AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An object is placed at a distance of 30 \( \mathrm{cm} \) from a concave tens of focal length \( 30 \mathrm{cm} \)
(i) Use lens formula to determine the
distance of the image from the lens.
(ii) List four characteristics of the
image (nature position, size, erect/inverted) in this case.
(iii) Draw a labelled diagram to justify
your answer apart (ii)
Subject: Physics
On a linear escalator running between
two points \( A \) and \( B, \) a boy takes time \( t_{1} \)
to move from \( A \) to \( B \), if the boy runs with a constant speed on the escalator.
If the boy runs from \( B \) to \( A \), he takes
time \( t_{2} \) to reach \( B \) from \( A \). The time
taken by the boy to move from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) if he stands still on the escalator will be
(The escalator moves from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) )
A \( \cdot \frac{t_{1} t_{2}}{t_{2}-t_{1}} \)
В. \( \frac{2 t_{1} t_{2}}{t_{2}-t_{1}} \)
c. \( \frac{t_{1}^{2}+t_{2}^{2}}{t_{1} t_{2}} \)
D. \( \frac{t_{1}^{2}-t_{2}^{2}}{t_{1} t_{2}} \)
Subject: Maths
The Cartesian equation of line \( 6 x- \) \( \mathbf{2}=\mathbf{3} \boldsymbol{y}+\mathbf{1}=\mathbf{2} z-\mathbf{2} \) is given by
\( ^{\text {A } \cdot \frac{3 x-1}{3}}=\frac{3 y+1}{6}=\frac{z-1}{3} \)
B. \( \frac{3 x+1}{3}=\frac{3 y-1}{6}=\frac{z-1}{3} \)
c. \( \frac{3 x-1}{3}=\frac{3 y-1}{6}=\frac{z-1}{3} \)
D. \( \frac{3 x-1}{6}=\frac{3 y-1}{3}=\frac{z-1}{3} \)
Subject: Maths
In the figure above, line \( \iota \) (not shown) is
perpendicular to segment \( A B \) and
bisects segment \( A B \). Which of the
following points lies on line \( \iota \) ?
A \( \cdot(0,2) \)
В \( \cdot(1,3) \)
\( c .(3,1) \)
D. (3,3)
E. 6,6
Subject: Physics
You are given 'mn' wires of equal
resistance, If \( m \) wires are in series and
n such combinations are in parallel the
resultant resistance is \( R_{1} \). If \( n \) wires are
in series and m such combinations are
in parallel, the resultant resistance is
\( R_{2} . \) Then \( \frac{R_{1}}{R_{2}} \) is:
A . 1: 1
B. \( m: n \)
\( \mathbf{c} \cdot m^{2}: n^{2} \)
D. \( n^{2}: m^{2} \)
Subject: Physics
If \( \vec{p} \& \vec{s} \) are not perpendicular to each other and \( \vec{r} \times \vec{p}=\vec{q} \times \vec{p} \& \vec{r} . \vec{s}=0 \)
\( \operatorname{then} \vec{r}= \)
A \( \cdot \vec{p} . \vec{s} \)
В \( \cdot \vec{q}+\left(\frac{\vec{q} . \vec{s}}{\vec{p} . \vec{s}}\right) \vec{p} \)
c. \( \vec{q}-\left(\frac{\vec{q} . \vec{s}}{\vec{p} . \vec{s}}\right) \vec{p} \)
D. \( \vec{q}+\mu \vec{p} \) for all scalars \( \mu \)
Subject: Maths
If \( \frac{\mathbf{d} \boldsymbol{y}}{\mathbf{d} \boldsymbol{x}}=\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}} \) and \( \boldsymbol{y}(1)=\mathbf{1} \) then \( \boldsymbol{y}(\boldsymbol{2}) \)
equals
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( 2 \pm \sqrt{10} \)
c. \( 2 \pm \sqrt{12} \)
D. \( -2 \pm \sqrt{10} \)
Subject: Physics
A cell can be balanced against \( 110 \mathrm{cm} \) and 100
\( \mathrm{cm} \) of potentiometer wire, respectively with and
without being short circuited through a resistance of 10 . Its internal resistance
is -
A. 2.0 ohm
B. zero
c. 1.0 ohm
D. 0.5 ohm
Subject: Physics
Assertion
In the measurement of physical quantities direct and indirect methods
are used.
