AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Chlorine atoms in the upper
atmosphere cause the breakdown of
ozone.
\( \boldsymbol{C l}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{C l O} \)
\( \boldsymbol{C l O}+\boldsymbol{O} \rightarrow \boldsymbol{C l}+\boldsymbol{O}_{2} \)
Which statements about these chlorine
atoms are correct?
1. The chlorine atoms act as catalysts.
2. The chlorine atoms are free radicals.
3. The chlorine atoms are formed by heterolytic fission of a covalent bond in
chlorofluorocarbons.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \frac{2 \sqrt{b}}{\sqrt{a}+\sqrt{b}}+ \)
\[
\left(\frac{a^{3 / 2}+b^{3 / 2}}{\sqrt{a}+\sqrt{b}}-\frac{1}{(a b)^{-1 / 2}}\right)(a-b)^{-1}
\]
Subject: Physics
A partical having mass 10 g oscillates according to the equation \( \boldsymbol{x}= \) \( (2.0 c m) \sin \left[\left(100 s^{-1}\right) t+\frac{6}{\pi}\right] . \) Find
(a) the amplitude, the time period and
the force constant
(b) the position, the velocity and the
acceleration at \( t=0 \)
Subject: Chemistry
A piece of steel has a volume of \( 12 \mathrm{cm}^{3} \) and a mass of 96 g. Find its density in \( \mathrm{kg} / \mathrm{m}^{3} \)
Density \( =x \times 10^{3} k g / m^{3} . \) What is the
value of \( x ? \)
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 8
Subject: Physics
Two blocks each of the mass \( m \) are
attached to the ends of massless rod
which pivots as shown in fig. Initially the rod is held in the horizontal position
and then released. Calculate the net
torque on this system above pivot.
\( \mathbf{A} \cdot\left(m l_{2} g-m l_{1} g\right) \hat{k} \)
B. \( \left(m l_{1} g+m l_{2} g\right) \hat{k} \)
\( \mathbf{c} \cdot\left(m l_{1} g-m l_{2} g\right) \hat{k} \)
D. \( -\left(m l 1 g+m l_{2} g\right) \hat{k} \)
Subject: Maths
If area bounded by to curves \( \boldsymbol{y}^{2}=4 a x \)
and \( y=m x \) is \( \frac{a^{2}}{3}, \) then the value of \( m \) is
A .2
B. - 1
\( c \cdot \frac{1}{2} \)
D. none of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})^{4} \cdot(\boldsymbol{x}-\boldsymbol{2})^{n}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
Then \( f(x) \) has
This question has multiple correct options
A. a maximum at \( x=1 \) if \( n \) is odd
B. a maximum at \( x=1 \) if \( n \) is even
c. a minimum at \( x=2 \) if \( n \) is even
D. a maximum at \( x=2 \) if \( n \) is odd
Subject: Maths
A solution of the differential equation \( \left(\frac{d y}{d x}\right)^{2}-x \frac{d y}{d x}+y=0 \)
\( \mathbf{A} \cdot y=2 \)
в. \( y=2 x \)
\( \mathbf{c} \cdot y=2 x-4 \)
D. \( y=2 x^{2}-4 \)
Subject: Chemistry
Out of the complexes \( \left.\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right)\right]^{3+} \)
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-},\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \) and
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C l})_{6}\right]^{3-}, \) the most stable one is:
\( \left.\left.^{\mathbf{A}} \cdot_{[F e}\left(H_{2} O\right)_{6}\right)\right]^{3+} \)
B. \( \left[F e(C N)_{6}\right]^{3-} \)
\( c \)
\( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \)
\( D \)
\( \left[F e(C l)_{6}\right]^{3-} \)
Subject: Maths
The set of all values of \( ^{\prime} x^{\prime} \) satisfying the inequation \( \left(\frac{1}{|x|-3}\right) \leq \frac{1}{2} \) is
A \( (-\infty,-5) \cup(-3,3) \cup[5, \infty) \)
B . \( (-\infty,-5] \cup[-3,3] \cup[5, \infty) \)
c. \( (-\infty,-5) \cup(-3,3) \cup(5, \infty) \)
D. None of the above
Subject: Chemistry
Which of the following reaction occurs at
the cathode during the charging of lead
storage battery?
