
Subject: Physics
A body at \( 50^{0} \) cools in a surrounding
maintained at \( 30^{0} \) C. The temperature
at which the area of cooling is half that
of the begining is
A \( \cdot 16.3^{0} \mathrm{C} \)
в. 26.3 \( ^{0} \) С
\( c \cdot 40^{0} c \)
D. \( 46.3^{0} \mathrm{C} \)
Subject: Chemistry
Which of the following statements are
correct?
This question has multiple correct options
A \( \cdot \) The angular momentum of \( 3 p \) -orbital is \( \frac{h}{\sqrt{2} \pi} \)
B. The sixth electron of carbon atom has the quantum numbers \( n=2, \ell=1, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
C. Magnetic moment of \( V^{4+} \) ions is 1.73 BM \( (\mathrm{V}=23) \)
D. For azimuthal quantum number \( \ell=3 \), the maximum
number of electrons is 6
Subject: Chemistry
At \( 300 K, \) the initial pressure of a
reactant \( R \) is 100 mm. After 60 secs, the
pressure becomes 75 mm. Find the
average rate of the reaction.
A \( \cdot 10 \times 10^{-5} \) molL \( ^{-1} \) se \( c^{-1} \)
B. \( 5 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
C. \( 4.22 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
D. \( 2.22 \times 10^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
Subject: Chemistry
Which atoms should have smaller value
of \( (\boldsymbol{I} \boldsymbol{E})_{1} ? \)
(a) Oxygen or sulphur
(b) Nitrogen or phosphorus
\( \begin{array}{ll}\text { A } \cdot \text { (a) } S(b) & P\end{array} \)
B. (a) \( O \) (b) \( P \)
c. (a) \( S \) (b) \( N \)
D. Noneofthese