AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is the set of products formed when propanol
\( C_{2} H_{2} O H, \) undergoes a combustion
reaction?
A \( \cdot C O_{2(g)} \) and \( H_{2} O_{(l)} \)
B. \( C O_{2(g)} \) and \( H_{2} O_{(g)} \)
\( \mathbf{c} \cdot C_{(a)}, O_{2(g)} \) and \( H_{2} O_{(g)} \)
D. \( C_{(a)}, H_{2(g)} \) and \( H_{2} O_{(g)} \)
E \( \cdot C O_{2(g)}, H_{2} O_{(g)} \) and \( O_{2(g)} \)
Subject: Chemistry
The correct name of
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right]\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{C l}_{4}\right] \) is:
A. Tetraammine dichloro platinum (IV) tetrachloro platinate(II)
B. Dicholoro tetra mmine platinum (IV) tetrachloro platinate (II)
C . Tetrachloro platinum
(II) tetraammine platinate (IV)
D. Tetrachloro platinum (II) dichloro tetraamine platinate \( (1 V) \)
Subject: Maths
Which step in the following problem is wrong? \( \boldsymbol{a}=\boldsymbol{b}=\mathbf{1} \)
\( \boldsymbol{a}=\boldsymbol{b} \)
step-1: \( a^{2}=a b \)
step-2: \( a^{2}-b^{2}=a b-b^{2} \)
step-3: \( (\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{a}-\boldsymbol{b})=\boldsymbol{b}(\boldsymbol{a}-\boldsymbol{b}) \)
step- \( 4: a+b=\frac{b(a-b)}{a-b} \)
\( \boldsymbol{a}+\boldsymbol{b}=\boldsymbol{b} \)
\( \mathbf{1}+\mathbf{1}=\mathbf{1} \)
\( \mathbf{2}=\mathbf{1} \)
A. Step-4
B. Step-3
c. step- -
D. Step- -
Subject: Maths
A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined as
\( f(x)=x^{3}+4 . \) Is it a bijection or not? In
case it is a bijection, then find \( \boldsymbol{f}^{-1}(\mathbf{3}) \)
Subject: Physics
A ball is dropped from a bridge \( 122.5 \mathrm{m} \) above a river. After 2 s, a second ball is
thrown down after it. What must its
initial velocity be so that both hit the water at the same time?
A. \( 49 \mathrm{m} / \mathrm{s} \)
B. \( 55.5 \mathrm{m} / \mathrm{s} \)
c. \( 26.1 \mathrm{m} / \mathrm{s} \)
D. \( 9.8 \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sin ^{2} \boldsymbol{x}\right) \)
\( \mathbf{A} \cdot \sin 2 x \)
B. \( \cos 2 x \)
\( c \cdot \sin 4 x \)
D. \( \cos 4 x \)
Subject: Maths
On the set \( Z \), of all integers \( * \) is defined by \( a * b=a+b-5 . \) If \( 2 *(x * 3)=5 \)
then \( \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .5 \)
D. 10
Subject: Maths
For a zoo to incur a profit,it needs to sell
at least 350 admission tickets each
day. Four student groups, each of which includes 48 students, have purchased
tickets for admission. If \( z \) represents
the number of additional ticket sold
today, and the zoo made its daily profit goal successful, which of the following inequalities could represent all
possible values for \( z ? \)
\( \mathbf{A} \cdot 4(48)+z \leq 350 \)
B \( \cdot 4(48)+z \geq 350 \)
\( \mathbf{c} \cdot 4(48)-z \leq 350 \)
\( \mathbf{D} \cdot 4(48)-z \geq 350 \)
Subject: Physics
Rahul takes 6 hours more than than
Pathak to cover a distance of \( 540 k m \). If
instead, Rahul doubles his speed, he
would reach the destination one and a
half hours before Pathak. Find Pathak's
speed.
A. \( 36 \mathrm{kmph} \)
B. \( 60 \mathrm{kmph} \)
c. \( 45 \mathrm{kmph} \)
D. \( 40 \mathrm{kmph} \)
Subject: Physics
A spherical capacitor has an inner sphere of radius \( 12 \mathrm{cm} \) and an outer
sphere of radius \( 13 \mathrm{cm} . \) The outer sphere is earthed and the inner sphere is given
a charge of \( 2.5 \mu C . \) The space between
the concentric spheres is filled with a liquid of dielectric constant 32
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated
sphere of radius 12 cm. Explain why the latter is much smaller.
