AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The increasing order of the atomic radii of the following elements is :
(a) \( C \)
(b) \( \boldsymbol{O} \)
\( (c) F \)
(d) \( C l \)
\( \boldsymbol{B} \boldsymbol{r} \)
A \( \cdot(b)<(c)<(d)<(a)<(e) \)
в. \( (c)<(b)<(a)<(d)<(e) \)
c. \( (d)<(c)<(b)<(a)<(e) \)
D. \( (a)<(b)<(c)<(d)<(e) \)
\( e \)
Subject: Chemistry
In the reaction, \( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 C O(g), \) the equilibrium pressure is 12
atm. If \( 50 \% \) of \( C O_{2} \) reacts, \( K_{p} \)
is
Subject: Maths
Let L be the set of all lines in XY-plane and \( \mathrm{R} \) be the relation in L defined as
\( \boldsymbol{R}=\left\{\left(\boldsymbol{L}_{1}, \boldsymbol{L}_{2}\right): \boldsymbol{L}_{1} \text { is parallel to } \boldsymbol{L}_{2}\right\} \)
Show that \( R \) is an equivalence relation. Find the set of all lines related to the
line \( y=2 x \)
Subject: Maths
If \( n(A)=5 \) and \( n(B)=7, \) then the
number of relations on \( \boldsymbol{A} \times \boldsymbol{B} \) is :
\( \mathbf{A} \cdot 2^{3} \)
B. \( 2^{4} \)
\( c \cdot 2^{25} \)
D. \( 2^{70} \)
E \( .2^{35 \times 35} \)
Subject: Chemistry
Calculate the dissociation constant of
water at \( 25^{\circ} \mathrm{C} \) from the following data.
Specific conductance of \( \boldsymbol{H}_{2} \boldsymbol{O}=\mathbf{5} . \boldsymbol{8} \times \)
\( 10^{-8} m h o c m^{-1},: \lambda_{H^{+}}^{\infty}=350.0 \) and
\( \lambda_{O H^{-}}^{\infty}=198.0 m h o c m^{2} \)
The ans is \( k \times 10^{-16} \) mole/litre. find \( k \)
A . 1.8
в. 100
\( c . \)
D. 0.01
Subject: Maths
There are two coins, one unbiased with probability \( \frac{1}{2} \) of getting heads and the other one is biased with probability \( \frac{3}{4} \) of getting heads. A coin is selected at random and tossed. It shows heads up.
Then the probability that the
unbiasedcoin was selected is
A \( \cdot \frac{2}{3} \)
в. \( \frac{3}{5} \)
c. \( \frac{1}{2} \)
D. \( \frac{2}{5} \)
Subject: Maths
In the given figure, if 0 is the centre of a
circle, \( P Q \) is a chord and the tangent
\( P R \) at \( P \) makes an angle of \( 50^{\circ} \) with \( P Q \)
find \( \angle P O Q \)
\( A \cdot 40 \)
в. 80
\( c \cdot 100 \)
D. 120
Subject: Physics
\( K \) is the radius of gyration of a thin rod
when it is rotating about an axis perpendicular to the length of the rod and is passing through it's centre. The length of that rod is :
A . \( 12 K \)
в. \( 3 K \)
c. \( 2 \sqrt{3} K \)
D. \( \sqrt{3} K \)
Subject: Physics
If the terminal speed of a sphere of gold
(density \( \left.=19.5 k g / m^{3}\right) \) is \( 0.2 m / s \) in a viscous liquid(density \( \left.=1.5 k g / m^{3}\right) \) find the terminal speed of a sphere of silver (density \( =10.5 k g / m^{3} \) ) of the same size in the same liquid
A. \( 0.4 m / s \)
В. \( 0.133 m / s \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)
Subject: Chemistry
Which of the following statements
regarding orbitals is false?
A. \( 1 s \) orbital has one nodal region.
B. \( 2 s \) orbital is spherical with one nodal region.
C \( .2 p_{x} \) orbital is dumb bell with one nodal plane.