Reason
The accuracy and precision of
measuring instruments along with
errors in measurements should be
taken into account, while expressing
the result.
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. Assertion is incorrect but Reason is correct
Subject: Physics
Frequency of oscillation of a body is
6 \( H z \) when force \( F_{1} \) is applied and
\( 8 H z \) when \( F_{2} \) is applied. If both forces
\( F_{1} \& F_{2} \) are applied together then, the frequency of oscillation is :
\( \mathbf{A} \cdot 14 H z \)
в. \( 2 \mathrm{Hz} \)
c. \( 10 H z \)
D. \( 10 \sqrt{2} \mathrm{Hz} \)
Subject: Maths
The given figure shows a rectangle ABC inscribed in a circle as shown
alongside. \( f(A B=28 \mathrm{cm} \text { and } B C=21 \mathrm{cm}, \) Find the
area of the shaded portion of the given
figure
A . \( 374.5 \mathrm{cm}^{2} \)
В. 374.5 \( m^{2} \)
c. \( 3.745 \mathrm{cm}^{2} \)
D. \( 37.45 \mathrm{cm}^{2} \)
Subject: Maths
\( \operatorname{Let} f(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, \) then
\( \lim _{x \rightarrow \frac{\pi}{4}} f(x)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. -
Subject: Chemistry
2.2 \( g \) of an alcohol (A) when treated with
\( \boldsymbol{C H}_{3}- \) Mgl liberates \( 560 \mathrm{mL} \) of \( \boldsymbol{C H}_{4} \) at
STP. Alcohol (A) on dehydration followed by ozonolysis gives ketone (B) along with (C). Oxime of ketone (B) contains
\( 19.17 \% \) N. (A) on oxidation gives ketone
(D) having the same number of the carbon atom.
The molecular mass of (A) is?
A . 74
B. 88
\( c \cdot 60 \)
D. 102
Subject: Maths
If \( a^{2}, b^{2}, c^{2} \) are in A.P., then the following are also in A.P. \( \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c}}, \frac{\boldsymbol{b}}{\boldsymbol{c}+\boldsymbol{a}}, \frac{\boldsymbol{c}}{\boldsymbol{a}+\boldsymbol{b}} \)
A. True
B. False
Subject: Chemistry
The equilibrium constant for the
reaction, \( \boldsymbol{S n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{S} \boldsymbol{n}^{2+}+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \boldsymbol{a} \boldsymbol{t} \boldsymbol{2} \boldsymbol{5}^{\circ} \boldsymbol{C} \) is:
\( \boldsymbol{E}^{\circ}\left(\boldsymbol{S} \boldsymbol{n}^{2+} \mid \boldsymbol{S} \boldsymbol{n}\right)=\mathbf{0 . 1 4} \)
A \( .5 .5 \times 10^{4} \)
B. \( 2.3 \times 10^{2} \)
c. \( 1.1 \times 10^{2} \)
D. 1.009
Subject: Maths
The contrapositive of \( (\boldsymbol{p} \vee \boldsymbol{q}) \Rightarrow \boldsymbol{r} \) is
A \( \cdot r \Rightarrow(p \vee q) \)
в. \( r \Rightarrow(p \vee q) \)
c. \( r \Rightarrow \sim p \wedge \sim q \)
D. \( R \Rightarrow(q \vee r) \)
Subject: Chemistry
Identify the final product of the reaction
\[
\mathrm{CH}_{3} \mathrm{MgBr}+\mathrm{CH}_{2} \mathrm{CH}_{2} \rightarrow \stackrel{\mathrm{H}, \mathrm{O}^{+}}{\longrightarrow} ?
\]
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H_{3} C H_{2} O H \)
\( c \)
\[
\triangle
\]
D. \( C H_{3} C H_{2} C H_{2} O H \)
Subject: Maths
The complex number \( z \) satisfying the
equations \( |z|-\mathbf{4}=|z-i|-|z+\mathbf{5} i|= \)
\( \mathbf{0}, \) is
This question has multiple correct options
A. \( \sqrt{3}-i \)
В. \( 2 \sqrt{3}-2 i \)
c. \( -2 \sqrt{3}-2 i \)
D. 0
Subject: Chemistry
Alkene \( (\mathrm{X})\left(C_{5} H_{1} 0\right) \) on ozonolysis gives a mixture of two compounds \( (Y) \) and \( (Z) \) Compound (Y) gives positive Fehling's test and iodoform test. Compound \( (z) \) does not give Fehling's test but give iodoform test. Compounds \( (X),(Y) \) and
(z) are?
