AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
The plot of volume \( (V) \$ \) versus
pressure \( (P) \) at constant temperature
is a hyperbola in the first quadrant.
Reason
\( \boldsymbol{V} \propto \mathbf{1} / \boldsymbol{P} \) at constant temperature
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
The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is:
A \( \frac{2 \sin \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)
B. \( \frac{1+\cos \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)
c. \( \frac{(1-\cos \theta)-2 i \sin \theta}{(1-\cos \theta)^{2}+4 i^{2} \sin ^{2} \theta} \)
D. \( \frac{1-\cos \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)
Subject: Physics
In figure, a particle has mass \( \boldsymbol{m}=\mathbf{5} \boldsymbol{g} \)
and charge \( \boldsymbol{q}^{\prime}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{9}} \boldsymbol{C} \) starts from
rest at point \( a \) and moves in a straight line to point \( b \). What is its speed \( v \) at point \( b ? \)
A \( .2 .65 \mathrm{cms}^{-1} \)
B. \( 3.65 \mathrm{cms}^{-1} \)
c. \( 4.65 \mathrm{cms}^{-1} \)
D. \( 5.65 \mathrm{cms}^{-1} \)
Subject: Chemistry
Identify the reagents underlined in the following equations as nucleophiles or electrophiles:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{O H}^{-} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
Two infinitely long parallel conducting plates having surface charge densities \( +\sigma \) and \( -\sigma \) respectively, are separated
by a small distance. The medium
between the plates is vacuum. If \( \varepsilon_{0} \) is
the dielectric permittivity of vacuum
then the electric field in the region between the plates is:
A. 0 volt \( / m \)
в. \( \sigma / 2 \varepsilon_{0} \) volt \( / \mathrm{m} \)
c. \( \sigma / \varepsilon_{0} \) volt \( / \mathrm{m} \)
D. \( 2 \sigma / \varepsilon_{0} \) volt \( / \mathrm{m} \)
Subject: Maths
If \( x>0, \) then the minimum value of \( \boldsymbol{x}^{1000}+\boldsymbol{x}^{900}+\boldsymbol{x}^{90}+\boldsymbol{x}^{6}+\frac{\mathbf{1 9 9 6}}{\boldsymbol{x}} \) is
A . 1000
B. 2000
\( c \cdot \) 1996
D. 3000
Subject: Physics
If the half lives of a radioactive element
for \( \alpha \) and \( \beta \) decay are 4 years and 12 years respectively, then the percentage
of the element that remains after 12
years will be
A . \( 6.25 \% \)
B . \( 12.5 \% \)
c. \( 25 \% \)
D. 50 \%
Subject: Physics
A reversible engine converts one-sixth of the heat supplied into work. When the
temperature of the sink is reduced by
\( 62^{\circ} \mathrm{C}, \) the efficiency of the engine is
doubled. The temperature of the source and sink are:
A \( \cdot 99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
в. \( 80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 95^{\circ} C, 37^{\circ} C \)
D . \( 90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
Subject: Maths
Consider the binary operation o defined
by the following tables on set \( \boldsymbol{S}= \)
\[
\{a, b, c, d\}
\]
\( \begin{array}{llll}\circ & \text { a } & \text { b } & \text { c } & \text { d }\end{array} \) \( \begin{array}{lllll}\mathrm{a} & \mathrm{a} & \mathrm{a} & \mathrm{a} & \mathrm{a} \\ \mathrm{b} & \mathrm{a} & \mathrm{b} & \mathrm{c} & \mathrm{d} \\ \mathrm{c} & \mathrm{a} & \mathrm{c} & \mathrm{d} & \mathrm{b} \\ \mathrm{d} & \mathrm{a} & \mathrm{d} & \mathrm{b} & \mathrm{c}\end{array} \)
Show that the binary operation is commutative. Write down the identitie
and list the inverse of elements.