D. \( 3 d_{x y} \) orbital has two nodal planes.
Subject: Maths
Let \( A \) and \( B \) be independent events with \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})=0.5 . \) Then find:
(i) \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}) \)
(ii) \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A}) \)
\( (\text { iii) } \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
(iv) \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
Subject: Physics
The plano-convex lens of focal length 20 \( \mathrm{cm} \) and \( 30 \mathrm{cm} \) are placed together to form a double convex lens, the final
focal length will be :
\( \mathbf{A} \cdot 12 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
\( \mathbf{c} \cdot 20 c m \)
D. \( 30 \mathrm{cm} \)
Subject: Maths
Two supplementary angles are in the ratio \( 5: 7 . \) Find the smallest angle.
\[
\begin{array}{l}
1^{s t} \text { angle }=\frac{5}{12} \times 180^{\circ} \text { and } \\
2^{n d} \text { angles }=\frac{7}{12} \times 180^{\circ}
\end{array}
\]
\( \mathbf{A} \cdot 80 \)
B. 75
c. 65
D. 90
Subject: Chemistry
For a zero order reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{P}, \boldsymbol{t}_{1 / 2} \)
is:
(k is the rate constant, \( [A]_{0} \) is the initial
concentration of \( \boldsymbol{A} \) )
\( ^{A} \cdot \frac{[A]_{0}}{2 k} \)
B. \( \frac{\ln 2}{k} \)
c. \( \frac{1}{k[A]_{0}} \)
D. \( \frac{\ln 2}{[A]_{0} k} \)
Subject: Physics
Two stars \( S_{1} \) and \( S_{2} \) are located at
distances \( d_{1} \) and \( d_{2} \) respectively. Also if
\( d_{1}>d_{2} \) then which of the following
statements is true?
A. The parallax of \( S_{1} \) and \( S_{2} \) are same
B. The parallax of \( S_{1} \) is twice as that of \( S_{2} \)
C. The parallax of \( S_{1} \) is greater than parallax of \( S_{2} \)
D. The parallax of \( S_{2} \) is greater than parallax of \( S_{1} \)
Subject: Chemistry
The \( p H \) of \( H C l \) is \( 1.1 .10 m l \) of this
solution is reacted with \( 40 \mathrm{ml} \) of
NaOH solution whose \( p H=12 . \) The
\( p H \) of resulting solution is:
\( (\log (1.2)=0.108) \)
\( \mathbf{A} \cdot 2.892 \)
B. 1.892
c. 32.892
D. 11.842
Subject: Physics
A toy car of mass \( 5 \mathrm{kg} \) moves up a ramp
under the influence of force \( F \) plotted
against displacement. The maximum height attained is given by
A \( \cdot y_{\max }=20 \mathrm{m} \)
B \( \cdot y_{\max }=15 \mathrm{m} \)
\( \mathbf{c} \cdot y_{\max }=11 m \)
\( y_{\max }=5 m \)
Subject: Physics
The instantaneous emf and current
equations of an RLC series circuit are \( e=200 \sin \left(\omega t-\frac{\pi}{6}\right) \)
\( i=20 \sin \left(\omega t+\frac{\pi}{6}\right) \)
The average power consumed per cycle is
A. zero
в. \( 2000 \mathrm{W} \)
c. \( 1000 W \)
D. \( 500 W \)
Subject: Physics
A current \( i \) is flowing through the wire of
diameter \( d \) having drift velocity of
electrons \( v_{d} \) in it. What will be new drift
velocity when diameter of wire is made \( \frac{\boldsymbol{d}}{\boldsymbol{4}} \)
\( \mathbf{A} \cdot 4 V_{d} \)
в. \( \frac{V_{d}}{4} \)
\( \mathbf{c} \cdot 16 V_{d} \)
D. \( \frac{V_{d}}{16} \)
Subject: Maths
\( \int(\sin x)^{99}(\cos x)^{-101} d x=_{-} \ldots-C_{ } \)
A. \( \frac{(\tan x)^{100}}{100} \)
B. \( \frac{(\tan x)^{2}}{2} \)
c. \( \frac{(\tan x)^{98}}{98} \)
D. \( \frac{(\tan x)^{97}}{97} \)
Subject: Maths
\( \lim _{x \rightarrow 2} \frac{x^{7}-128}{x^{5}-32}= \)
A \( \cdot \frac{5}{28} \)
в. \( \frac{7}{5} \)
c. \( \frac{28}{5} \)
D. 5 \( \overline{7} \)
Subject: Maths