Subject: Chemistry
The half period of a first order reaction is 10 minutes. Then its rate constant is:
A \( \cdot 6.93 \times 10^{2} \min ^{-1} \)
B . \( 0.693 \times 10^{-2} \mathrm{min}^{-1} \)
c. \( 6.93 \times 10^{-2} \min ^{-1} \)
D. \( 69.3 \times 10^{-1} \mathrm{min}^{-1} \)
Subject: Physics
At what temperature will the resistance of a copper wire become three times its value at \( 0^{0} \) C? [Temperature coefficient
of resistance for copper \( =4 \times \) \( \left.10^{-3} p e r^{0} C\right]: \)
\( \mathbf{A} \cdot 500^{0} C \)
B . \( 450^{\circ} \mathrm{C} \)
c. \( 600^{0} C \)
D. None of these
Subject: Maths
Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{a^{2}+x^{2}}-a}{x^{2}} \)
A \( \cdot \frac{1}{\sqrt{a}} \)
в. \( \frac{1}{\sqrt{2 a}} \)
\( c \cdot \frac{1}{a} \)
D. \( \frac{1}{2 a} \)
Subject: Chemistry
Which one of the following statement(s)
is/are true?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta E=0 \) for combustion of \( C_{2} H_{6}(g) \) in a sealed rigid
adiabatic container
\( \mathbf{B} \cdot \Delta_{f} H^{o}(S, \text { monolithic}) \neq 0 \)
C . If dissociation energy of \( C H_{4}(g) \) is \( 1656 k J / \) mol and
\( C_{2} H_{6}(g) \) is \( 2812 k J / m o l, \) then value of \( C-C \) bond energy will be \( 328 k J / m o l \)
D. If \( \Delta H_{f}\left(H_{2} O, g\right)=-242 k J / m o l ; \Delta H_{v a p}\left(H_{2} O, l\right)= \)
\( 44 k J / m o l \) then \( \Delta_{f} H^{o}\left(O H^{-}, a q\right) \) will be \( -142 k J / m o l \)
Subject: Physics
Two capacitors of \( 1 \mu F \) and \( 2 \mu F \) are connected in series and this
combination is changed upto a potential difference of 120 volt. What will be the potential difference across \( 1 \mu F \) capacitor:
A . \( 40 v o l t \)
B. 60 volt
c. \( 80 v \) olt
D. \( 120 v o l t \)
Subject: Maths
\( \int_{2}^{4} \frac{\sqrt{x^{2}-4}}{x^{4}} d x= \)
\( A \cdot \frac{3}{32} \)
B. \( \frac{\sqrt{3}}{32} \)
\( c \cdot 3 \)
8
D. \( \frac{\sqrt{3}}{8} \)
Subject: Physics
Students \( A, B \) and \( C \) measure the
diameter of a wire using three different screw gauges of least count 0.01
\( \mathrm{cm}, 0.05 \mathrm{cm} \) and \( 0.001 \mathrm{cm} \) respectively. Each one makes 10 measurements.The
measurements will be more precise for
\( A \cdot A \)
B. B
\( c \cdot c \)
D. all
Subject: Maths
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}-\boldsymbol{3} \) on \( [\mathbf{1}, \boldsymbol{3}] \)
Subject: Physics
density \( +\sigma \) and \( -\sigma \) are parallel to each other as show in figure. Electric field at
