AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The diagram shows the change \( x \) in the length of a thin uniform wire caused by the application of stress \( F \) at two
different temperatures \( T_{1} \) and \( T_{2} . \) The
variations shown suggest that:
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
c. \( T_{1}=T_{2} \)
D. None of these
Subject: Physics
A sphere is projected up an inclined
plane with a velocity \( v_{0} \) and zero angular velocity as shown. The coefficient of friction between the
sphere and the plane is \( \mu=\tan \theta . \) If
the total time of rise of the sphere is
\( \frac{\boldsymbol{x} \boldsymbol{v}_{0}}{\boldsymbol{g} \sin \theta}, \) find the value of \( \boldsymbol{2} \boldsymbol{x} \)
Subject: Maths
find the 7 th term in the expansion of \( \left(4 x-\frac{1}{2 \sqrt{x}}\right)^{13} \)
A \( .439296 x^{7} \)
В. \( 439296 x^{4} \)
c. \( 439396 x^{7} \)
D. \( 43396 x^{4} \)
Subject: Maths
ff \( y=e^{4 x}+2 e^{-x} \) satisfies the equation
\( \boldsymbol{y}_{3}+\boldsymbol{A} \boldsymbol{y}_{1}+\boldsymbol{B} \boldsymbol{y}=\mathbf{0} \) then the value of
\( A B \) is
Subject: Chemistry
What are the peculiarities of the series
\( \boldsymbol{C H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{4} \boldsymbol{H}_{10}-_{--}-_{-} \) etc?
Write the general formula of these compounds.
Subject: Physics
The work done in pulling up a block of
wood weighing \( 2 k N \) for a length of \( 10 m \) on a smooth plane inclined at an angle
of \( 15^{\circ} \) with the horizontal is:
\begin{tabular}{l} 
A. \( 5.17 k J \) \\
\hline
\end{tabular}
в. \( 6.42 k J \)
c. \( 7.03 k J \)
D. \( 9.82 k J \)
Subject: Physics
A potentiometer wire is \( 100 \mathrm{cm} \) long and a constant potential difference is maintained across it. Two cells are
connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 \( \mathrm{cm} \) and \( 10 \mathrm{cm} \) from the positive end of the wire in the two cases. The ratio of
emf's is:
A . 5: 1
в. 5: 4
\( c .3: 4 \)
D. 3: 2
Subject: Maths
If \( (a, b)(c, d) \) and \( (a-c, b-d) \) are collinear
then
A \( \cdot \frac{a}{b}=\frac{c}{d} \)
в. \( \frac{a}{d}=\frac{b}{c} \)
c. \( \frac{a}{c}=\frac{d}{b} \)
D. \( \frac{a}{b}=\frac{b}{c} \)
Subject: Chemistry
Calculate the \( \% \) p-character in the orbital occupied by the lone pairs in water molecules:
[Given : \( \angle H O H \) is \( 104.5^{\circ} \) and \( \cos \) \( (\mathbf{1 0 4 . 5})=-\mathbf{0 . 2 5}] \)
A . \( 80 \% \)
B . 20\%
c. \( 70 \% \)
D. 75\%
Subject: Physics
The diagram shows the graphs of
pressure vs density for a given mass of
an ideal gas at two temperatures \( T_{1} \) and \( T \)
2
\( A \cdot T_{1}>T_{2} \)
B. \( T_{1}=T_{2} \)
\( c \cdot T_{1}<T_{2} \)
D. Any of the three are possible
Subject: Maths
\( \operatorname{Let} P(x)=x^{3}-6 x^{2}+B x+C \) has \( 1+5 \)
as a zero and \( \mathrm{B}, \mathrm{C} \) real number, then
value of \( (\mathrm{B}+\mathrm{C}) \) is
A . -70
B. 70
\( c \cdot 24 \)
D. 138
Subject: Chemistry
Write the stoichiometric coefficient for
the following reaction:
\( \boldsymbol{x} \boldsymbol{I}_{2}+\boldsymbol{y} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{z} \boldsymbol{I}^{-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
B. \( x-(3), y-(2), z-(3) \)
\( c \cdot x-(3), y-(6), z-(5) \)
\( D \cdot x-(3), y-(3), z-(3) \)
Subject: Maths
If \( (x-1),(x+1) \) and \( (x-2) \) are
factors of \( \boldsymbol{x}^{4}+(\boldsymbol{p}-\boldsymbol{3}) \boldsymbol{x}^{3}-(\boldsymbol{3} \boldsymbol{p}- \)
5)\( x^{2}+(2 p-9) x+6, \) what is the value
of p?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D.