If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \infty\right)=\frac{\pi}{2} \) for
\( \mathbf{0}<|\boldsymbol{x}|<\sqrt{\mathbf{2}}, \) then \( \boldsymbol{x} \) equal
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{-1}{2} \)
D. -1
Subject: Maths
The mean of the ungrouped data is given by
\( ^{\mathrm{A}} \cdot \operatorname{Mean}=\frac{\sum x_{i}}{\sum f} \)
B. \( \operatorname{Mean}=\frac{\sum x}{n} \)
c. \( \operatorname{Mean}=\frac{\sum f x}{\sum n} \)
D. mean \( =a+\frac{\sum f x}{\sum n} \)
Subject: Maths
If \( p \) and \( p^{\prime} \) are the perpendiculars from
the origin upon the \( \operatorname{lines} x \sec \theta+ \)
\( \boldsymbol{y} \csc \boldsymbol{\theta}=\boldsymbol{a} \) and \( \boldsymbol{x} \cos \boldsymbol{\theta}-\boldsymbol{y} \sin \boldsymbol{\theta}= \)
\( a \cos 2 \theta \) respectively then
A \( \cdot 4 p^{2}+p^{\prime 2}=a^{2} \)
B \cdot \( p^{2}+4 p^{\prime 2}=a^{2} \)
C \( \cdot p^{2}+p^{\prime 2}=a^{2} \)
D. none of these
Subject: Physics
A block of mass \( 20 \mathrm{kg} \) is acted upon by
a force \( \boldsymbol{F}=\mathbf{3 0} \boldsymbol{N} \) at an angle \( \mathbf{5 3}^{\mathbf{0}} \) with
the horizontal in downward direction as
shown. The coefficient of friction
between the block and the horizontal
surface is \( 0.2 . \) The friction force acting
on the block by the ground is \( (g= \) \( \left.10 m / s^{2}\right) \)
A . 40.0
B. 30.0 N
c. \( 18.0 \mathrm{N} \)
D. 44.8 N
Subject: Physics
In the circuit shown here,cells \( A \) and \( B \)
have emf \( 10 V \) each and the internal
resistance is \( 5 \Omega \) for \( A \) and \( 3 \Omega \) for \( B \). For
what value of \( R \) will the potential difference across the cell A will be zero?
A . 0
B. 1 ohm
c. 2 ohm
D. 3 ohm
Subject: Chemistry
At STP, a container has 1 mole of \( A r, 2 \)
moles of \( C O_{2}, 3 \) moles of \( O_{2} \) and 4
moles of \( N_{2} . \) Without changing the total
pressure of \( \boldsymbol{O}_{2} \) is removed, the partial
pressure of \( \boldsymbol{O}_{2} \) is:
A. changed by about \( 16 \% \)
B. halvedd
c. changed by \( 26 \% \)
D. unchanged.
Subject: Physics
A girl in a swing is \( 2.5 m \) above ground
at the maximum height and at \( 1.5 m \)
above the ground at the lowest point. Her maximum velocity in the swing is
\( \left(g=10 m s^{-2}\right) \)
В. \( 2 \sqrt{5} \mathrm{ms}^{-1} \)
D. \( 3 \sqrt{2} \mathrm{ms}^{-1} \)
E \( \cdot 4 \sqrt{2} m s^{-1} \)
Subject: Chemistry
Which of the following is a set of green
house gases?
A. \( O_{3}, N O_{2}, S O_{2}, C l_{2} \)
в. \( C O_{2}, C H_{4}, N_{2} O, O_{3} \)
\( \mathrm{c} \cdot O_{3}, N_{2}, C O_{2}, \mathrm{NO}_{2} \)
D. \( C H_{4}, O_{3}, N_{2}, S O_{2} \)
Subject: Biology
Match the following.
\( \begin{array}{ll}\text { A. Incisors } & \text { 1. Grinding teeth } \\ \text { B. Canines } & \text { 2. Cracking teeth } \\ \text { C. Premolars } & \text { 3. Cutting teeth } \\ \text { D. Molars } & \text { 4. Tearing teeth }\end{array} \)
\( A \cdot A-2, B-4, C-1, D-3 \)
B. A- 2, B-1 , C-4, D-3
C \( . A-3, B-2, C-4, D-1 \)
D. A- 3, B-4, C-2, D-1
Subject: Chemistry
Solubility curves of two ionic salts \( X \& \)
W are given below:
In which case the value of \( \Delta \boldsymbol{H}_{\text {sol.}}<\mathbf{0}: \)
\( A \cdot x \)
B. W
\( c \cdot \operatorname{Both}(x) \&(w) \)
D. None of these
Subject: Physics
\( A 16 \mathrm{cm} \) long pencil is placed as shown
in figure. The central point \( C \) is \( 45 \mathrm{cm} \) away from a \( 20 \mathrm{cm} \) focal length lens and \( 15 \mathrm{cm} \) above the optic axis. Find the length of image.