Subject: Maths
The sum of three expressions is \( x^{2}+ \) \( y^{2}+z^{2} . \) If two of them are \( 4 x^{2}-5 y^{2}+ \)
\( 3 z^{2} \) and \( -3 x^{2}+4 y^{2}+2 z^{2}, \) the third
expression is
A \( \cdot 2 x^{2}+2 z^{2} \)
в. \( 2 y^{2} \)
c. \( 2 x^{2}+2 y^{2}-z^{2} \)
D. \( 2 y^{2}-4 z^{2} \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{y}=\log \left(\boldsymbol{e}^{\boldsymbol{x}} \sin ^{\boldsymbol{5}} \boldsymbol{x}\right) \)
Subject: Physics
Acceleration of 3 rd maxima w.r.t 3 rd
maxima on other side of central
maxima at \( t=3 s \) is
A \( \cdot 0.02 m s^{-2} \hat{i} \)
B. \( 0.03 m s^{-2} \hat{i} \)
\( \mathbf{c} \cdot 10 m s^{-2 \hat{i}} \)
D. \( 0.6 m s^{-2} \hat{i} \)
Subject: Chemistry
The \( B C l_{3} \) is a planar molecule whereas
\( N C l_{3} \) is pyramidal, because:
A. \( B-C l \) bond is more polar than \( N-C l \) bond
B. \( N-C l \) bond is more covalent than \( B-C l \) bond
c. nitrogen atom is smaller than boron atoms
D. \( B C l_{3} \) has no lone pair but \( N C l_{3} \) has a lone pair of electrons
Subject: Maths
The differential equation for which \( \sin ^{-1} x+\sin ^{-1} y=c \) is given by:
A \( \cdot \sqrt{1-x^{2}} d y+\sqrt{1-y^{2}} d x=0 \)
B \( \cdot \sqrt{1-x^{2}} d x+\sqrt{1-y^{2}} d y=0 \)
C \( . \sqrt{1-x^{2}} d x-\sqrt{1-y^{2}} d y=0 \)
D. \( \sqrt{1-x^{2}} d y-\sqrt{1-y^{2}} d x=0 \)
Subject: Maths
The mode for the following frequency
distribution:
\begin{tabular}{lllll} 
Size of & \multicolumn{1}{l} { Size } \\
items & Frequency & of items & Frequency \\
\( 0-4 \) & 5 & \( 20-24 \) & 10 \\
\( 4-8 \) & 7 & \( 24-28 \) & 6 \\
\( 8-12 \) & 9 & \( 28-32 \) & 3 \\
\( 12-16 \) & 17 & \( 32-36 \) & 1 \\
\( 16-20 \) & 12 & \( 36-40 \) & 0 \\
\hline
\end{tabular}
\( \mathbf{S}: \)
\( \mathbf{A} \cdot 32.66 \)
B . 14.61
\( \mathbf{c} \cdot 14 \)
D. none of these
Subject: Physics
The spring shown in figure is
unstretched when a man starts pulling
the block. The mass of the block is \( M . \) If
the man exerts a constant force \( \boldsymbol{F} \)
The energy stored in the spring when the block passes through the
equilibrium position is
\( ^{A} \cdot \frac{2 F^{2}}{k} \)
B. \( \frac{F^{2}}{k} \)
\( ^{\mathbf{c}} \cdot \frac{F^{2}}{4 k} \)
D. \( \frac{F^{2}}{2 k} \)
Subject: Chemistry
The value of charge on th oil droplets experimentally observed were \( -1.6 \times 10^{-19} \) and \( -4 \times 10^{-19} \) coulomb.
the value of the electron charge, indicates by these result is:
A. \( 1.6 \times 10^{-19} \)
В. \( -2.4 \times 10^{-19} \)
c. \( -4 \times 10^{-19} \)
D. \( -0.8 \times 10^{-19} \)
Subject: Physics
What is the speed of Light \( c \) ?