\( \mathbf{A} \cdot P b \rightarrow P b^{2+}+2 e^{-} \)
B \( \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
\( \mathbf{c} \cdot P b O_{2}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
D \( \cdot P b S O_{4}(s)+2 H_{2} O \rightarrow P b O_{2}(s)+4 H^{+}+S O_{4}^{2-}+2 e^{-} \)
Subject: Physics
Two metallic spheres \( S 1 \) and \( S 2 \) are
made of the same material and have
got identical surface finish. The mass of
S1 is thrice that of \( S 2 . \) Both the spheres
are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The rate of the initial rate of cooling of
S1 to that of \( S 2 \) is?
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D. \( \frac{3}{1} \)
Subject: Chemistry
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 0 4} \) at \( \boldsymbol{m} \) at \( \boldsymbol{8} 99 \) K for the
equilibrium shown below. What is the equilibrium concentration of \( C_{2} H_{6} \) when it is placed in a flask at 4.0 atm pressure and allowed to come to
equilibrium?
\( \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Subject: Chemistry
In the reaction sequence:
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \frac{\boldsymbol{C H}_{3} M \boldsymbol{g} \boldsymbol{B r}}{\longrightarrow} \boldsymbol{C H}_{4}+ \)
\( (\boldsymbol{A}) \frac{(i) C O_{2}}{(i i) H_{2} O / H^{\oplus}}(B) \)
(B) will be :
A \( \cdot C H_{3}-C \equiv C-C H_{3} \)
B . \( C H_{3}-C \equiv C-M g B r \)
c. \( C H_{3}-C \equiv C- \) COOH
D. \( C H_{3}-C H \equiv C H-C O O H \)
Subject: Maths
Prove the following identities :
\[
\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2 c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}
\end{array} \mid=
\]
\( \mathbf{2}(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)
Subject: Maths
If two angle of a triangle are \( \sin ^{-1}\left(\frac{1}{\sqrt{5}}\right) \) and \( \sin ^{-1}\left(\frac{1}{\sqrt{10}}\right), \) then third angle is
\( A \cdot \frac{\pi}{4} \)
B.
\( c \cdot \frac{3 \pi}{4} \)
D. \( \frac{2 \pi}{3} \)
Subject: Physics
If the charge of \( 10 \mu C \) and \( -2 \mu C \) are
given to two plates of a capacitor which
are connected across a battery of \( 12 V \)
find the capacitance of the capacitor.
в. \( 0.5 \mu F \)
c. \( 0.41 \mu F \)
D. \( 0.66 \mu F \)
Subject: Physics
The radius of each coil of a Helmholtz
galvanometer is \( 0.1 m \) and number of
turns in each is \( 25 . \) When a current is
passed in it then the deflection of
magnetic needle observed as \( 45^{\circ} . \) If the
horizontal component of earth's magnetic field is \( 0.314 \times 10^{-4} T \) then
the value of current will be
\( \mathbf{A} \cdot 0.14 A \)
B. \( 0.28 A \)
c. \( 0.42 A \)
D. \( 0.07 A \)
Subject: Physics
If the shortest wavelength of the continuous X-ray spectrum coming out of a Coolidge tube is \( 0.01 n m \), then the de Broglie wavelength of the electron reaching the target metal in the Coolidge tube is approximately \( \left(h c=12400 e V A, h=6.63 \times 10^{-34} \) in \right.
MKS, mass of electron= \( 9.1 \times \)
\( \left.10^{-31} k g\right) \)
A . 0.35
в. 0.035
\( c .35 \)
D. 1350
Subject: Physics
The needle of the dip circle of a place
stay at \( 30^{0} . \) The dip circle is inclined at
an angle towards \( 30^{0} \) with the magnetic
meridian. The true dip at the place is:
A \( \cdot \tan ^{-1} \sqrt{3} \)
B. \( \tan ^{-1} \frac{\sqrt{3}}{2} \)
c. \( \tan ^{-1} \frac{1}{2} \)
D. \( \tan ^{-1} \frac{3}{2} \)
Subject: Physics
The area of pistons in a hydraulic machine are \( 5 c m^{2} \) and \( 625 c m^{2} . \) The
force on the smaller piston so that a
load of \( 1250 N \) on the larger piston can be supported, is \( X \) N. Find \( \frac{X}{2} \) N.