the
This question has multiple correct options
A. points to the left or to the right of the sheets is zero.
B. midpoint between the sheets is zero.
C. midpoint of the sheets is \( \sigma / \varepsilon_{0} \) and is directed towards right
D. midpoint of the sheets is \( 2 \sigma / \varepsilon_{0} \) and is directed towards right
Subject: Maths
The D.E whose solution is \( y=\frac{c}{x} \) is:
A. \( y_{1}+x y=0 \)
в. \( y_{1}=x y \)
c. \( x \cdot d y+y \cdot d x=0 \)
D. \( x . d y-y . d x=0 \)
Subject: Physics
In the Bohr Model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton
and the electron. If \( a_{o} \) is the radius of
the ground state orbit, \( m \) is the mass,
and \( e \) is the charge on the electron, and
\( \epsilon_{o} \) is the permittivity of vacuum, then the speed of the electron is:
A . 0
в. \( \frac{e}{\sqrt{\epsilon_{o} a_{o}}} \)
c. \( \frac{e}{\sqrt{4 \pi \epsilon_{c} a_{o} m}} \)
D. \( \sqrt{\frac{4 \pi \epsilon_{o} a_{o} m}{e}} \)
Subject: Physics
The magnitude of the induced emf in a coil of inductance \( 30 m H \) in which the
current changes from \( 6 A \) to \( 2 A \) in \( 2 s \)
is:
A \( .0 .06 \mathrm{V} \)
в. \( 0.6 \mathrm{V} \)
c. \( 1.06 V \)
D. \( 6 V \)
Subject: Physics
The ends \( A \) and \( B \) of a rod of length \( l \) have velocities of magnitudes \( \left|\overrightarrow{\boldsymbol{v}}_{\boldsymbol{A}}\right|= \)
\( \boldsymbol{v} \quad \) and \( \left|\overrightarrow{\boldsymbol{v}}_{\boldsymbol{B}}\right|=2 \boldsymbol{v}, \) respectively. If the
inclination of \( \vec{v}_{A} \) relative to the rid is \( \alpha \)
find the:
(a) inclination \( \beta \) of \( \vec{v}_{B} \) relative to the
rod.
(b) angular velocity of the rod
Subject: Maths
If \( \lim _{n \rightarrow \infty} \frac{n .3^{n}}{n(x-2)^{n}+n .3^{n+1}-3^{n}}=\frac{1}{3} \)
then the range of \( x \text { is (When } n \in N) \)
A. [2,5)
()
B \( \cdot(1,5) \)
c. (-1,5)
\( D \cdot(-\infty, \infty) \)
Subject: Physics
A number of capacitors, each of equal
capacitance \( C, \) are arranged as shown
in the figure. The equivalent
capacitance between \( A \) and \( B \) is :
A \( \cdot n^{2} C \)
B. \( (2 n+1) C \)
c. \( \frac{(n-1) n}{2} C \)
D. \( \frac{(n+1) n}{2} C \)
Subject: Chemistry
The racemic mixture of Alanine
\( \left(\begin{array}{c}\mathbf{C H}_{3} \mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{O} \mathbf{O} \mathbf{H} \\ \mathbf{N} \mathbf{H}_{2}\end{array}\right) \) can be resolved
by using:
(a) \( (+)-2-B u t a n o \)
(b) (I) - 2-Chlorobutanoic acid
\( (c)(\pm)-2-B u t a n o \)
(d) (dl mix)-2-Chlorobutanoic acid
\( A \cdot a \) and \( b \) only
B. a and conly
C. \( b \) and \( d \) only
D. a and donly
Subject: Physics
The plot of velocity (v) versus
displacement \( (x) \) of a particle executing
simple harmonic motion is shown in figure. The time period of oscillation of
particle is
\( \mathbf{A} \cdot \frac{\pi}{2} s \)
B. \( \pi s \)
\( c \cdot 2 \pi s \)
D. \( 3 \pi s \)
Subject: Chemistry
What is correct acidic strength of nitrogen oxides?