A \( \cdot c=3 \times 10^{-8} \mathrm{ms}^{-1} \)
B . \( c=3 \times 10^{8} k m s^{-1} \)
c. \( c=3 \times 10^{8} \mathrm{mms}^{-1} \)
D. \( c=3 \times 10^{8} \mathrm{ms}^{-1} \)
Subject: Maths
The number of sides of two regular polygons A and B are in ratio 1: 3. If each
interior angle of polygon \( \mathrm{B} \) is \( 168^{\circ} . \) Find each interior angle of polygon \( A \)
A \( .144^{\circ} \)
B. 120
\( c \cdot 72 \)
D. 22.5
Subject: Physics
What work should be done in order to
squeeze all water from a horizontally located cylinder (figure shown above) during the time \( t \) by means of a constant force acting on the piston? The volume of water in the cylinder is equal
to \( V \), the cross-sectional area of the
orifice to \( s, \) with \( s \) being considerably less than the piston area. The friction
and viscosity are negligibly small
\( A=\frac{1}{2} \rho \frac{V^{3}}{(S t)^{2}} \)
B. \( A=\frac{3}{2} \rho \frac{V^{3}}{(S t)^{2}} \)
\( c \)
D. None of thes
Subject: Maths
\( \boldsymbol{z}=\mathbf{3 0} \boldsymbol{x}+\mathbf{2 0} \boldsymbol{y}, \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{8}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \geq \)
\( 4,6 x+4 y \geq 12, x \geq 0, y \geq 0 \) has
A. Unique solution
B. Infinitely many solution
C . Minimum at (4,0)
D. Minimum 60 at point (0,3)
Subject: Physics
open end of a cylindrical vessel of
radius \( R \) and height \( 2 R \) as shown in figure. the flux of the electric field
through the surface (curved surface \( + \)
base ) of the vessel is
\( \mathbf{A} \cdot \frac{Q}{\varepsilon_{0}} \)
B. \( \frac{Q}{2 \varepsilon_{\text {d }}} \)
\( c \cdot \frac{Q}{4 \varepsilon_{0}} \)
D. \( \frac{Q}{\sqrt{5} \varepsilon_{0}} \)
Subject: Chemistry
Hydroboration-oxidation of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}= \)
\( \boldsymbol{C H}_{2} \) produces:
A. \( C H_{3} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{3} \)
c. \( C H_{3} C H(O H) C H_{2} O H \)
D. \( C H_{3} C O C H_{3} \)
Subject: Chemistry
Electron affinity of chlorine is \( -3.61 \mathrm{eV} \) \( I P \) value of the same element is 12.967
eV. \( 3 \times 10^{23} \) atoms of chlorine are
converted to \( C l^{-} \) ions and the energy
liberated is used to ionize chlorine
atoms to \( C l^{+} \) ions. How many chlorine atoms could be ionized in the above
process?
A \( .5 .45 \times 10^{21} \)
В. \( 6.11 \times 10^{18} \)
c. \( 8.35 \times 10^{22} \)
D. \( 7.11 \times 10^{28} \)
Subject: Maths
A purchases an article for Rs. 3,600 and sells it to B for Rs. \( 4,800 . \) B, in turn, sells the article to \( C \) for Rs. \( 5,500 . \) If the sales-
\( \operatorname{tax}(\text { under } V A T) \) is \( 10 \%, \) find the VAT
levied on \( A \) and \( B \).
A. VAT levied A= Rs. 140, VAT levied B= Rs. 50
B. VAT levied A= Rs. 130, VAT levied B= Rs. 60
c. VAT levied A= Rs. 120, VAT levied B= Rs. 70
D. None of these
Subject: Maths
The values of \( x \) at which \( f(x)=\sin x \) is stationary are given by
A. \( \mathrm{n} \pi, \forall n \in Z \)
в. \( (2 \mathrm{n}+1) \frac{\pi}{2}, \forall n \in Z \)
c. \( \frac{\mathrm{n} \pi}{4}, \forall n \in Z \)
D. \( \frac{\mathrm{n} \pi}{2}, \forall n \in Z \)
Subject: Maths
The sum of the first \( n \) terms of an A.P is
\( 4 n^{2}+2 n . \) Find the \( n \) th term of this A.P.