A \( \cdot X=C_{6} H_{5} C O C H_{3}, Y=C H_{3} C H O, Z= \)
\( C H_{3} C O C H_{3} \)
B. \( X=C H_{3}-C H=\underset{C H_{3}}{C}-C H_{3}, Y= \)
\( C H_{3} C H O, Z=C H_{3} C O C H_{3} \)
c. \( X=C H_{3} C H_{2} C H=C H_{2}, Y= \)
\( C H_{3} C H_{2} C H O, Z=H C H O \)
D. \( X=C H_{3}-C H=C H-C H_{3}, Y= \)
\( C H_{3} C H O, Z=C H_{3} C H O \)
Subject: Physics
Which of the air pressures is
appropriate for the production of cathode rays in the discharge tube?
\( A \cdot 1 \mathrm{cm} \) нв
B. \( 1 \mathrm{mm} \) Нg
c. \( 0.001 \mathrm{cm} \) Hg
D. 0.001 \( \mathrm{mm} \) ну
Subject: Chemistry
The oxidation state of \( \mathrm{Mn} \) in \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}} \)
is:
\( A \cdot+5 \)
\( B \cdot+4 \)
\( c \cdot+7 \)
\( D \cdot+6 \)
Subject: Maths
A unit vector parallel to the intersection of the planes \( \vec{r} \cdot(\hat{i}-\hat{j}+\hat{k})=5 \) and \( \vec{r} \)
\( (2 \hat{i}+\hat{j}-3 \hat{k})=4 \) can be
This question has multiple correct options
\( \frac{2 \hat{i}+5 \hat{j}+3 \hat{k}}{\sqrt{38}} \)
B. \( \frac{2 \hat{i}-5 \hat{j}+3 \hat{k}}{\sqrt{38}} \)
c. \( \frac{-2 \hat{i}-5 \hat{j}-3 \hat{k}}{\sqrt{38}} \)
D. \( \frac{-2 \hat{i}+5 \hat{j}-3 \hat{k}}{\sqrt{38}} \)
Subject: Chemistry
Assertion
Oxygen is more electronegative than
sulphur, yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic, while \( \boldsymbol{H}_{2} \boldsymbol{O} \)
is neutral.
Reason
H-S bond is weaker than O-H bond.
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
Simplify : \( \frac{\boldsymbol{a}^{3}-\mathbf{2 7}}{\mathbf{5 a}^{2}-\mathbf{1 6 a}+\mathbf{3}} \div \)
\( \frac{\boldsymbol{a}^{2}+\mathbf{3} \boldsymbol{a}+\mathbf{9}}{\mathbf{2 5 a}^{2}-\mathbf{1}} \)
Subject: Chemistry
\( K M n O_{4} \) reacts with oxalic acid
according to the equation \( 2 M n O_{4}^{-}+5 C_{2} O_{4}^{2-}+16 H^{+} \rightarrow \)
\( \mathbf{2} M n^{2+}+\mathbf{1 0} C O_{2}+\mathbf{8} H_{2} O \)

Here \( , 20 m L \) of \( 0.1 \mathrm{M} K M n O_{4} \) is
equivalent to:

This question has multiple correct options
A \( \cdot 120 m L \) of 0.25 M \( H_{2} C_{2} O_{4} \)
B. \( 50 m L \) of 0.10 M \( H_{2} C_{2} O_{4} \)
c. \( 25 m L \) of 0.20 M \( H_{2} C_{2} O_{4} \)
D. \( 50 m L \) of \( 0.20 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \)
Subject: Physics
Two short magnets of magnetic moment \( 1000 A m^{2} \) are placed as
shown at the corners of a square of side
10 \( c m . \) The net magnetic induction at \( P \)
is
A \( .0 .1 T \)
B. \( 0.2 T \)
c. \( 0.3 T \)
D. \( 0.4 T \)
Subject: Physics
A uniform chain of mass \( M \) and length
\( \boldsymbol{L} \) is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in
this position. Any portion that strike the floor comes to rest. Assuming that the chain does not form a heap on the floor,
calculate the force exerted by it on the
floor when a length \( x \) has reached the
floor
Subject: Maths
A plane passes through (1,-2,1) and is
perpendicular to the planes \( 2 x-2 y+ \)