A. 5
B. 10
c. 1250
D. None of the above
Subject: Maths
The area included between the
parabolas \( y=\frac{x^{2}}{4 a} \) and \( y=\frac{8 a^{3}}{x^{2}+4 a^{2}} \) is
A \( a^{2}\left(2 \pi+\frac{2}{3}\right) \)
в. \( a^{2}\left(2 \pi-\frac{8}{3}\right) \)
c. \( _{a^{2}}\left(\pi+\frac{4}{3}\right) \)
D. \( a^{2}\left(\pi-\frac{4}{3}\right) \)
Subject: Chemistry
Which of the following shows the Lewis
dot formula for \( \boldsymbol{C O}_{2} \) ?
\( A \cdot: \ddot{O}:: C:: \ddot{O} \)
в. \( : \ddot{O}: \ddot{C}:: \ddot{O} \)
\( c \ldots \ddot{o}:: C: \ddot{O} \)
\( \mathrm{D} \cdot: \ddot{O}: C: \ddot{O} \)
Subject: Maths
If \( h(x)=x^{2}-2, \) then the value of \( \frac{1}{2} h\left(\frac{1}{2}\right) \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
в.
\( c \cdot-\frac{7}{8} \)
D. 7 8
Subject: Maths
The geometric mean of the first n terms
of the series \( a, a r, a r^{2}, \dots, \) is
A \( \cdot a r^{n / 2} \)
2
B \( . a r^{n} \)
c. \( a r^{(n-1) / 2} \)
D. \( a r^{n-1} \)
Subject: Physics
three idntical spherical ball \( A, B, C \) are placed on a table as shown in the figure along a straight line. \( \mathrm{B} \) and \( \mathrm{C} \) are at rest initilly. the ball \( A \) hits \( B \) head -on with a speed of \( 10 \mathrm{ms}^{-1} \).then after all collision
s( assumed to be elastic )A and B are brought to rest and \( C \) takes off with a
velocity of
\( \mathbf{A} \cdot 5 m s^{-1} \)
B. \( 10 m s^{-1} \)
c. \( 2.5 m s^{-1} \)
D. \( 7.5 m s^{-1} \)
Subject: Physics
The self induction of a coil having 400 turns is \( 10 \mathrm{mH} \). The magnetic flux through the cross section of the coil corresponding to current \( 2 \mathrm{mA} \) is :
A \( \cdot 2 \times 10^{-5} \mathrm{Wb} \)
В. \( 8 \times 10^{-3} \mathrm{Wb} \)
c. \( 4.3 \times 10^{-5} \mathrm{Wb} \)
D. \( 4.8 \times 10^{-3} \mathrm{Wb} \)
Subject: Physics
The dimensions of \( \frac{1}{\mu_{0} \in_{0}} \) is (where
symbols have their usual menaing)
A \( \cdot\left[L^{2} T^{-2}\right] \)
в. \( [A] \)
C \( \cdot\left[M L^{2} T^{-2}\right] \)
D. \( \left[M L^{-2} T^{-2}\right. \)
Subject: Chemistry
Identify the electronic configuration of an element whose atomic radii is determined by taking half the internuclear distance between like
atoms.