A. \( 5 n-2 \)
B. \( 8 n-2 \)
c. \( 3 n-2 \)
D. None of these
Subject: Maths
If
\( \boldsymbol{\theta} \) and \( \phi \) are angles in the 1 st quadrant such that \( \tan \theta=\frac{1}{7} \) and \( \sin \phi=\frac{1}{\sqrt{10}} \)
\( \mathbf{A} \cdot \theta+2 \phi=90^{\circ} \)
B . \( \theta+2 \phi=60^{\circ} \)
c. \( \theta+2 \phi=30^{\circ} \)
D. \( \theta+2 \phi=45^{\circ} \)
Subject: Maths
\( \mathbf{n} \)
fig., \( A B \) and \( C D \) are two diameters of \( a \)
circle (with centre 0) perpendicular to
each other and 0 D is the diameter of the
smaller circle. If \( \boldsymbol{O} \boldsymbol{A}=\mathbf{1 4} \boldsymbol{c m}, \) find the
area of the shaded region
Subject: Physics
The current passing through a choke coil of \( 5 H \) is decreasing at the rate of \( 2 A / s . \) The e.m.f. developed across the coil is
A . \( 10 V \)
в. \( -10 V \)
\( \mathrm{c} .2 .5 \mathrm{V} \)
D. \( -2.5 V \)
Subject: Chemistry
\( 25.3 g \) of sodium carbonate, \( N a_{2} C O_{3} \) is dissolved in enough water to make \( 250 m L \) of solution. If sodium cabonate
dissociates completely, molar
concentration of sodium ion, \( N a^{+} \) and
carbonate ion \( C O_{3}^{2-} \) are respectively:
(Molar mass of \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3}= \)
\( \left.106 g \quad m o l^{-1}\right) \)
A. \( 0.955 M \) and \( 1.910 M \)
в. \( 1.910 M \) and 0.955 М
c. \( 1.90 M \) and \( 1.910 M \)
D. \( 0.477 M \) and \( 0.477 M \)
Subject: Maths
Find the area of the closed figure bounded by the following curves \( \boldsymbol{y}=\sqrt{\boldsymbol{x}}, \boldsymbol{y}=\sqrt{\mathbf{4}-\mathbf{3} \boldsymbol{x}}, \mathbf{y}=\mathbf{0} \)
A \( \cdot \frac{8}{9} \)
B. \( \frac{7}{9} \)
\( c \cdot \frac{5}{9} \)
D.
Subject: Physics
Which of the following is an example of nuclear fusion reaction?
\( \mathbf{A} \cdot \underset{90}{233} T H+_{0}^{1} n \rightarrow_{90}^{234} T H \)
B . \( _{48}^{13} \mathrm{Cd}+_{0}^{1} n \rightarrow_{48}^{114} \mathrm{Cd}+\gamma-\mathrm{ray} \)
\( \mathbf{c} \cdot_{i H}^{3} H+_{1}^{1} H \rightarrow_{2}^{4} H e \)
D \( \cdot \frac{239}{92} U \rightarrow_{93}^{239} N p+_{-1}^{0} e \)
Subject: Physics
A body of mass \( 10 k g \) at rest is acted upon simultaneously by two forces \( 4 N \)
and \( 3 N \) at right angles to each other.
The kinetic energy of the body at the end
of \( 10 s \) is
\begin{tabular}{l} 
A. \( 50 \mathrm{J} \) \\
\hline
\end{tabular}
в. \( 100 J \)
c. \( 125 J \)
D. \( 144 J \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{lll}\boldsymbol{k}-\boldsymbol{2} \boldsymbol{x}, & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x} \leq-1 \\ 2 \boldsymbol{x}+\boldsymbol{3}, & \boldsymbol{i f} & \boldsymbol{x}>-1\end{array}\right. \)
If \( f \) has a local minimum at \( x=-1 \)
then the possible value of \( k \) is
A. \( -1 / 2 \)
B. -
\( c \cdot 1 \)
\( D \)
Subject: Maths
Find the area of the region \( \{(x, y) \)
\( \left.\boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{2}\right\} \)
\( \mathbf{A} \cdot \pi-2 \)
B. \( \pi-1 \)
c. \( 2 \pi-2 \)
D. \( 4 \pi-2 \)
Subject: Physics
Two positive point charges are of \( 12 C \) and \( 8 C \) are \( 10 \mathrm{cm} \) apart from each other
The work done in bringing them \( 4 c m \) closer is
A . \( 5.8 J \)
в. \( 13 e V \)
c. \( 5.8 e V \)
D. \( 13 J \)
Subject: Maths
If \( y=a \cos (\log x)-b \sin (\log x), \) then
the value of \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D.