Subject: Physics
Find the magnetic moment of the spiral
with a given current.
A \( \cdot p=25 m A \cdot m^{2} \)
B . \( p=15 \mathrm{mA} \cdot \mathrm{m}^{2} \)
C \( \cdot p=30 \mathrm{mA} \cdot \mathrm{m}^{2} \)
D. \( p=50 \mathrm{mA} \cdot \mathrm{m}^{2} \)
Subject: Chemistry
Ethyl chloride on reduction with \( L i A l H_{4} \)
gives compound \( x \) as important
product. \( x \) on chlorination with one mole
of \( C l_{2} \) in the presence of light at
ordinary temperature gives \( y \). What is \( y \)
\( ? \)
A. \( C H_{3} C l \)
в. \( C H_{2} C l_{2} \)
\( \mathbf{c} \cdot C_{2} H_{5} C l \)
\( \mathrm{D} \cdot C_{2} H_{4} C l_{2} \)
Subject: Physics
Two identical balls \( A \& 13 \) of mass \( m \)
each are placed on a fixed wedge as shown in figure Ball B is kept at rest and it is released just before two balls
collides. Bali A roll down without
slipping on inclined plane \( \& \) collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is:
A \( \cdot \frac{m g h}{7} \)
B. \( \frac{m g h}{2} \)
c. \( \frac{2 m g h}{5} \)
D. \( \frac{7 m g h}{5} \)
Subject: Chemistry
The electronic configuration of \( \boldsymbol{E} \boldsymbol{u} \)
(Atomic No. 63 ), \( G d \) (Atomic No. 64 ) and
Tb (Atomic No. 65 ) are :
A \( \cdot[X e] 4 f^{7} 6 s^{2},[X e] 4 f^{8} 6 s^{2} \) and \( [X e] 4 f^{8} s d^{1} 6 s^{2} \)
B . \( [X e] 4 f^{7} 5 d^{1} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{9} 6 s^{2} \)
C \( \cdot[X e] 4 f^{6} 5 d^{1} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{8} 5 d^{1} 6 s^{2} \)
D \cdot \( [X e] 4 f^{7} 6 s^{2},[X e] 4 f^{7} 5 d^{1} 6 s^{2} \) and \( [X e] 4 f^{9} 6 s^{2} \)
Subject: Chemistry
When molecules are in a condensed
physical state (liquid or solid), they exert attractive intermolecular forces
(IMF), on one another. One example of this type of attractive force is hydrogen bonding.

Which of the labelled arrows \( (\leftarrow \text { and } \leftrightarrow) \) in the diagram BEST illustrated
hydrogen bonding for ammonia, \( N H_{3} ? \)
A. Hydrogen Bond
в.
c.
D. None of the above
Subject: Chemistry
The process is spontaneous at the given temperature, if
A. \( \Delta H \) is \( +v e \) and \( \Delta S \) is \( -v e \)
B. \( \Delta H \) is \( -v e \) and \( \Delta S \) is \( +v e \)
\( \mathrm{c} . \Delta H \) is \( +v e \) and \( \Delta S \) is \( +v e \)
D. \( \Delta H \) is \( +v e \) and \( \Delta S \) is equal to zero
Subject: Chemistry
The combustions of benzene (I) gives
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(l) . \) Given that heat of
combustion of benzene at constant
volume is \( -3263.9 k J \) mol\( ^{-1} \) at \( 25^{\circ} C \)
heat of combustion \( \left(\text { in } k J m o l^{-1}\right) \) of
benzene at constant pressure will be:
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A \( .+3260 \)
B . -3267.6
\( \mathbf{c} .+4152.6 \)
D. -452.46
Subject: Chemistry
A current is passed through 500 mLof
an aqueous solution of \( \boldsymbol{C a} \boldsymbol{I}_{2} \). After
sometime, it is observed that 50
millimoles of \( I_{2} \) have been formed.