A . \( 14.2 \mathrm{cm} \)
B. \( 12.3 \mathrm{cm} \)
\( c .17 .1 \mathrm{cm} \)
D. \( 4.5 \mathrm{cm} \)
Subject: Chemistry
Which of the following is/are examples of pseudo unimolecular reactions?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O_{2} C_{2} H_{5}+H_{2} O \stackrel{H}{\rightarrow} C H_{3} C O_{2} H+C_{2} H_{5} O H \)
\( ^{\mathbf{B}} \cdot C_{12} H_{22} O_{11}+H_{2} O \stackrel{H}{\rightarrow}^{\oplus} \quad \begin{array}{ll}C_{6} H_{12} O_{6} & =C_{6} H_{12} O_{6} \\ & (G l u \operatorname{cose})\end{array}=\quad(\text {Fructose}) \)
\( \mathbf{c} \cdot C H_{3} C O C l+H_{2} O \rightarrow C H_{3} C O_{2} H+H C l \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{OH}}{\rightarrow} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)
Subject: Physics
The force acting on a pole of strength of \( 20 \mathrm{Am} \) is \( 8 \times 10^{-4} \mathrm{N}, \) when placed in a
magnetic field. The magnetic induction field strength is :
A. \( 4 \times 10^{-6} \) т
B. \( 0.4 \times 10^{4} \mathrm{T} \)
\( c \cdot 4 G \)
D. \( 4 \times 10^{-5} \mathrm{T} \)
Subject: Chemistry
Which element among the following will not have an oxidation number of \( -1 ? \)
A. \( F \) in \( H F \)
B. \( C l \) in \( N a C l \)
\( c \cdot O \operatorname{in} H_{2} O_{2} \)
D. \( F \) in \( N a F \)
E \( . H \) in \( N a_{2} H P O_{4} \)
Subject: Maths
If \( \boldsymbol{y}=\frac{\log \boldsymbol{x}}{\boldsymbol{x}}, \) then prove by
mathematical induction
\( \boldsymbol{y}_{n}= \)
\( \frac{(-1)^{n}(n !)}{x^{n+1}}\left[\log x-1-\frac{1}{2}-\dots-\frac{1}{n}\right] \)
Subject: Chemistry
Which compound in each of the
following pairs would have the higher boiling point ? Explain your answers.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \boldsymbol{o r} \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O C H}_{3} \)
\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \) or \( \boldsymbol{H} \boldsymbol{O C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{H} \)
(c)
(d)
\( (e) \)
\( (\mathrm{g}) \)
(h) Hexane \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{3} \) or nonane \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{7} \mathrm{CH}_{3} \)
\( (\mathbf{i}) \)
Subject: Physics
A wheel of moment of inertia \( 5 \times \)
\( 10^{-3} k g m^{2} \) is making 20 rev \( / s . \) The
torque required to stop it in \( 10 s \) is :
A \( \cdot 2 \pi \times 10^{-2} N m \)
В . \( 2 \pi \times 10^{2} N m \)
\( \mathbf{c} \cdot 4 \pi \times 10^{-2} N m \)
D. \( 4 \pi \times 10^{2} N m \)
Subject: Physics
The collector supply voltage in \( \mathrm{CE} \) transistor amplifier is \( 10 V . \) The base
current is \( 10 \mu A \) in the absence of the
signal voltage and the voltage between the collector and the emitter is \( 4 V \). The
current gain \( (\beta) \) of a transistor is 200
then the value of the load resistance \( \boldsymbol{R}_{\boldsymbol{L}} \)
\( \mathbf{A} \cdot 2 k \Omega \)
в. \( 1 k \Omega \)
\( c .3 k \Omega \)
D. \( 4 k \Omega \)
Subject: Maths
The value of \( \int \frac{\ln n\left(1-\left(\frac{1}{x}\right)\right) d x}{x(x-1)} \) is
A \( \cdot \frac{1}{2}\left[m\left(1-\frac{1}{x}\right)^{2}\right]+C \)
B \( \cdot \frac{1}{2}\left[m\left(1+\frac{1}{x}\right)\right]^{2}+C \)
c. \( \frac{1}{2} \ln (x(x-1))+C \)
D \( \cdot \frac{1}{2}[\ln (x(x-1))]^{2}+C \)
Subject: Maths
The odds in favour of India winning any
cricket match is \( 2: 3 . \) What is the
probability that if India plays 5 matches, it wins exactly 3 of them?