\( z=0 \) and \( x-y+2 z=4 . \) Then the
distance of the plane from the point
(1,2,2) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \sqrt{2} \)
\( D \cdot 2 \sqrt{2} \)
Subject: Chemistry
Carbonic acid, \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \) is a diprotic
acid for which \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4 . 2} \times \mathbf{1 0}^{-\mathbf{7}} \) and
\( \boldsymbol{K}_{2}=\mathbf{4 . 7} \times \mathbf{1 0}^{-11} . \) Which solution will
produce a \( p H \) closest to \( 9 ? \)
A \( .0 .1 M H_{2} C O_{3} \)
в. \( 0.1 M \) Na\( _{2} \) С \( O_{3} \),
c. \( 0.1 M \) NaHCO\( _{3} \)
Subject: Chemistry
Consider the following ligands \( N H_{2}^{-} \)
acac (Acetylacetone), \( O H^{-}, \) Gly, \( O_{2}^{-} \) Phen, DMG, \( N O_{2}^{-}, C O_{3}^{2-}, C l^{-}, C H_{3} C O O^{-}, e n, S O_{4}^{2} \)
Then calculate value of " \( \boldsymbol{P}+\boldsymbol{Q}-\boldsymbol{R}- \)
\( \boldsymbol{S}^{\prime \prime} . \) Here
P: Total number of ligands which act as bridging as well as monodentate only.
Q: Total number of flexidentate ligands.
R: Total number of bidentate ligands only.
S: Total number of unsymmetrical bidentate ligands.
\( A \)
B. 2
\( c .5 \)
D. 6
Subject: Physics
The increasing order of frequencies for infrared rays, Ultraviolet rays-, X-rays and Y-rays will be-
A. y-rays, X-rays, Infrared rays, Ulterviolet rays
B. X-rays,Y-rays Infrared rays,Ultraviolet rays
C. Infrared rays, Ultraviolet rays,X-rays, Y-rays
D. Ultraviolet rays,X-rays, Y-rays Infrared rays
Subject: Chemistry
The mass of one litre of a sample of ozonized oxygen at NTP was found to be 1.5 g. When 100 mL of this mixture at NTP were treated with turpentine oil, the
volume was reduced to \( 90 \mathrm{mL} \), hence, the molar mass (in gm) of ozone is (write the answer as the interger at
ten's digit place):
Subject: Maths
Prove that, \( [\boldsymbol{x}]+[\mathbf{5} \boldsymbol{x}]+[\mathbf{1 0 x}]+[\mathbf{2 0 x}]= \)
\( 36 k+35 . k \varepsilon I \) does not have any real
solution. Here [.] denotes greatest integer function.
Subject: Physics
The mean free path of the molecule of a
certain gas at \( 300 \mathrm{K} \) is \( 2.6 \times 10^{-5} \mathrm{m} \)
The collision diameter of the molecule
is \( 0.26 \mathrm{nm} . \) Calculate
(a) pressure of the gas, and
(b) number of molecules per unit
volume of the gas.
B. (a) \( 1.281 \times 10^{22} \mathrm{m}^{-3} \) (b) \( 5.306 \times 10^{3} \mathrm{Pa} \)
D. (a) 2.56 \( \times 10^{23} \mathrm{m}^{-3} \) (b) \( 10.612 \times 10^{2} \mathrm{Pa} \)
Subject: Maths
\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^{3}} \) equals:
A \( \cdot \frac{1}{24} \)
B. \( \frac{1}{16} \)
c. \( \frac{1}{2} \)
D.
Subject: Chemistry
Assertion
According to Dobernier's, a group of three similar elements arranged in their increasing atomic weights so that atomic weight of middle is equal to the
arithmetic mean of the other two
elements.
Reason
Atomic weight is equal to one twelfth of mass of a carbon atom.