\( \mathbf{A} \cdot[H e] 2 s^{2} 2 p^{5} \)
B . \( [A r] 4 s^{2} \)
c. \( [N e] 3 s^{2} \)
D \( \cdot[K r] 4 d^{5} 5 s^{2} \)
Subject: Physics
In an experiment, the percentage of
error occurred in the measurement of
physical quantities \( A, B, C \) and \( D \) are \( 1 \% \) \( 2 \%, 3 \% \) and \( 4 \% \) respectively. Then the
maximum percentage of error in the measurement \( \mathbf{X}, \) where \( \boldsymbol{X}=\frac{\boldsymbol{A}^{\mathbf{2}} \boldsymbol{B}^{\mathbf{1} / \mathbf{2}}}{\boldsymbol{C}^{\mathbf{1} / \mathbf{3}} \boldsymbol{D}^{\mathbf{3}}} \)
will be
A \( \cdot\left(\frac{3}{13}\right) \% \)
B. \( 16 \% \)
c. \( -10 \% \)
D. \( 10 \% \)
Subject: Chemistry
The oxidation number of \( C \) in
\( \boldsymbol{C H}_{4}, \boldsymbol{C H}_{3} \boldsymbol{C l}, \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{C H} \boldsymbol{C l}_{3} \) and
\( C C l_{4} \) are respectively :
в. +2,+4,0,-4,-2
c. -4,-2,0,+2,+4
D. -2,-4,0,+4,+2
Subject: Biology
Which of the following are correct?
(i) \( \quad \) Diploblastic :
Poriferans, Coelenter " Diploni :
and What is and
Platyhelminthes to
(ii) \( \quad \) Triploblastic: \( \quad \) Chordates Triploblastic:
(iii) Acoelomata:
(iv) Pseudocoelomata
:
Aschelminthes/Roundv
Eucoelomata:
\( (v) \)
Annelids to Chordates
\( \mathbf{A} \cdot(\mathrm{i}),(\mathrm{iii}),(\mathrm{iv}) \) and \( (\mathrm{v}) \)
B. (iii) and (v)
C \( . \) (i), (ii), and (v)
D. (i), (ii), (iii), (iv) and (v)
Subject: Physics
\( \ln \) a \( L C \) circuit. Angular frequency at resonance is \( \boldsymbol{w} \). What will be the new
angular frequency when inductor's
introduces is made 2 times and
capacitance is made 4 times?
A \( \cdot \frac{w}{\sqrt{2}} \)
в. \( \frac{w}{2 \sqrt{2}} \)
c. \( 2 w \)
D. \( \frac{2 w}{\sqrt{2}} \)
Subject: Chemistry
Explain the given reactions with the examples. Oxidation reaction:
A \( \cdot C_{2} H_{5} O H \stackrel{A l k . K M n O_{4}}{\longrightarrow} C H_{2} O H C O O H \)
в. \( C_{2} H_{5} \) ОН \( \frac{\text {Аlк.КМп} O_{4}}{\longrightarrow} C H_{3} C H_{3} \)
c. \( C_{2} H_{5} O H \frac{A l k . K M n O_{4}}{\longrightarrow} C H_{3} C H_{2} O H \)
D. \( C_{2} H_{5} O H \frac{A l k . K M n O_{4}}{\longrightarrow} C H_{3} C O O H \)
Subject: Chemistry
The correct order of acidic strength is:
A. \( K_{2} O>C a O>M g O \)
в. \( C O_{2}>N_{2} O_{5}>S O_{3} \)
c. \( N a_{2} O>M g O>A l_{2} O_{3} \)
D. \( C l_{2} O_{7}>S O_{2}>P_{4} O_{10} \)
Subject: Maths
Factorize \( (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y})^{2}+(\boldsymbol{b} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{y})^{2} \) by
the grouping method
A \( \cdot\left(x^{2}+y^{2}\right)\left(a^{2}+b^{2}\right) \)
В - \( \left(2 x^{2}+y^{2}\right)\left(a^{2}+b^{2}\right) \)
c. \( \left(2 x^{2}+y^{2}\right)\left(2 a^{2}-b^{2}\right) \)
D. \( \left(x^{2}+2 y^{2}\right)\left(a^{2}-b^{2}\right) \)
Subject: Physics
A stream of electrons enters an electric
field normal to the lines of force with a
velocity of \( 3 \times 10^{7} m / s . \) The electric
intensity is \( 1800 \mathrm{V} / \mathrm{m} \). While traveling through a distance of \( 10 \mathrm{cm}, \) the electron beam is deflected by \( 2 \mathrm{mm} \) Then e/m in coulomb per kg will be
A \( \cdot 2 \times 10^{-11} \)
в. \( 2 \times 10^{7} \)
\( c \cdot 2 \times 10^{11} \)
D. \( 2 \times 10^{14} \)
Subject: Maths
Which of the following equation is a linear differential equation of order 3 ?