A. \( N_{2} O>N O>N_{2} O_{3}>N O_{2} \)
в. \( N_{2} O<N O<N_{2} O_{3}<N O_{2} \)
c. \( N O>N_{2} O_{3}>N_{2} O_{4}>N_{2} O_{5} \)
D. \( N O<N_{2} O_{3}<N_{2} O_{4}<N_{2} O_{5} \)
Subject: Chemistry
\( N H_{3}+H_{2} O \longrightarrow(C)+(D)( \) both oxy
acid)
A \( \cdot(c): H N O_{2} ; \quad(D): H N O_{2} \)
B \( \cdot(\mathrm{C}): H_{2} N O_{3} ; \quad \) (D) \( : H N O_{3} \)
C \( \cdot(\mathrm{C}): H N O_{2} ; \quad(\mathrm{D}): H N O_{3} \)
D. None of these
Subject: Physics
One mole of an ideal gas \( \left(C_{v, m}=\frac{5}{2} R\right) \) at \( 300 \mathrm{K} \) and 5 atm is expanded adiabatically to a final
pressure of 2 atm against a
constant pressure of 2 atm. Final temperature of the gas is:
\( \mathbf{A} \cdot 270 \mathrm{K} \)
B. 273 к
c. \( 248.5 \mathrm{k} \)
D. 200 к
Subject: Physics
In the AC circuit shown, \( X_{L}=7 \Omega, R= \)
\( 4 \Omega \) and \( X_{c}=4 \Omega . \) The reading of the
ideal voltmeter \( V_{2} \) is \( 8 \sqrt{2} \). The reading
of idea voltmeter \( V_{1} \) will be :
A. 20 volt
B. 7 volt
\( c \cdot 8 \) volt
D. 10 volt
Subject: Maths
Assertion
If three points \( P, Q \) and \( R \) have position vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \) respectively, and \( 2 \vec{a}+3 \vec{b}-5 \vec{c}=0, \) then the points \( P, Q \)
and \( R \) must be collinear.
Reason
If for three points \( A, B \) and \( C, A B= \) \( \lambda \overrightarrow{A C}, \) then points \( A, B \) and \( C \) must be
collinear.
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: Biology
Match the columns and choose the
correct option from the following.
Hair like
cells in roots
of Monstera A Macrosclereids
\begin{tabular}{llc|l} 
B & Osteosclereids & 2 & Bone like cells xerophytes \\
C & Astrosclereids & 3 & Star shaped cells in hygrophytes \\
D & Trichosclereids & 4 & Stone like cells in seed coat of Fabaceae \\
\hline
\end{tabular} 1.
\( A \cdot A-4, B-2, C-3, D-1 \)
B. A- \( 4, B-3, C-2, D-1 \)
c. \( A-4, B-2, C-1, D-3 \)
D. \( A-2, B-4, C-3, D-1 \)
Subject: Maths
A garage mechanic keeps a box of good springs to use as replacements on
customers cars. The box contains 5
springs. A colleague, thinking that the springs are for scrap, tosses three faulty springs into the box. The mechanic picks two springs out of the box while servicing a car. Find the probability that the second spring drawn is faulty.
A \( \cdot \frac{1}{8} \)
B. \( \frac{2}{8} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{4}{8} \)
Subject: Physics
the velocity of the CM of the rod.
A \( \cdot \frac{5}{7} v_{0} \) at \( \tan ^{-1} \frac{4}{3} \) below horizontal
B. \( \frac{5}{7} v_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizontal
C. \( \frac{5}{6} v_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizontal
D. \( \frac{5}{6} v_{0} \) at \( \tan ^{-1} \frac{4}{3} \) below horizontal
Subject: Maths
The equation \( \frac{x^{2}}{2-r}+\frac{y^{2}}{r-5}+1=0 \)
represents an ellipse, if
\( \mathbf{A} \cdot r>2 \)
В. \( 2<r<5 \)
\( \mathbf{c} \cdot r>5 \)
D. \( r \in(2,5) \)
Subject: Chemistry
For the industrial preparation of nitric acid from ammonia, when ammonia is heated with excess air in presence of a
catalyst, at \( 900^{\circ} \mathrm{C}, \mathrm{NO} \) is obtained. Which line of entry describes the undefined reagents, products and reaction conditions?