\( ^{\mathbf{A}} \cdot_{^{5}} C_{3}\left(\frac{2}{5}\right)^{2}\left(\frac{3}{5}\right)^{3} \)
\( ^{\mathrm{B}} \cdot_{^{5}} C_{3}\left(\frac{2}{3}\right)^{2}\left(\frac{1}{3}\right)^{3} \)
\( ^{\mathbf{c}} \cdot_{^{5}} C_{3}\left(\frac{2}{5}\right)^{3}\left(\frac{3}{5}\right)^{2} \)
\( ^{\mathrm{D} \cdot}^{5} C_{3}\left(\frac{2}{3}\right)^{2}\left(\frac{1}{3}\right)^{2} \)
Subject: Chemistry
Two liquids \( X \) and \( Y \) form an ideal solution.
The mixture has a vapour pressure of \( 400 \mathrm{mm} \) at \( 300 \mathrm{K}, \) when mixed in the
molar ratio of 1: 1 and a vapour pressure of \( 350 \mathrm{mm} \) when mixed in the molar
ratio of 1: 2 at the same temperature. The vapour pressures of the two pure liquids \( X \) and \( Y \) respectively are?
A. 250mm, 550mm
B. 350mm, 450mm
c. \( 350 \mathrm{mm}, 700 \mathrm{mm} \)
D. 550mm, 250mm
Subject: Maths
Given the relation \( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{3})\} \)
on the set \( A=\{1,2,3\} \), the minimum
number of ordered pairs which when added to \( R \) make it an equivalence
relation is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
\( D \)
Subject: Biology
The given graph shows an oxygen dissociation curve for haemoglobin.
Where in the body will haemoglobin be saturated at the percentages shown at
points 1,2 and 3 on the graph?
A. Left ventricle1Pulmonary vein2 Vena cava3
B. Left ventricle2Pulmonary vein1Vena cava3
c. Left ventricle2Pulmonary vein3Vena caval
D. Left ventricle3Pulmonary vein2Vena cava
Subject: Physics
A circular loop of radius \( 2 \mathrm{cm} \), is placed in a time varying magnetic field with rate of \( 2 T / \)sec. Then induced electric
field in this loop will be:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 0.002 \mathrm{V} / \mathrm{m} \)
c. \( 0.01 V / m \)
D. \( 2 V / m \)
Subject: Physics
Assertion
A small power circuit that is isolated from ground typically is less dangerous.
Reason
Its contacting just one power wire will
not form a complete circuit path, and it
is too small to collect large dangerous
atmospheric charge potentials.
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: Physics
A coil of \( 10^{-2} H \) inductance carries a
current \( \boldsymbol{I}=2 \sin (\mathbf{1 0 0} \boldsymbol{t}) \boldsymbol{A} . \) When current
is half of its peak value then at that instant the induced emf in coil :-
A . \( 1 V \)
B. \( \sqrt{2} V \)
c. \( \sqrt{3} V \)
D. 2
Subject: Maths
The relation P defined from R to R as a P
\( \mathbf{b} \Leftrightarrow 1+\mathbf{a b}>\mathbf{0}, \) for all \( \mathbf{a}, \mathbf{b} \boldsymbol{\epsilon} \mathbf{R} \) is
A . reflexive only
B. reflexive and symmetric only
c. transitive only
D. equivalence
Subject: Physics
The range of clinical thermometer is
A \( .37^{\circ} \mathrm{C} \) to \( 42^{\circ} \mathrm{C} \)
B \( \cdot 95^{\circ} F \) to \( 110^{\circ} F \)
\( \mathbf{c} \cdot 90^{\circ} F \) to \( 112^{\circ} F \)
D. \( 95^{\circ} C \) to \( 104^{\circ} C \)
Subject: Maths
The area of a traingle is 5 square units, two of its verices are (2,1) and \( (3,-2) . \) The
third vertex lies on \( y=x+3 \).The third vertex is
\( ^{\mathbf{A}} \cdot\left(\frac{7}{2}, \frac{3}{2}\right) \)
в. \( \left(-\frac{3}{2}, \frac{3}{2}\right) \)