[Note: The original question asks for linear equation, but it should be linear differential equation]
A \( \cdot \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}} \frac{d y}{d x}+y=x \)
B. \( \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}}+y^{2}=x^{2} \)
c. \( \quad x \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}}=e^{x} \)
D. \( \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=\log x \)
Subject: Maths
A parabola with axis parallel to \( x \) axis
passes through \( (\mathbf{0}, \mathbf{0}),(\mathbf{2}, \mathbf{1}),(\mathbf{4},-\mathbf{1}) . \) Its
length of latus rectum is
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{7}{3} \)
D. \( \frac{1}{3} \)
Subject: Chemistry
The work done when 2 moles of an ideal
gas is compressed from a volume of
\( 5 m^{3} \) to \( 1 d m^{3} \) at an initial temperature
of \( 300 K, \) under a pressure of \( 100 k P a \)
is:
A. \( 499.9 k J \)
в. \( -499.9 k J \)
\( \mathbf{c} .-99.5 k J \)
D. \( 42495 k J \)
Subject: Chemistry
Assertion (A): Noble gases have
highest ionization energies in their respective periods. Reason (R): The outermost shell of noble
gases is completely filled.
A. Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are correct and \( R \) is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true
Subject: Physics
An ideal cell having a steady emf of
2 volts is connected across the
potentiometer wire of length \( 10 m \). The
potentiometer wire is of magnesium and having resistance of \( 11.5 \Omega / m . \) An another cell gives a null point at \( 6.9 m \). If
a resistance of \( 5 \Omega \) is put in series with potentiometer wire, the new position of the null point is given as \( \frac{x}{10} m . \) Find \( x \)
Subject: Maths
Arrange in ascending order:
\( \mathbf{2 5 6 . 3 6}, \mathbf{2 5 6 . 5 6}, \mathbf{2 5 6 . 2 6}, \mathbf{2 5 6 . 4 6} \)
A . 256.36,256.56,256.26,256.46
B . 256.26,256.56,256.36,256.46
c. 256.36,256.46,256.26,256.56
D. 256.26,256.36,256.46,256.56
Subject: Maths
suitable common differences given in
column B.
Column A
Column B
A. \( -2,2,6,10, \dots \)
1. \( \frac{2}{3} \)
B. \( a=18, n=10, a_{n}=0 \)
2. -5
\( \mathbf{C} \cdot \boldsymbol{a}=\mathbf{0}, \boldsymbol{a}_{\mathbf{1 0}}=\mathbf{6} \)
3. 4
D. \( \boldsymbol{a}_{\mathbf{2}}=\mathbf{1 3}, \boldsymbol{a}_{\boldsymbol{4}}=\mathbf{3} \)
4. -4
\( 5 .-2 \)
6. \( \frac{1}{2} \)
7. 5
A. A-3, B-5, C-1, D-2
B. A-4, B-1, C-3, D-2
C. A-2, B-7, C-5, D-6
D. \( A-7, B-4, C-2, D-2 \)
Subject: Physics
The height of water level in a tank is \( \boldsymbol{H} \)
The range of water stream coming out of a hole at depth \( \frac{\boldsymbol{H}}{\mathbf{4}} \) from upper water level will be.