Which of the following statements is(are) correct?
This question has multiple correct options
A. The number of faradays of charge passed through the solution is \( 0.10 F \)
B. The volume of dry \( H_{2} \) at \( S T P \) that has been formed during electrolysis is \( 1120 \mathrm{mL} \).
c. The \( p H \) of the solution is nearly 0.7
D. The mass of calcium produced is \( 2.0 g \).
Subject: Chemistry
Assertion
Osmotic pressure of \( 0.1 N \) urea solution
is less than that of \( 0.1 M \) NaCl
solution.
Reason
Osmotic pressure is not colligative property.
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
The press plungers of a Bramah
(hydraulic) press is \( 40 \mathrm{cm}^{2} \) in crosssection and is used to lift a load of
mass \( 800 k g . \) What minimum force is
required to be applied to the pump plunger if its cross-sectional area is
\( 0.02 m^{2} ? \)
Subject: Chemistry
The increasing order of the strength of hydrogen bond in the following mentioned linkages is
(i) \( \boldsymbol{O}-\boldsymbol{H}-\boldsymbol{S} \) (ii) \( \boldsymbol{S}-\boldsymbol{H}-\boldsymbol{O} \)
\( \boldsymbol{F}-\boldsymbol{H}-\boldsymbol{O}(\text { iv }) \boldsymbol{F}-\boldsymbol{H}-\boldsymbol{O} \)
A \( \cdot(i)<(i i)<(i v)<(i i i) \)
B. \( (i i)<(i)<(i v)<(i i i) \)
c. \( (i)<(i i)<(i i i)<(i v) \)
D. \( (i i)<(i)<(i i i)<(i v) \)
Subject: Maths
The order of a matrix \( \left[\begin{array}{lll}2 & 5 & 7\end{array}\right] \) is
\( A \cdot 3 \times 3 \)
B. \( 1 \times 1 \)
\( c \cdot 3 \times 1 \)
D. \( 1 \times 3 \)
Subject: Physics
Mark the incorrect option.
A. Ampere's law states that flux \( B \) through any closed
surface is \( \mu_{0} \) times the current passing through the area bounded by closed sourface
B. Gauss's law for magnetic field in magnetostatics serves the same purpose as Gauss's law for electric for electric field in electrostatics
C. Gauss's law for magnetic field states that the flux of \( B \) through any closed surface is always zero, whether or not there are currents within the surface
D. All the above
Subject: Physics
What is the electric potential at the centre of a hemisphere of radius \( \mathrm{R} \) and
having surface charge density \( \sigma ? \)
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
c. \( \frac{\sigma}{\varepsilon_{0}} R \)
D. \( \frac{\sigma}{2 \varepsilon_{0}} R \)
Subject: Chemistry
Assertion
In an electrochemical cell, the electrode
that is the site of reduction is called the
anode.
Reason
Oxidation always occurs at the cathode.
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: Chemistry
Consider the reactions:
\( 2 S_{2} O_{3}^{2-}(a q)+I_{2}(s) \longrightarrow S_{4} O_{6}^{2-}(a q)+ \)
\( 2 I^{-}(a q) \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(l) \longrightarrow \)
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{4} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\mathbf{1 0} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
Why does the same reductant
thiosulphate react differently with iodine and bromine?