Subject: Maths
A sphere of radius \( r, \) inside a cube
touches each one of the six sides of the cube. What is the volume of the cube in
terms of \( r ? \)
\( \mathbf{A} \cdot 8 r^{3} \)
B \( .2 r^{3} \)
\( \mathbf{c} \cdot 4 r^{3} \)
D. \( \frac{4}{3} \pi r \)
Subject: Maths
\( f\left(\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right], \) then verify that
\[
\boldsymbol{A}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \boldsymbol{A}=\boldsymbol{I}|\boldsymbol{A}|
\]
Subject: Physics
A car travels with a uniform velocity of \( 25 m s^{-1} \) for 5 s. The brakes are then
applied and the car is uniformly retarded and comes to rest in further 10
s. Find the distance travelled by the car
after applying the brakes.
A . 25 m
B. \( 625 \mathrm{m} \)
c. \( 125 \mathrm{m} \)
D. \( 0 m \)
Subject: Maths
The ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) cuts \( x \) axis at
A and y axis at \( \mathrm{B} \) and the line joining the focus \( \mathrm{S} \) and \( \mathrm{B} \) makes an angle \( \frac{3 \pi}{4} \) with x-axis. Then the eccentricity of the ellipse is
A. \( \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{3} \)
Subject: Physics
In the equation of \( \boldsymbol{A C}, \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
the current amplitude and frequency will respectively be
A \( \cdot I_{0}, \frac{\omega}{2 \pi} \)
В. \( \frac{I_{0}}{2}, \frac{\omega}{2 \pi} \)
\( c \cdot I_{r m s}, \frac{\omega}{2 \pi} \)
D. \( I_{0}, \omega \)
Subject: Maths
Given that \( \boldsymbol{X} \sim \boldsymbol{B}(\boldsymbol{n}=\mathbf{1 0}, \boldsymbol{p}) . \) If
\( \boldsymbol{E}(\boldsymbol{X})=\mathbf{8}, \) then the value of \( \boldsymbol{p} \) is
A . 0.6
в. 0.7
c. 0.8
D. 0.4
Subject: Maths
If \( a, b, c \) and \( d \) are points on a number line such that \( a<b<c<d, b \) is twice
as far from \( c \) as from \( a \), and \( c \) is twice as
far from \( b \) as from \( d \), then what is the
value of \( \frac{c-a}{d-b} ? \)
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Physics
The coefficient of mutual induction
between two coils is 1.25 H. If the rate
of fall of current in the primary is 80 As
\( -1, \) then the induced emf in the
secondary coil will be
A. \( 100 V \)
в. \( 64 V \)
c. \( 12.5 V \)
D. \( 0.016 V \)
Subject: Physics
Calculate the weight of the block at a distance of four times of Earth radii
from the center of the Earth. It is given that \( g \) is the acceleration due to gravity at the surface of Earth and mass of the
block is \( \mathrm{m} \)
A. \( 16 \mathrm{mg} \)
B. \( 4 \mathrm{mg} \)
c. \( 2 \mathrm{mg} \)
D. \( \frac{1}{4} \mathrm{mg} \)
E \( \cdot \frac{1}{16} \mathrm{mg} \)
Subject: Physics
Match the Column I with Column II
\begin{tabular}{lll|l} 
& Column I & & Column II \\
& & \\
(A) & Smaller the & & If the same \\
& resistance & & voltage is \\
greater the & (p) & applied \\
current in a & & across a \\
circuit & & resistance \\
(B) & Gmaller the resistance the current is same & (q) & If the same current is passed \\
(C) & Greater the resistance smaller the power & (r) & When resistances are connected in series \\
(D) & Greater the resistance greater the power & (s) & When resistances are connected in parallel
\end{tabular}
\( A \cdot A-r \)
, B-p, C-q, D-s
B. A-p, B-r, C-q, D-s
C. A-r, B-p, C-S, D-q
D. A-s, B-r, C-p, D-
Subject: Chemistry
What is \( Z \) in the following reaction sequence? \( C_{6} H_{5} N H_{2} \frac{(i) N a N O_{2}+H C l / 27}{(i i) H_{3} P O_{2}+H_{2} O(i i i) C O, H C l ; a n h y} \)
\( Z \)
A. \( C_{6} H_{5} C O_{2} H \)
в. \( C_{6} H_{5} O H \)
c. \( C_{6} H_{5} C H O \)
D. \( C_{6} H_{6} \)
Subject: Maths