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. Assertion is incorrect but Reason is correct
Subject: Maths
If \( A(2,2,-3), B(5,6,9), C(2,7,9) \) be
the vertices of a triangle. The internal bisector of the angle \( A \) meets \( B C \) at the
point \( D, \) then find the coordinates of \( D \)
A \( \cdot\left(\frac{13}{2}, \frac{7}{2}, 9\right) \)
В \( \cdot\left(\frac{7}{2}, \frac{13}{2}, 9\right) \)
c. \( \left(\frac{9}{2}, \frac{7}{2}, 9\right) \)
D. \( \left(\frac{13}{2}, \frac{9}{2}, 9\right) \)
Subject: Maths
If \( \boldsymbol{m} \sin \boldsymbol{\theta}=\boldsymbol{n} \sin (\boldsymbol{\theta}+\boldsymbol{2} \boldsymbol{\alpha}), \) then
\( \tan (\boldsymbol{\theta}+\boldsymbol{\alpha}) \cdot \cot \boldsymbol{\alpha} \) equal to
A. \( \frac{1-n}{1+n} \)
в. \( \frac{m+n}{m-n} \)
c. \( \frac{m-n}{m+n} \)
D. \( \frac{1+n}{1-n} \)
Subject: Physics
A N-pole of a very long magnetic needle is placed at a distance of \( 20 \mathrm{cm} \) from a
point P. If the pole strength of the magnetic needle is \( 40 \mathrm{Am} \), the magnetic induction at the point \( \mathrm{P} \) is
\( \mathbf{A} \cdot 10^{-3} \mathbf{T} \)
B . \( 10^{-4} \mathrm{T} \)
\( \mathbf{c} \cdot 10^{-6} \mathbf{T} \)
D. \( 10^{-8} \) T
Subject: Physics
A satellite is to be placed in equatorial geostationary orbit around earth for communication. The height of such a satellite is
\( \left[M_{E}=6 \times 10^{24} k g, R_{E}=6400 k m, T=\right. \)
A \( .3 .57 \times 10^{5} m \)
В. \( 3.57 \times 10^{6} m \)
c. \( 3.57 \times 10^{7} m \)
D. \( 3.57 \times 10^{8} m \)
Subject: Chemistry
For the reaction in equilibrium,
\[
N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g)
\]
The concentrations of \( N_{2} O_{4} \) and \( N O_{2} \)
at equilibrium are \( 4.8 \times 10^{-2} \) and
\[
1.2 \times 10^{-2} \text {mol } L^{-1} \text {respectively. The }
\]
value of \( K_{c} \) for this reaction is:
A \( \cdot 3 \times 10^{-3} \) molL \( ^{-1} \)
-
B. \( 3 \times 10^{3} \) molL \( ^{-1} \)
c. \( 3.3 \times 10^{2} \) molL \( ^{-1} \)
D. \( 3 \times 10^{-1} \mathrm{molL}^{-1} \)
Subject: Maths
Multiply:
\( -5 c d^{2} \) by \( -5 c d^{2} \)
\( \mathbf{A} \cdot 25 c^{2} d^{5} \)
\( \mathbf{B} \cdot 25 c^{3} d^{4} \)
\( \mathbf{C} \cdot 25 c^{2} d^{3} \)
D. \( 25 c^{2} d^{4} \)
Subject: Maths
if \( \lim _{x \rightarrow 0} \frac{a \sin x-b x+c x^{2}+x^{3}}{2 x^{2} \log (1+x)-2 x^{3}+x^{4}} \)
exists and is finite, then
A \( \cdot a=-6, L=-\frac{3}{40} \)
B. \( a=-6, L=\frac{3}{40} \)
c. \( b=6, c=0 \)
D. \( a=-6, b=-6, L=\frac{3}{40} \)
Subject: Physics
Two SHMs are given by \( \boldsymbol{Y}_{\mathbf{1}}= \)
\( A \sin \left(\frac{\pi}{2} t+\phi\right) \) and \( Y_{2}=B \sin \left(\frac{2 \pi t}{3} t+\right. \)
\( \phi \). The phase difference between these
two after '1' sec is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{4} \)
D.