Subject: Chemistry
In a first-order reaction the
concentration of the reactant is
decreased from \( 1.0 M \) to \( 0.25 M \) in
20 min. The rate constant of the
reaction would be:
A .10 min \( ^{-1} \)
B. 6.931 min \( ^{-1} \)
\( \mathbf{c} \cdot 0.6931 \mathrm{min}^{-1} \)
D. 0.06931 min\( ^{-1} \)
Subject: Physics
A drilling machine of power \( \boldsymbol{P} \) watt is used to drill a hole in copper block of mass \( M \) kg. If the specific heat of copper is \( s J k g^{-1} o C^{-1} \) and \( 40 \% \) of the power is lost due to heating of the machine, the rise in the temperature of
the block in \( T \) seconds will be (in \( ^{o} C \) )
A \( \cdot \frac{0.6 P T}{M s} \)
в. \( \frac{0.6 P}{M s T} \)
c. \( \frac{0.4 P T}{M s} \)
D. \( \frac{0.4 P}{M s T} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\boldsymbol{x} \epsilon \boldsymbol{Z}: \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1 2}\} . \) Show that
\( \mathrm{R}=\{(a, b): a, b \epsilon A,|a-b| \) is divisible
by \( 4\} \) is an equivalence relation. Find
the set of all elements related to \( 1 . \) Also
write the equivalence class [2]
Subject: Physics
A car moving with speed of \( 40 \mathrm{km} / \mathrm{hr} \) can be stopped by applying brakes after at least \( 2 m \). If the same car is moving
with a speed of \( 80 \mathrm{km} / \mathrm{hr} \) what is the minimum stopping distance?
A \( .2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 8 m \)
Subject: Chemistry
Which of the following set of species do
not have planar structure?
A \( \cdot I_{3}^{-}, C H_{3}, C l O_{3}^{-}, S i F_{6}^{2}- \)
B . \( I_{3}^{+}, I C l_{4}^{-}, A l_{2} C l_{6} . T e C l_{4} \)
c. \( S C l_{2}^{-}, N_{2} O_{5}, S F_{4}, X e O F_{4} \)
D. \( I_{2} C l_{6}, X e F_{2}, B r F_{4}^{-}, X e F_{5}^{-} \)
Subject: Physics
A resistor of \( 100 \Omega \), a pure inductance coil of \( L=0.5 \mathrm{H} \) and capacitor are in series in a circuit containing an a.c sources of \( 200 \mathrm{V}, 50 \mathrm{Hz} \). In the circuit, current is added is ahead of the voltage
by \( 30^{0} . \) Find the value of the capacitance
A . 1.46
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
The following table shows ages of 300 patients getting medical treatment in a
hospital on a particular day.
Find the median age of patients
Age (in 1 20
30
years)
\[
\text { 20 } \quad 30
\]
40
50
No. of \( \quad \) 60 \( \quad 42 \) Patients \( \begin{array}{llll}60 & 42 & 55 & 70\end{array} \)
\( \mathbf{A} \cdot 33.73 \) years
B. 38.73 years
C. 42.37 years
D. 44.73 years
Subject: Maths
Factorise the expression: \( 10 a b+4 a+ \)
\( 5 b+2 \)
A . \( (a+1)(5 b+1) \)
B . \( (2 a-1)(5 b+1) \)
c. \( (a+1)(b+10) \)
D. \( (2 a+1)(5 b+2) \)
Subject: Chemistry
Find the concentration of \( \boldsymbol{H}^{+}, \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \)
and \( C O_{3}^{2-} \) in a \( 0.01 M \) solution of
carbonic acid if the pH of the solution is \( \mathbf{4 . 1 8}, \mathbf{K}_{\mathbf{1}}=\mathbf{4 . 4 5} \times \mathbf{1 0}^{-\mathbf{7}}, \mathbf{K}_{\mathbf{2}}=\mathbf{4 . 6 9} \times \)
\( 10^{-11} \)
Subject: Physics
Figure shows a potentiometer circuit
for comparison of two resistances. The
balance point with a standard resistor
\( R=10.0 \Omega \) is found to be \( 58.3 \mathrm{cm}, \) while
that with the unknown resistance \( X \) is
\( 68.5 \mathrm{cm} . \) Determine the value of \( \mathrm{X} \). What