The ratio in which the plane \( \vec{r} \cdot(\vec{i}- \) \( \mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}})=17 \) divides the line joining
the points \( -2 \vec{i}+4 \vec{j}+7 \vec{k} \) and \( 3 \vec{i}- \) \( \mathbf{5 j}+\mathbf{8 k} \) is
A .1: 5
B. 1: 10
\( c .3: 5 \)
D. 3: 10
Subject: Physics
A particle executes SHM about a point
other than \( x=0 \) as shown in the graph
Choose a CORRECT option(s)
This question has multiple correct options
A. Amplitude is equal to \( 4 m \)
B. Equilibrium position is at \( x=0 \)
C. Equilibrium position is at \( x=2 m \)
Angular frequency \( \frac{2 \pi}{3} \)
Subject: Physics
A fixed container of height \( ^{\prime} \boldsymbol{H}^{\prime} \) with
large cross-sectional area \( ^{\prime} A^{\prime} \) is
completely filled with water. orifice of
cross-sectional area \( ^{\prime} a^{\prime} \) are made, one
at the bottom and the other on the vertical wall container at a distance
\( H / 2 \) from the top of the container. Find
the time taken by the water level of a
height of \( \boldsymbol{H} / \mathbf{2} \) to get reduced to ground level.
Subject: Physics
A primary monochromatic coherent
source is used in \( Y D S E \) and half of the
space between the primary source and the slits is filled with a transparent
liquid of refractive index \( \mu \) with respect
to air, such that path of the wave \( S S_{2} \) is
through this liquid. Everywhere else there is air and slits are sealed with equal glass plates. Find the ocation of central maximum.
Subject: Physics
A metallic rod of length \( L \) and mass \( M \) is moving under the action of two
unequal forces \( F_{1} \) and \( F_{2} \) (directed opposite to each other) acting at its ends along its length. lgnore gravity and any external magnetic field. If specific charge of electrons is \( (e / m), \) then the
potential difference between the ends of the rod is steady state must be:
A \( \cdot\left|F_{1}-F_{2}\right| m L / e M \)
B . \( \left(F_{1}-F_{2}\right) m L / e M \)
\( \mathbf{c} \cdot[m L / e M] \ln \left[F_{1} / F_{2}\right] \)
D. None
Subject: Physics
An object is placed
(i) Asymmetrically
\( (i i) \) Symmetrically, between two plane
mirrors inclined at an angle of \( 50^{\circ} . \) Find
the number of images formed.
A \( \cdot(1) 7,(i i) 7 \)
B. (1) 6, ( ii)6
c. \( (1) 6,(i i) 7 \)
D. \( (1) 7,(i i) 6 \)
Subject: Maths
Find the equation of the circle with
center at (-3,5) and passes through
the point (5,-1)
A \( \cdot(x+3)^{2}+(y-5)^{2}=100 \)
B. \( (x-3)^{2}+(y-5)^{2} \)
C. \( (x+3)^{2}+(y-5)^{2} \)
D. None of the above
Subject: Maths
If \( f(z)=\frac{1-z^{3}}{1-z}, \) where \( z=x+i y \) with \( z \neq 1, \) then \( R e \overline{\{f(z)\}}=0 \) reduces to
A \( \cdot x^{2}+y^{2}+x+1=0 \)
B . \( x^{2}-y^{2}+x-1=0 \)
c. \( x^{2}-y^{2}-x+1=0 \)
D. \( x^{2}-y^{2}+x+1=0 \)
E \( \cdot x^{2}-y^{2}+x+2=0 \)
Subject: Chemistry
In an experiment, 20 g of vanadium \( (V) \) oxide (molar mass \( =182 \) g/mol) was
reduced by excess of zinc dust in acidic solution to vanadium
(II) ions. If the
required number of moles of iodine to
reoxidise vanadium
(II) to \( V O^{2+} \) is
\( 22 \times 10^{-x}, \) then what is the value of \( x ? \)
Subject: Chemistry
All alkali metals dissolve in anhydrous liquid ammonia to give a blue color solution. It is the ammoniated electron
which is responsible for the blue color of the solution, and the electrical conductivity is due to ammoniated
cation, \( \left[M\left(N H_{3}\right)_{x}\right]^{+} \) as well as the
ammoniated electron, \( \left[e\left(N H_{3}\right)_{y}\right]^{-} \) values of \( x \) and \( y \) depend on the extent of
solvation by \( N H_{3} . \) Dilute solutions are
paramagnetic due to free ammoniated electrons.