Subject: Chemistry
A metal \( M \) readily forms water-soluble
sulphate \( M S O_{4}, \) water-insoluble
hydroxide \( M(O H)_{2} \) and oxide \( M O . \) The
oxide and hydroxide are soluble in NaOH. The \( M \) is:
\( A . B e \)
в. \( M g \)
\( c . C a \)
D. \( S r \)
Subject: Physics
A thin prism of glass is placed in air and water successively. If \( \mu=\frac{3}{2} \) and \( \mu=\frac{4}{3} \)
then the ratio of deviations produced by the prism for a small angle of incidence when placed in air and water is
\( A \cdot 4: 1 \)
B. 3:4
\( c \cdot 1: \)
D. 9: 16
Subject: Physics
A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a
tensile force of \( 400 \mathrm{N} \) is applied to each
end of the wire. What minimum
diameter is required for the wire?? \( \boldsymbol{Y}_{\text {steel}}=\mathbf{2 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \)
Subject: Maths
A coin is tossed 150 times and the
outcomes are recorded. The frequency distribution of the outcomes \( H \) (i.e.,
head) and \( T \) (i.e., tail) is given below :
Outcome
\[
\begin{array}{ll}
\boldsymbol{H} & \boldsymbol{T} \\
& \\
85 & 65
\end{array}
\]
Frequency
Find the value of \( P(H) \), i.e., probability of
getting a head in a single trial.
\( \mathbf{A} \cdot P(H)=0.769(\text { approx }) \)
B . \( P(H)=0.663 \) (approx)
\( \mathbf{c} \cdot P(H)=0.567(\text { approx }) \)
D. None of these
Subject: Physics
The figure is a graph of the coordinate
of a spider crawling along the \( x \) -axis. \( (a) \)
Graph its velocity and acceleration as
functions of time,
(b) In a motion
diagram, show the position, velocity,
and acceleration of the spider at the five
times: \( t=2.5 s, t=10 s, t=20 s, l=30 s \)
and \( t=37.5 \) s.
Subject: Chemistry
Consider the following reaction
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{E} ; \boldsymbol{K}_{c}=\mathbf{6} \)
\( \mathbf{2} \boldsymbol{B}+\boldsymbol{C} \rightleftharpoons \mathbf{2} \boldsymbol{D} ; \boldsymbol{K}_{c}=\mathbf{4} \)
What will be the equilibrium constant
\( \left.K_{c}\right) \) for the following reaction? \( \boldsymbol{A}+\boldsymbol{D} \rightleftharpoons \boldsymbol{E}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C} \)
Subject: Physics
On an unbaked road, a cyclist
negotiating a bend of radius \( r \) at
velocity \( v \) must lean inwards by an
angle \( \theta \) equal to
A \( \cdot \tan ^{-1}\left(v^{2} / g\right) \)
B. \( \tan ^{-1}(g / v) \)
c. \( \tan ^{-1}\left(v^{2} / g r\right) \)
D. \( \tan ^{-1}\left(r g / v^{2}\right) \)
Subject: Maths
In a hockey match, both teams \( A \) and \( B \)
scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team \( A \) was
asked to start, find their respective probabilities of winning the match and state whether the decision of the referee
was fair or not.
Subject: Maths
Let, \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) be an invertible function
If \( f(x)=2 x^{3}+3 x^{2}+x-1, \) then
\( f^{\prime-1}(5)= \)
A \( \cdot \frac{1}{13} \)
B.
\( c \cdot 6 \)
D. can not be determined
Subject: Chemistry
The ammonia evolved from the
treatment of \( 0.30 g \) of an organic compound for the estimation of nitrogen was passed in 100 m \( L \) of 0.1 \( M \) sulphuric acid. The excess of acid required \( 20 m L \) of 0.5 sodium hydroxide solution hydroxide solution for complete neutralization. The organic compound is:
A. acetamide
B. thiourea
c. urea
D. benzamide
Subject: Chemistry
Which of the following give \( \boldsymbol{S}_{\boldsymbol{N}} \mathbf{1} \)
reaction?
Select the correct answer.
I.
II.
III.
\( \mathbf{I V} \)
\( \mathbf{A} \cdot(I),(I I) \) and \( (I I I) \)
B. \( (I) \) and \( (I I) \)
C \( .(I I),(I I I) \) and \( (I V) \)
D. \( (I),(I I I) \) and \( (I V) \)
Subject: Chemistry
Which statements are correct about the
figure given below?