might you do if you failed to find a balance point with the given cell of emf
\( \epsilon ? \)
Subject: Chemistry
On a given condition, the equilibrium
concentration of \( \mathrm{HI}, \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are 0.80 0.10 and 0.10 mole/litre. The equilibrium
constant for the reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \)
\( 2 H I \) will be-
A . 64
B. 12
\( c \cdot 8 \)
D. 0.8
Subject: Chemistry
In the reaction \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}+ \)
\( S, \) the oxidizing agent is :
A \( . H_{2} \)
в. \( C l_{2} \)
c. \( H C l \)
D. \( S \)
Subject: Physics
A copper wire of resistance \( R \) is cut in
to ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have
a resistance
A. \( R \)
в. \( \frac{R}{4} \)
c. \( \frac{R}{5} \)
D. \( \frac{R}{25} \)
Subject: Physics
Two plano convex lenses of same material and of focal lengths \( 20 \mathrm{cm} \& 5 \) cm should be arranged such that the combination is free from chromatic
aberration. Then effective focal length of the combination will be:
A. \( 20 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 12.5 \mathrm{cm} \)
\( D \cdot 8 \mathrm{cm} \)
Subject: Maths
Evaluate: \( \cos \left[2 \tan ^{-1}\left[\frac{1}{7}\right]\right] \)
\( A \cdot \sin \left(4 \cot ^{-1} 3\right) \)
B. \( \sin \left(3 \cot ^{-1} 4\right) \)
\( c \cdot \cos \left(3 \cot ^{-1} 4\right) \)
D. \( \cos \left(4 \cot ^{-1} 4\right) \)
Subject: Chemistry
Although F is more electronegative than
H, the resultant dipole moment of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
is much more than that of \( N F_{3} \). It can
be explained as:
A. the lone pair of nitrogen opposes the dipole moment of \( N F_{3} \) while it is added to the dipole moment of \( N H_{3} \)
B. all the dipoles of \( N F_{3} \) are in same direction
c. all the dipoles of \( N H_{3} \) are in opposite direction
D. \( N H_{3} \) has a regular geometry while \( N F_{3} \) has irregular geometry which makes dipole moment of \( N H_{3} \) more than \( N F_{3} \)
Subject: Physics
The current in the primary circuit of a potentiometer wire is \( 0.5 \mathrm{A}, \rho \) for the
wire is \( 4 \times 10^{-7} \Omega-m \) and area of
cross-section of wire is \( 8 \times 10^{-6} m^{2} \)
The potential gradient in the wire would be
A. 25 mV/meter
B. 2.5 mV/meter
c. 25 v/meter
D. 10 V/meter
Subject: Physics
An electric dipole consists of two
oppositecharges of magnitude \( 1 \mu \mathrm{C} \)
separated by a distanceof 2cm. The dipole is placed in an electric filed
\( 10^{-5} \mathrm{Vm}^{-1} . \) The maximum torque does
the field exerton the dipole is
\( \mathbf{A} \cdot 10^{-3} \mathrm{Nm} \)
В. \( 2 \times 10^{-13} \mathrm{Nm} \)
c. \( 3 \times 10^{-13} \mathrm{Nm} \)
D. \( 4 \times 10^{-13} \mathrm{Nm} \)
Subject: Biology
Identify the parts as \( A, B, C, D \) in the
given diagram
A . A- Oviduct, B- Uterus, C- Oviduct, D- Ovary
B. A- Cervix, B- Uterus, C- - Ovary, D- Tumor
C. A- Uterus, B- Uterine cavity, C- Oviducal funnel, D Ovary
D. A- Cervix, B- Uterine cavity, C- Fallopian tube, D- Ovary
Subject: Physics
For a coil having \( \boldsymbol{L}=2 \boldsymbol{m} \boldsymbol{H}, \) current
flow through it is \( I=t^{2} e^{-t} \) then the time
at which emf become zero: -
\( \mathbf{A} \cdot 2 s \)
B . \( 1 s \)
c. \( 4 s \)
D. \( 3 s \)
Subject: Chemistry
Which of the following are
diastereomers?
i. Me H
ì.