What happens if alkali metals are allowed to react with concentrated
liquid ammonia?
A. Paramagnetic character of solvated electrons is retained.
B. Solvated electrons associate to form electron-pairs and paramagnetic character decreases
c. Reducing character is increased.
D. Reducing character is not affected.
Subject: Chemistry
Assertion
lonisation potential increases with
increase in nuclear charge of the
elements.
Reason
lonization energies increase moving from left to right across a period.
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: Biology
If expiratory reserve volume is \( 1100 \mathrm{ml} \) residual volume is \( 1200 \mathrm{ml} \) and tidal
volume is \( 500 \mathrm{ml} \), what shall be the
functional residual capacity?
A . \( 1600 \mathrm{ml} \)
B. 2800 m!
c. \( 2300 \mathrm{ml} \)
D. \( 1200 \mathrm{ml} \)
Subject: Physics
An object of mass \( m \) sliding along a frictionless surface collides with the
stationary object of mass \( m \). The two
bodies stick together. If the kinetic
energy of the two-body system is \( \boldsymbol{E} \) Calculate the initial velocity of the first object before impact?
A \( \cdot \sqrt{E / 2 m} \)
B. \( \sqrt{2 E / 2 m} \)
c. \( \sqrt{2 E / m} \)
D. \( \sqrt{E / m} \)
E \( .2 \sqrt{E / m} \)
Subject: Physics
A gas is kept at \( 13^{\circ} \mathrm{C} \) in a vessel. If the
volume of the gas is kept constant and is heated, the pressure will be doubled to its initial pressure at a temperature
\( \mathbf{A} \cdot 576 \mathrm{K} \)
B. 286 K
c. \( 143 \mathrm{k} \)
D. 73
Subject: Chemistry
For the data given, calculate the energy
deficit in the formation \( B e C l_{2} \) (it is a
stable molecule)
I. \( \boldsymbol{E}_{1} \) for \( \boldsymbol{B e}=\mathbf{8 9 9 k J} / \boldsymbol{m o l} \)
I. \( \boldsymbol{E} \). for \( \boldsymbol{B e}=\mathbf{1 7 5 7 k J} / \boldsymbol{m o l} \)
I.A. for \( C l=-348 k J / \) mol
Subject: Maths
Range of \( \sin ^{-1} x-\cos ^{-1} x \) is
\( ^{\mathbf{A}} \cdot\left[\frac{-3 \pi}{2}, \frac{\pi}{2}\right] \)
В \( \cdot\left[\frac{-5 \pi}{3}, \frac{\pi}{3}\right. \)
\( ^{\mathbf{c}} \cdot\left[\frac{-3 \pi}{2}, \pi\right] \)
D. \( [0, \pi] \)
Subject: Chemistry
At a certain temperature, equilibrium
constant \( \left(K_{c}\right) \) is 16 for the reaction:
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \)
If we take 1 mole of each of the four
gases in \( 1 L \) container, what would be
the equilibrium concentration of \( N O \)
and \( N O_{2} ? \)
Subject: Physics
Three charges \( Q,+q \) and \( +q \) are placed
at the vertices of a right angle isosceles triangle as shown. The net electrostatic
energy of the configuration is zero, if \( \boldsymbol{Q} \)
is equal to:
\( \mathbf{A} \)
B.
\( \mathbf{c} .-2 q \)
D. \( +q \)
Subject: Physics
The relative permeability is represented
by \( \mu_{r} \) and the susceptibility by \( \chi \) for a magnetic substance. Then, for a paramagnetic substance. Then, for a paramagnetic substance
A \( \cdot \mu_{r}>1, \chi>0 \)
в. \( \mu_{r}>1, \chi<0 \)
c. \( \mu_{r}>1, \chi>0 \)
D. \( \mu_{r}<1, \chi<0 \)