A . catalyst at room temperaure \( \left(25^{\circ} \mathrm{C}\right) \) and \( \mathrm{NO}_{2} \)
B. catalyst at room temperature \( \left(25^{\circ} \mathrm{C}\right) \) and \( N_{2} \mathrm{O} \)
C. catalyst hight pressure and \( N O_{2} \)
D. catalyst hight pressure and \( N_{2} O_{3} \)
Subject: Physics
The horizontal and vertical components
of earth's magnetic field at a place are \( 0.3 G \) and \( 0.52 G . \) The earth's magnetic
field and the angle of dip are
A \( \cdot 0.3 \mathrm{G} \) and \( \rho=30^{\circ} \)
B. 0.4G and \( \rho=40^{\circ} \)
c. \( 0.5 \mathrm{G} \) and \( \rho=50^{\circ} \)
D. \( 0.6 \mathrm{G} \) and \( \rho=60^{\circ} \)
Subject: Chemistry
Assertion
Assertion: Liquids \( I F_{5} \) conducts
electricity
Reason
Reason: Liquid \( I F_{5} \) self ionizes as,
\( 2 I F_{5} \rightleftharpoons I F_{4}^{+}+I F_{6}^{-} \)
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 \( \cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac{x}{m}, x \in \)
\( \left(0, \frac{\pi}{4}\right) \).Find \( m \)
Subject: Physics
How many photons per second enter one
eye if you look directly at a 100 W light bulb \( 2.00 \mathrm{m} \) away? Assume a pupil diameter of \( 4.00 \mathrm{mm} \) and a wavelength of 600 nm. How many photons per
second enter your eye if a \( 1.00 \mathrm{m} \) W laser beam is directed into your eye? \( \lambda= \)
\( 633 n m) \)
Subject: Chemistry
Match the rate law given in column I with the dimensions of rate constant
given in column II and mark the
appropriate choice.
Column I Column I
(A) Rate\( =k\left[N H_{3}\right]^{0} \)
(i) \( \operatorname{mol} L^{-1} s^{-1} \)
(B) \( R a t e=k\left[H_{2} O_{2}\right]\left[I^{-}\right] \)
(ii) \( L m o l^{-1} s^{-1} \)
(C) \( \operatorname{Rate}=k\left[C H_{3} C H O\right]^{3 / 2} \)
\( s^{-1} \)
(D) \( \operatorname{Rate}=k\left[C_{2} H_{5} C l\right] \)
(iv) \( L^{1 / 2} m o l^{-1 / 2} s^{-1} \)
\( \mathbf{A} \cdot(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
c. \( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
Subject: Chemistry
Suppose the elements \( X \) and \( Y \)
combine to form two compounds \( \boldsymbol{X} \boldsymbol{Y}_{2} \)
and \( X_{3} Y_{2} . \) When 0.1 mole of \( X Y_{2} \)
weighs \( 10 g \) and 0.05 mole of \( X_{3} Y_{2} \)
weighs \( 9 g \), the atomic weights of \( X \) and
\( \boldsymbol{Y} \) are:
Subject: Chemistry
Fischer Ringe's method makes use of :
A \( \cdot \mathrm{CaC}_{2} \)
B. \( \mathrm{Ca}(\mathrm{CN})_{2} \)
\( c \cdot \mathrm{CaC}_{2}+\mathrm{CaCl} \)
\( \mathrm{D} \cdot \mathrm{CaCN}_{2}+\mathrm{CaCl}_{2} \)
Subject: Maths
I : Length of the perpendicular from \( \left(x_{1}, y_{1}\right) \) to the line \( a x+b y+c=0 \) is \( \left|\frac{\boldsymbol{a} \boldsymbol{x}_{1}+\boldsymbol{b} \boldsymbol{y}_{1}+\boldsymbol{c}}{\sqrt{\boldsymbol{a}^{2}+\boldsymbol{b}^{2}}}\right| \)
II : The equation of the line passing through (0,0) and perpendicular to \( a x+b y+c=0 \) is
\( b x-a y=0 . \) Then which of the
following is true?
A. only I
B. only II
c. both 18 ॥
D. neither I nor II
Subject: Maths
Solve: \( 5 x-3<3 x+1, \) where \( x \) is an
integer.
\( \mathbf{A} \cdot\{-3,-2,-1,0,1,2,3\} \)
B . \{-5,-4,-3,-2,-1,0,1,2\}
c. \{-4,-3,-2,-1,0,1\}
D \( \cdot\{-2,-1,0,1,2\} \)
Subject: Chemistry
\( 0.25 g \) of an element \( M \) reacts with
excess fluorine to produce \( 0.547 g \) of the
hexafluoride \( M F_{6} . \) What is the
element?