A. \( \frac{\sqrt{3} H}{2} \)
в. \( \frac{2 H}{\sqrt{3}} \)
c. \( \frac{H}{\sqrt{3}} \)
D. \( \sqrt{3} H \)
Subject: Physics
If the mass of a body is \( 12.1 g \) and the
density is \( 2.2 g / c c, \) its volume is
\( \mathbf{A} \cdot 5.5 \mathrm{cm}^{3} \)
в. \( 8 c c \)
\( c .11 c c \)
D. \( 55 c c \)
Subject: Physics
The plates of a parallel plate capacitor are charged to \( 200 \mathrm{V} \) and then, the charging battery is disconnected. Now, a dielectric
slab of dielectric constant 5 and
thickness \( 4 \mathrm{mm} \) is inserted between the
capacitor plates. To maintain the original
capacity, the increase in the separation between the plates of the capacitor is:
A. \( 1.6 \mathrm{mm} \)
B. \( 3.2 \mathrm{mm} \)
\( \mathrm{c} .0 .8 \mathrm{mm} \)
D. \( 4.8 \mathrm{mm} \)
Subject: Physics
The electric potential at a point in free
space due to a charge \( Q \) coulomb is \( Q \times 10^{11} V . \) The electric field at that
point is
A \( \cdot 12 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
B . \( 4 \pi \varepsilon_{0} Q \times 10^{22} V m^{-1} \)
C \( .12 \pi \varepsilon_{0} Q \times 10^{20} \mathrm{Vm}^{-1} \)
D. \( 4 \pi \varepsilon_{0} Q \times 10^{20} V m^{-1} \)
Subject: Chemistry
I. Under standard conditions the states
of the elemental forms of the halogens are: iodine-solid, bromine-liquid,
chlorine-gas, fluorine-gas.
II. Diatomic halogen molecules exhibit dispersion forces and increase in mass moving down through the family.
A. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false
Subject: Chemistry
Dioxane used as a solvent is obtained
by distilling with
\( \mathbf{A} \cdot \) glycerol, conc. \( H_{2} S O_{4} \)
B. glycerol, conc. \( H_{3} P O_{4} \)
C . glycol, conc. \( H_{2} S O_{4} \)
D. glycol, conc. \( H_{3} P O_{4} \)
Subject: Maths
The radius of a sphere of lead is \( 8 \mathrm{cm} \)
The number of spheres of radius \( 5 \mathrm{mm} \) made by melting it will be
A. 6000 approx
B. Greater than 4000 and less than 5000
c. Greater than 3000 and less than 4000
D. Less than 3000
Subject: Maths
The following data shows the number of visitors to a zoological park every hour. Calculate the average number of visitors to the park during the whole
day.
Time \( \begin{array}{ll}10- & 11-12 \\ 11 & \text { noon } \quad 12-1 \\ \text { a.m } & \text { p.m }\end{array} \)
Number of 30 40
34
visitors
Subject: Maths
\( f(\Omega A=5 \mathrm{cm}, A B=8 \mathrm{cm} \text { and } O D \) is
perpendicular to \( A B, \) then \( C D \) is equal
to:
\( A \cdot 2 \mathrm{cm} \)
B. \( 3 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
\( 0.5 \mathrm{cm} \)
Subject: Biology
One hormone hastens maturity period in juvenile conifers, a second hormone controls xylem differentiation, while the third increases the tolerance of plants
to various stresses. They are
respectively
A. Auxin, Gibberellins, cytokinin
B. Auxin, Gibberellins, ABA
c. Gibberellin, Auxin, Cytokinin
D. Gibberellin, Auxin, ABA
Subject: Physics
An isosceles triangle is formed with
rods of length \( L_{1} \& L_{2} \) as shown in the figure.The coefficient of linear
expansion \( \alpha_{1}=2 \times 10^{-5} /^{0} C \) and
\( \boldsymbol{\alpha}_{2}=\boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{5}} /^{\mathbf{0}} \boldsymbol{C} \) for the two pieces. If
the distance between apex and the
midpoint of the base remains
unchanged as the temperature is
varied, then \( \frac{L_{1}}{L_{2}} \) is equal to:
Subject: Physics
The displacement of a particle
executing SHM at any instant \( t \) is \( x= \)
\( 7 \cos 0.5 \pi t . \) The time taken by the
particle in reaching from mean position to extreme position will be
A . \( 4 s \)
B . \( 2 s \)
c. \( 1 s \)
D. \( 1 / 2 s \)