This question has multiple correct options
A. It is sucrose
B. Due to presence of hemi-acetal linkage, it is a non educing sugar
c. Left side unit is \( \alpha \) -D-Glucose and right side unit is \( \beta-D \) ructose
D. Due to absence of hemi-acetal linkage, it can't show mutarotation
Subject: Chemistry
Identify the sets of electronic transitions associated with release of
energy and absorption of energy.
\( A \cdot n=4 \) to \( n=1 ; n=2 \) to \( n=1 \)
B. \( n=4 \) to \( n=3 ; n=4 \) to \( n=2 \)
\( c \cdot n=3 \) to \( n=5 ; n=2 \) to \( n=3 \)
D. \( n=3 \) to \( n=2 ; n=1 \) to \( n=2 \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})-\boldsymbol{x} \boldsymbol{y} \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \lim _{\boldsymbol{h} \rightarrow \mathbf{0}} \frac{\boldsymbol{f}(\boldsymbol{h})}{\boldsymbol{h}}=\mathbf{3}, \) then the
area bounded by the curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \)
and \( \boldsymbol{y}=\boldsymbol{x}^{2} \) is:
A . 1
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
If \( \boldsymbol{y}=\log \left[\tan \left(\frac{\boldsymbol{\pi}}{\boldsymbol{4}}+\frac{\boldsymbol{x}}{2}\right)\right] \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \cdot \sec x \)
B. \( \sin x \)
c. \( \operatorname{cosec} x \)
D. \( \sec \frac{x}{2} \)
Subject: Physics
A solenoid of length \( 1.0 m, \) radius \( 1 \mathrm{cm} \)
and total turns 1000 wound on it,
carries a current of 5 A. Calculate the
magnitude of the axial magnetic field inside the solenoid. If an element was to
move with a speed of \( 104 m / s \) along the
axis of this current carrying solenoid, what would be the force experienced by this electron?
Subject: Physics
Photons of energy 7 e \( V \) are incident on two metals \( A \) and \( B \) with work functions
\( 6 \mathrm{eV} \) and \( 3 \mathrm{eV} \) respectively. The minimum de Broglie wavelengths of the emitted photoelectrons with maximum
energies are \( \lambda_{A} \) and \( \lambda_{B}, \) respectively
where \( \boldsymbol{\lambda}_{\boldsymbol{A}} / \boldsymbol{\lambda}_{\boldsymbol{B}} \) is nearly:
A. 0.5
B. 1.4
\( c \cdot 4.0 \)
D. 2.0
Subject: Maths
If \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+ \)
\( c=0 \) represents a pair of parallel lines, then \( \sqrt{\frac{g^{2}-a c}{f^{2}-b c}}= \)
A.
B. \( \sqrt{\frac{a}{b}} \)
\( c \cdot \sqrt{\frac{b}{a}} \)
\( D \cdot \frac{b}{a} \)
Subject: Chemistry
Name the following:
a) An element which forms the triple
covalent bond.
b) An element which obtains the noble
gas configuration of neon by losing three electrons.
c) An element which gains two electrons to obtain the noble gas configuration of neon.
d) Name a compound which is an exception to the octet rule.
e) \( \ln S O_{2} \) molecule, which element is a
donor of electrons.
Subject: Chemistry
The charge required to reduce 1 mole
\( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) to \( \mathrm{Cr}^{3+} \) ions is:
\( \mathbf{A} \cdot 3 F \)
B. \( 3 C \)
\( \mathbf{c} \cdot 6 F \)
D . \( 2 \times 6.023 \times 10^{23} e^{-} \)
Subject: Chemistry
Find the accurate statement for the
significance of Avogadro's number?
A. It is the conversion factor between grams and atomic mass units
B. It is a universal physical constant just as the speed of light.
C. It is the number of particles that is required to fill a \( 1- \) liter container.
D. It is the inverse diameter of an H atom.
E. It is the number of electrons in the universe.
Subject: Physics
Ratio of electric and magnetic field due to moving point charge if its speed is
\( 4.5 \times 10^{5} \mathrm{m} / \mathrm{s} \)
A \( .2 \times 10^{1} \)
B . \( 3 \times 10^{11} \)
\( c \cdot 2 \times 10^{8} \)
D. \( 3 \times 10^{12} \)