A \( . C r \)
в. \( M o \)
\( c \cdot s \)
D. \( T e \)
Subject: Physics
A mass \( m=20 \) g has a charge \( q=3.0 \)
mC. It moves with a velocity of \( 20 \mathrm{m} / \mathrm{s} \)
and enters a region of electric field of \( 80 \mathrm{N} / \mathrm{C} \) in the same direction as the
velocity of the mass. The velocity of the mass after 3 seconds in this region is:
Subject: Chemistry
Exactly \( 100 \mathrm{m} L \) of oxygen is collected
over the water of \( 23^{\circ} \mathrm{C} \) and \( 800 \mathrm{mm} \)
pressure. Calculate the approximate value of the volume of dry oxygen at NTP. (as nearest integer)
[Vapour pressure of water at \( 23^{\circ} \mathrm{C} \) is 21
\( m m \)
Subject: Chemistry
When NaCl is added to the reaction
mixture of an oil and caustic soda, the
soap is thrown out because
A. \( N a C l \) is an ionic compound
B. Soap is insoluble in the presence of chloride ions
C. The solubility product of \( N a C l \) decreases in the presence of soap
D. The solubility product of the soap is exceeded due to the increased concentration of \( N a^{+} \) ions
Subject: Physics
The balancing length for a cell is \( 560 \mathrm{cm} \) in a potentiometer experiment. When an external resistance of \( 10 \Omega \) is connected
in parallel to the cell, the balancing length changes by \( 60 \mathrm{cm} \). If the internal resistance of the cell is \( \frac{N}{10} \Omega, \) where \( N \) is an integer then value of \( \mathrm{N} \) is
Subject: Physics
At sea level, the atmospheric pressure is \( 1.04 \times 10^{5} \) Pa. Assuming \( g= \)
\( 10 m s^{-2} \) and density of air to be uniform
and equal to \( 1.3 k g m^{-3}, \) find the height of the atmosphere
\( A \cdot 8000 \mathrm{km} \)
B. 8000 \( \mathrm{mm} \)
c. \( 8000 \mathrm{cm} \)
D. 8000 \( \mathrm{m} \)
Subject: Maths
Find \( a, b \) in \( \int \frac{x+2}{\left(x^{2}+3 x+3\right) \sqrt{x+1}} d x= \)
\( \frac{\boldsymbol{a}}{\sqrt{\boldsymbol{b}}} \tan ^{-1}\left\{\frac{\boldsymbol{x}}{\sqrt{\mathbf{3}(\boldsymbol{x}+\mathbf{1})}}\right\}+\boldsymbol{C} \)
This question has multiple correct options
\( \mathbf{A} \cdot a=2 \)
B. \( b=3 \)
\( \mathbf{c} \cdot a=3 \)
\( \mathbf{D} \cdot b=2 \)
Subject: Maths
In a city, three daily newspapers \( A, B, C \) are published, \( 42 \% \) read \( A ; 51 \% \) read \( B \); \( 68 \% \) read \( C ; 30 \% \) read \( A \) and \( B ; 28 \% \) read \( \mathrm{B} \) and \( \mathrm{C} ; 36 \% \) read \( \mathrm{A} \) and \( \mathrm{C} ; 8 \% \) do not read any of the three newspapers.
What is the percentage of persons who read only one paper?