c. \( \left(-\frac{3}{2}, \frac{13}{2}\right) \)
D \( \cdot\left(\frac{7}{2}, \frac{5}{2}\right) \)
Subject: Chemistry
The \( \$ \$ \) IUPAC \( \$ \$ \) name of
\( \left[N i\left(N H_{3}\right)_{4}\right]\left[N i C l_{4}\right] \) is:
A. Tetrachloronickel (II)-tetraamminenickel(II)
B. Tetraamminenickel(II)-tetrachloronickel(II)
C. Tetraamminenickel(II)-tetrachloronickelate(II)
D. Tetrachloronickel (II)-tetraamminenickelate(O)
Subject: Physics
An object \( A B \) is placed parallel and
close to the optical axis between focus
\( F \) and center of curvature \( C \) of a
converging mirror of focal length \( \boldsymbol{f} \) as
shown in figure. Then
This question has multiple correct options
A. Image of \( A \) will be closer than that of \( B \) from the
mirror
B. Image of \( A B \) will be parallel to the optical axis
c. Image of \( A B \) will be a straight line inclined to the optical axis
D. Image of \( A B \) will not be a straight line
Subject: Physics
A bullet fired into a block looses half of
its velocity after penetrating through a distance of \( 0.6 \mathrm{m} . \) Before coming to rest, the total distance traveled would be:
A . \( 0.8 \mathrm{m} \)
B. 1.2 \( m \)
\( c \cdot 1.6 m \)
D. 0.2 \( m \)
Subject: Maths
If \( \int_{a}^{b} x^{3} d x=0 \) and \( \int_{a}^{b} x^{2} d x=\frac{2}{3}, \) then
what are the values of \( a \) and \( b \)
respectively?
A. -1,1
в. 1,1
c. \( 0, \)
D. 2,-2
Subject: Maths
The value of the integral \( \int_{-1}^{1}\left\{\frac{x^{2013}}{e^{|x|}\left(x^{2}+\cos x\right)}+\frac{1}{e^{|x|}}\right\} d x \) is
equal to
A. 0
B. \( 1-e^{-1} \)
\( c \cdot 2 e^{-1} \)
D. \( 2\left(1-e^{-1}\right) \)
Subject: Maths
Factorise
(i) \( a^{4}-b^{4} \)
(ii) \( p^{4}-81 \)
(iii) \( x^{4}- \)
\( (y+z)^{4} \)
\( \left(\text { iv ) } x^{4}-(x-z)^{4}\right. \)
\( a^{4}-2 a^{2} b^{2}+b^{4} \)
Subject: Chemistry
Which of the following statements
about anhydrous aluminium chloride is
correct?
A. It fumes in moist air.
B. It exists as dimer both in the vapour state below \( 350^{\circ} \mathrm{C} \)
and in non-polar solvents.
C. It is prepared by heating \( A l_{2} O_{3} \) in a stream of sulphur
chloride \( \left(S_{2} C l_{2}\right) \) vapour and chlorine.
D. All of these.
Subject: Physics
What will be the wave velocity, if the
radar gives 54 waves per min and wavelength of the given wave is \( 10 m ? \)
\( \mathbf{A} \cdot 4 m s^{-1} \)
B. \( 6 m s^{-1} \)
\( \mathrm{c} \cdot 9 m s^{-1} \)
D. \( 5 m s^{-1} \)
Subject: Physics
Q Type your question
\( M_{A}=2 M \) and \( M_{B}=M, \) as indicated
in the figure. The two masses are initially oriented along the Y-axis and connected by a rod of negligible mass of length \( \mathrm{D} \), forming a rigid body. A force of magnitude \( \boldsymbol{F}=|\overrightarrow{\boldsymbol{F}}| \) along the X-axis is
applied to the object at \( \mathrm{B} \) at \( t=0 \) for \( \mathrm{a} \)
short time interval \( \delta t . \) Neglect gravity. The expression for the magnitude of angular velocity of the system after the
collision is:
A \( \cdot \frac{F \delta t}{M D D} \)
в. \( \frac{2 F \delta t}{3 M D} \)
c. \( \frac{F \delta t}{2 M D} \)
D. \( \frac{3 F \delta t}{2 M D} \)
Subject: Chemistry
Give a balanced reaction in which
ammonia is oxidised by a metal oxide.