Subject: Maths
If \( f(x)=\max \left\{\sin x, \cos x, \frac{1}{2}\right\}, \) then the
area of the region bounded by the
curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{x}- \) axis \( \boldsymbol{y}- \) axis and
\( \boldsymbol{x}=2 \pi \) is
\( ^{\mathbf{A}} \cdot\left(\frac{5 \pi}{12}+3\right) \cdot \) sq.unit
в. \( \left(\frac{5 \pi}{12}+\sqrt{2}\right) \). sq.unit
c. \( \left(\frac{5 \pi}{12}+\sqrt{3}\right) \cdot \) sq.unit
D \( \cdot\left(\frac{5 \pi}{12}+\sqrt{2}+\sqrt{3}\right) \cdot \) sq.unit
Subject: Chemistry
In a vessel containing \( S O_{3}, S O_{2} \) and \( O_{2} \)
at equilibrium, some helium gas is introduced so that total pressure
increases while temperature and volume remain the same. According to Le Chatelier's principle, the dissociation
of \( \boldsymbol{S O}_{3} \)
A. increases
B. decreases
c. remains unalered
D. changes unpredictably
Subject: Physics
Using the relationship between
moments of inertia as \( \boldsymbol{I}_{\boldsymbol{x}}+\boldsymbol{I}_{\boldsymbol{y}}=\boldsymbol{I}_{\boldsymbol{z}} \)
where sub indices \( x, y, \) and \( z \) define three mutually perpendicular axes passing through one point, with axes 1 and 2 lying in the plane of the plate, the moment of inertia of a thin uniform
round disc of radius \( R \) and mass \( m \)
relative to the axis coinciding with one of its diameters is \( I=\frac{m R^{2}}{x} . \) Find the
value of \( \boldsymbol{x} \)
Subject: Maths
If the value of the determinant
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\ \boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\ \boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}\end{array}\right| \) is \( \left(\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{f}^{2}-\boldsymbol{b} \boldsymbol{g}^{2}-\right. \)
\( \left.c h^{2}\right), \) then what is the value of \( ^{\prime} x^{\prime} ? \)
Subject: Maths
If the function
\( \left\{\begin{array}{l}\boldsymbol{x}, \quad \text { if } \quad \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{c x}+\boldsymbol{k}, \quad \text { if } \quad \mathbf{1}<\boldsymbol{x}<\mathbf{4} \\ -\mathbf{2} \boldsymbol{x}, \quad \text { if } \quad \boldsymbol{x} \geq \mathbf{4}\end{array}\right. \)
is contionus everywhere, then the value
of \( c \) and \( k \) are respectively:
A. -3,-5
в. -3,5
c. -3,-4
D. -3,4
E . -3,3
Subject: Maths
The vector equation of the plane through the point (1,-2,-3) and
parallel to the vectors (2,-1,3) and
(2,3,-6) is \( \bar{r}= \)
A \( \cdot(1+2 t+2 s) \bar{i}-(2+t-3 s) \bar{j}-(3-3 t+6 s) \bar{k} \)
B. \( (1+2 t+2 s) \bar{i}+(2+t+3 s) \bar{j}-(3+3 t+6 s) \bar{k} \)
c. \( (1+2 t+2 s) \bar{i}+(2+t+3 s) \bar{j}+(3+3 t+6 s) \bar{k} \)
D. \( (1+2 t+2 s) \bar{i}+(2+t-3 s) \bar{j}+(3+3 t+6 s) \bar{k} \)
Subject: Physics
Two wires are made of the same
material and have the same volume.
The first wire has cross-sectional area \( A \) and the second wire has cross-sectional
area 3 A. If the length of the first wire is
increased by \( \Delta l \) on applying a force \( F \) how much force is needed to stretch the
second wire by the same amount?
A . 4 F
B. 9 F
\( c . F \)
D. 6 F
Subject: Physics
\( 150 \mathrm{g} \) of ice is mixed with \( 100 \mathrm{g} \) of water at temperature \( 80^{\circ} \mathrm{C} \). The latent heat of ice is 80 ca/g and the specific heat of water is \( 1 \mathrm{cal} / \mathrm{g}-^{\circ} \mathrm{C} \). Assuming no
heat loss to the environment, the amount of ice which does not melt is
A. \( 100 \mathrm{g} \)
B. 08
c. \( 150 \mathrm{g} \)
D. 50g
Subject: Maths
The D.E whose solution is \( \boldsymbol{y}= \)
\( a \cos (3 x+b) \) is?
A \( \cdot y_{2}+3 y=0 \)
В. \( y_{2}+y=0 \)
c. \( y_{2}+9 y=0 \)
D. \( y_{2}+6 y=0 \)