\( (\mathbf{I}) \)
iii. \( \underset{\mathbf{H}}{\mathbf{H}}+\underbrace{\mathbf{C O O} \mathbf{H}}_{\mathbf{M e}} \mathbf{B r} \)
iv.
A. (I) and (III)
B. (II) and (IV)
c. (I) and (II)
D. None of the above
Subject: Physics
Assertion
Two persons on the surface of moon
cannot talk to each other.
Reason
There is no atmosphere on moon.
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
A particle with restoring force proportional to displacement and resisting force proportional to velocity
is subjected to a force \( \boldsymbol{F} \) sinw. If the
amplitude of the particle is maximum
for \( \omega=\omega_{1} \) and the energy of the particle
is maximum for \( \omega=\omega_{2} \) then (where \( \omega_{0} \)
natural frequency of oscillation of particle)
\( \mathbf{A} \cdot \omega_{1}=\omega_{0} \) and \( \omega_{2} \neq \omega_{0} \)
B . \( \omega_{1}=\omega_{0} \) and \( \omega_{2}=\omega_{0} \)
C \( \cdot \omega_{1} \neq \omega_{0} \) and \( \omega_{2}=\omega_{0} \)
D. \( \omega_{1} \neq \omega_{0} \) and \( \omega_{2} \neq \omega_{0} \)
Subject: Maths
n given figure triangle \( \mathrm{ABCCCC} \)
circumscribes the circle with center 0
and radius \( 2 \mathrm{cm} \)
Area of \( \Delta A B C \) is \( 16 \mathrm{cm}^{2} \). find \( \mathrm{AB} \)
\( 5 \mathrm{cm} \)
\( 6 c \)
\( 7 \mathrm{cm} \)
Subject: Maths
Find the coefficient of range for the given data
\( \mathbf{5 9}, \mathbf{4 6}, \mathbf{3 0}, \mathbf{2 3}, \mathbf{2 7}, \mathbf{4 0}, \mathbf{5 2}, \mathbf{3 5}, \mathbf{2 9} \)
A . 0.46
B. 0.44
\( c .0 .56 \)
D. 0.124
Subject: Maths
In a packet there are m different books, n different pens and p different pencils. The number of selections of at least one
article of each type from the packet is
A \( \cdot 2^{m+n+p}-1 \)
B . \( (m+1)(n+1)(p+1)-1 \)
\( \mathbf{c} \cdot 2^{m+n+p} \)
D - \( \left(2^{m}-1\right)\left(2^{n}-1\right)\left(2^{p}-1\right) \)
Subject: Physics
A biconvex lens is made of material of
refractive index 1.5 each of radius of
curvature of lens surface is \( 20 \mathrm{cm} \). The
focal length of lens is:
A. \( 20 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( c \cdot 25 \mathrm{cm} \)
D. 30 cm
Subject: Chemistry
Which of the following nuclides belong
to actinium \( \left(U^{235}\right) \) series? This question has multiple correct options
\( \mathbf{A} \cdot P b^{207} \)
B . \( P o^{215} \)
c. \( P_{o^{213}} \)
D. \( _{1} H^{3} \)
Subject: Maths
A cloth merchant says that due to slump in the market, he sells the cloth at \( 10 \% \) loss, but he uses a false metre
scale and actually gain \( 20 \% \). Find the actual length of the scale.
\( A \cdot 80 \mathrm{cm} \)
B. 75 cm
c. \( 70 \mathrm{cm} \)
D. 60 \( m \)
Subject: Maths
Find the expansion of \( (3 x+1)(3 x+2)(3 x+5) \)
A \( \cdot 27 x^{3}+72 x^{2}+51 x+10 \)
B. \( 27 x^{3}-72 x^{2}+51 x+10 \)
c. \( 27 x^{3}+72 x^{2}-51 x+10 \)
D. None of these
Subject: Chemistry
Six grams of hydrogen gas at a temperature of \( 273 K \) was isothermally expanded to five times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. Find the total amount of heat
absorbed by the gas during the entire process (in joules).