\( A .38 \% \)
в. \( 48 \% \)
\( c .51 \% \)
D. None of the above
Subject: Physics
Two resistors are joined in series, then their equivalent resistance is \( 90 \Omega \) When the same resistors are joined in parallel, the equivalent resistance is \( 20 \Omega \)
The resistances of the two resistors will
be :
A. \( 70 \Omega, 20 \Omega \)
в. \( 80 \Omega, 10 \Omega \)
\( \mathbf{c} \cdot 60 \Omega, 30 \Omega \)
D. \( 50 \Omega, 40 \Omega \)
Subject: Maths
The value of \( \tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right] \) is
A \( \cdot \frac{1}{\sqrt{5}} \)
B. \( \sqrt{\frac{3}{10}} \)
c. \( \sqrt{\frac{5}{2}} \)
D. \( 1-\sqrt{\frac{5}{2}} \)
Subject: Chemistry
Indicate the types of isomerism exhibited by the following complexes and draw the structures for these
isomers:
\( \mathbf{A} \cdot K\left[\operatorname{Cr}\left(H_{2} O\right)_{2}\left(C_{2} O_{4}\right)_{2}\right] \)
в. \( \left[\operatorname{Co}(e n)_{3}\right] C l_{3} \)
\( ^{\mathbf{c}} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right]\left(N O_{3}\right)_{2} \)
D \( \cdot\left[\operatorname{Pt}\left(N H_{3}\right)\left(H_{2} O\right) C l_{2}\right] \)
Subject: Physics
The KE of the electron in an orbit of
radius 'r' in hydrogen atom is proportional to (e=electronic charge)
\( ^{A} \cdot \frac{e^{2}}{r^{2}} \)
B. \( \frac{e^{2}}{2 r^{3}} \)
c. \( \frac{e^{2}}{r} \)
D. \( \frac{e^{2}}{2 r^{2}} \)
Subject: Physics
A solid sphere of radius \( R \) made of a
material of bulk modulus B surrounded
by a liquid in a cylindrical container.A massless piston of area A floats on the surface of the liquid. Find the fractional decreases in the radius of the sphere
\( \left(\frac{d R}{R}\right) \) when a mass \( M \) is placed on the
piston to compress the liquid:
A \( \cdot\left(\frac{3 M g}{A B}\right) \)
B \( \cdot\left(\frac{2 M g}{A B}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{M g}{3 A B}\right) \)
D. \( \left(\frac{M g}{2 A B}\right) \)
Subject: Physics
A charge \( +q \) is fixed at each of the
points \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{5} \boldsymbol{x}_{0}, \dots \) upto
\( \infty \) on \( \mathrm{X} \) -axis and charge -q is fixed on
each of the points \( \boldsymbol{x}=\mathbf{2} \boldsymbol{x}_{0}, \boldsymbol{x}= \)
\( \mathbf{4} \boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{6} \boldsymbol{x}_{0}, \ldots \boldsymbol{u} \boldsymbol{p} \boldsymbol{a} \)
positive constant. Take the potential at a point due to a charge \( Q \) at a distance \( r \) from it to be \( \frac{Q}{4 \pi \epsilon_{0} r} . \) Then the potentia at the origin due to above system of
charges will be :
A . zero
в. \( \frac{q}{8 \pi \epsilon_{0} x_{0} \log _{e} 2} \)
c. inifinty
D. \( \frac{q \log _{e} 2}{4 \pi \epsilon_{6} x_{0}} \)
Subject: Physics
An object is placed at \( 15 \mathrm{cm} \) in front of convex lens of focal length 10 cm. Where shall we place a convex mirror of focal length \( 13 \mathrm{cm} \) so that real image and object coincide?
\( A \cdot 6 \mathrm{cm} \) from lens
B. 3 cm from lens
c. \( 4 \mathrm{cm} \) from lens
D. \( 2 \mathrm{cm} \) from lens
Subject: Chemistry
If, in the reaction \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
\( x \) is the part of \( N_{2} O_{4} \) which dissociates,
then the number of molecules at
equilibrium will be:
A
B. 3
\( c \cdot(1+x) \)
D. \( (1+x)^{2} \)
Subject: Chemistry
Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \quad \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) sol is:
A. \( N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
c. \( A l_{2}\left(S O_{4}\right)_{3} \)
D. \( N H_{4} C l \)
Subject: Maths
The maximum of \( \mathbf{f}(\mathbf{x})=\frac{\log \mathbf{x}}{\mathbf{x}^{2}}(\mathbf{x}>\mathbf{0}) \)
occurs at \( \mathbf{x}= \)
\( A \)
B. \( \sqrt{e} \)
\( c \cdot \frac{1}{e} \)
D. \( \frac{1}{\sqrt{\mathrm{e}}} \)
Subject: Physics
If \( 4 \times 10^{20} e V \) is required to move a
charge of \( 0.25 C \) between two points, the potential difference between these
two points is:
\( \mathbf{A} \cdot 256 V \)
в. \( \frac{1}{256} V \)
\( \mathbf{c} \cdot 256 \times 10^{+19} V \)
D. \( 250 V \)