A \( .4 N H_{3}+3 C u O \rightarrow 2 N_{2}+3 H_{2} O+3 C u \)
B. \( 2 N H_{3}+4 C u O \rightarrow N_{2}+3 H_{2} O+4 C u \)
\( \mathrm{c} \cdot 2 N H_{3}+C u O \rightarrow N_{2}+3 H_{2} O+C u \)
D. \( 2 N H_{3}+3 C u O \rightarrow N_{2}+3 H_{2} O+3 C u \)
Subject: Physics
Two trains of length \( 500 m \) and \( 1000 m \) moving in opposite direction with same
speed crosses each other in 10 sec, find their speed:
A. \( 75 \mathrm{m} / \mathrm{s} \)
в. \( 150 m / s \)
c. \( 100 \mathrm{m} / \mathrm{s} \)
D. None of these
Subject: Chemistry
Which of the following statements are
correct?
This question has multiple correct options
A. One mole of \( P h N H N H_{2} \) reacts with 3 mol glucose to
form osazone
B. One mole of D-fructose reacts with 3 mol \( P h N H N H_{2} \)
to form osazone
C. One mole of D-2-deoxy glucose reacts with 1 mol \( P h N H N H_{2} \) to form phenylhyrazone
D. One mole of D-3-deoxy glucose reacts with 3 mol \( P h N H N H_{2} \) to form osazone
Subject: Maths
The value of the definite integral \( \int \frac{d \theta}{1+\tan \theta}=\frac{501 \pi}{K} \) where \( a_{2}=\frac{1003 \pi}{2008} \) and
\( \boldsymbol{a}_{1}=\frac{\pi}{2008} \) The value of \( \mathrm{K} \) equalls
A. 2007
B. 2006
c. 2009
D. 2008
Subject: Maths
If \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)-\cos ^{1}\left(\frac{1-b^{2}}{1+b^{2}}\right)= \)
\( \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right), \) then what is the value
of \( x ? \)
\( A \cdot \frac{a}{b} \)
B. \( a b \)
\( c \cdot \frac{b}{a} \)
D. \( \frac{a-b}{1+a b} \)
Subject: Physics
image of an object approching a convex mirror of radius of curvature \( 20 \mathrm{m} \) along its optical axis so is observed to move from \( \frac{25}{3} m \) to \( \frac{50}{7} m \) into 30 s. what is the speed of the object in \( K m / h ? \)
A . 3
B. 4
\( c .5 \)
D. 6
Subject: Biology
(A) The sporophyte in liverworts is more elaborate than that in mosses.
(B) Salvinia is heterosporous.
(C) In Pinus, male and female cones are
borne on different trees.
(D) The life-cycle in all seed bearing plants is diplontic. The two wrongly matched statements
together are
A. Statement B and C
B. Statement A and B
c. Statement A and C
D. Statement A and D
Subject: Physics
A streamlined and almost symmetrical
car of mass \( M \) has centre of gravity at a
distance \( p \) from the rear wheel, \( q \) from
the front wheel and \( h \) from the road. If
the car has required power and friction,
the maximum acceleration developed without tipping over towards back is:
A \( \cdot \frac{p g}{h} \)
в. hg\( q \)
c. \( \frac{h M g}{q} \)
D. \( \frac{p h}{g} \)
Subject: Chemistry
Considering \( \triangle G=\triangle H-T \triangle S, \) a
spontaneous reaction will occur when :
A. \( \triangle G \) is positive and \( \triangle S \) is positive
B. \( \triangle G \) is positive and \( \triangle S \) is negative
c. \( \triangle H \) is negative and \( \triangle S \) is positive
D. \( \triangle H \) is negative and \( \triangle S \) is negative
E. \( \triangle H \) is positive and \( \triangle T \) is negative
Subject: Physics
In a series LCR circuit, the plot of \( \boldsymbol{I}_{\boldsymbol{m}} \) vs
\( \omega \) is shown in the figure. The bandwidth
of this plot will be then
A. Zero
B. \( 0.1 \mathrm{rads}^{-1} \)
c. \( 0.2 r a d s^{-1} \)
D. \( 0.4 \mathrm{rads}^{-1} \)