A . 78919.4
в. 78990.2
c. 80281.6
D. 80110.8
Subject: Physics
Two infinitely large sheets having
charge densities \( \sigma_{1} \) and \( \sigma_{2} \) respectively
\( \left(\sigma_{1}>\sigma_{2}\right) \) are placed near each other
separated by distance \( d . A \) charge \( q \) is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at
an angle of \( 45^{\circ} \) with the horizontal
towards plate having charge density \( \sigma_{2} \) by distance \( a(a<d) . \) Find work done
by electric field in the process.
Subject: Maths
Given that \( \vec{A}+\vec{B}+\vec{C}=0, \) out of three
vectors two are equal in magnitude and the magnitude of third vector is \( \sqrt{2} \) times that of either of two having equal magnitude. Then angle between vectors are given by
A \( \cdot 30^{\circ}, 60^{\circ}, 90^{\circ} \)
В . \( 45^{\circ}, 135^{\circ}, 150^{\circ} \)
c. \( 90^{\circ}, 135^{\circ}, 150^{\circ} \)
D. \( 90^{\circ}, 135^{\circ}, 135^{\circ} \)
Subject: Chemistry
Assertion
The electrical resistance of any object decreases with increase in its length.
Reason
Electrical resistance of any object
increases with increase in its area of
cross-section.
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 z satisfies \( |z-1|<|z+3| \) then \( \omega= \)
\( 2 z+3-i \) satisfies
This question has multiple correct options
A \( .|\omega-5-i|<|\omega+3+1| \)
B. \( |\omega-5|<|\omega+3| \)
C \( . I_{m}(i \omega)>1 \)
D \cdot \( |a r g(\omega-1)|<\frac{\pi}{2} \)
Subject: Physics
A 2 meter long aluminum pipe at \( 27^{\circ} \mathrm{C} \)
is heated until it is 2.0024 at \( 77^{\circ} \) C. The
coefficient of linear expansion of aluminum is :
A . \( 12 \times 10^{-6} /^{\circ} \mathrm{C} \)
B . \( 24 \times 10^{-6} /^{\circ} \mathrm{C} \)
c. \( 6 \times 10^{-6} /^{\circ} \mathrm{C} \)
D \( .20 \times 10^{-2} \)
Subject: Maths
Solve \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{1}=\boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{y}} \)
\( \mathbf{A} \cdot-1=(x+c) e^{x+y} \)
B \( \cdot 1=(x) e^{x+y}+c \)
\( \mathbf{c} \cdot 1=(x+c) e^{x-y} \)
\( \mathbf{D} \cdot-1=(x) e^{x-y}+c \)
Subject: Maths
If \( \boldsymbol{x}=\sec \boldsymbol{\theta}-\cos \boldsymbol{\theta} \) and \( \boldsymbol{y}=\sec ^{n} \boldsymbol{\theta}- \)
\( \cos ^{n} \theta, \) then \( \left(\frac{d y}{d x}\right)^{2} \) is equal to
A \( \cdot \frac{n^{2}\left(y^{2}+4\right)}{x^{2}+4} \)
\( ^{\text {В } \cdot} \frac{n^{2}\left(y^{2}-4\right)}{x^{2}} \)
\( ^{\mathbf{c}} \cdot_{n}\left(\frac{y^{2}-4}{x^{2}-4}\right) \)
D. \( \left(\frac{n y}{x}\right)^{2}-4 \)
Subject: Physics
Two plates are placed at a separation of \( 2 \mathrm{cm} . \) An electron placed at the perryferry of one plate reaches the second plate in 2 microsecond. Calculate the inner charge density of the surface assuming the case of infinite plate.
A . \( 0.505 \times 10^{-12} \mathrm{Cm}^{-2} \)
В. \( 0.15 \times 10^{-12} \mathrm{Cm}^{-2} \)
c. \( 1.01 \times 10^{-12} \mathrm{Cm}^{-2} \)
D. \( 0.505 \times 10^{-11} \mathrm{Cm}^{-2} \)