AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Multiple Correct Answers Type
Let \( \left[\epsilon_{0}\right] \) denote the dimensional formula
of the permittivity of vacuum and \( \left[\mu_{0}\right] \) that of the permeability of vacuum. If \( \mathrm{M} \) \( = \) mass, \( L= \) length, \( T= \) time, and \( l= \) electric current, then
This question has multiple correct options
A \( \cdot\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{2} I^{2} \)
B . \( \left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} I^{2} \)
c. \( \left[\mu_{0}\right]=M L T^{-2} I^{-2} \)
D. \( \left[\mu_{0}\right]=M L^{2} T^{-1} I \)
Subject: Maths
If \( (1+x)^{10}=a_{0}+a_{1} x+a_{2} x^{2}+\dots+ \)
\( a_{10} x^{10}, \) then the value of
\( \left(a_{0}-a_{2}+a_{4}-a_{6}+a_{8}-a_{10}\right)^{2}+ \)
\( \left(a_{1}-a_{3}+a_{5}-a_{7}+a_{9}\right)^{2} \) is
\( \mathbf{A} \cdot 2^{10} \)
B . 2
\( c \cdot 2^{20} \)
D. None of these
Subject: Maths
Which of the following values are possible?

This question has multiple correct options
\( \mathbf{A} \cdot \sin \theta=0 \)
в. \( \sec \theta=\frac{1}{2} \)
\( \mathbf{c} \cdot \tan \theta=1 \)
D. \( \operatorname{cosec} \theta=\sqrt{3} \)
Subject: Maths
The percentage of metals in a mine of
lead ore is \( 60 \% . \) Now the percentage of silver is \( \frac{3}{4} \% \) of metals and the rest is lead. If the mass of ore extracted from
this mine is \( 8000 k g \), the mass (in kg.) of lead is:
A. 4763
в. 4764
c. 4762
D. 476
Subject: Chemistry
\( \Delta H_{r} \) of which of the following reactions
is zero?
A \( \cdot H_{2}(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
B . \( 2 H(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
C \( \cdot 2 H(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
D \( \cdot H_{2}(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
Subject: Chemistry
Assertion
Alkyl benzene is not prepared by Friedel Craft's alkylation of benzene.
Reason
Alkyl halides are less reactive than acyl halides.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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 the extremities of the base of an
isosceles triangle are the points \( (2 a, 0) \) and \( (0, a), \) and the equation of one of the sides is \( x=2 a \), then the area of the
triangle is
A. \( 5 a^{2} \) squnits
в. \( \frac{5 a^{2}}{2} \) sq.units
c. \( \frac{25 a^{2}}{2} \) sq.units
D. None of these
Subject: Chemistry
Which of the following spectrochemical series is true?
A \( \cdot S C N^{-}<N H_{3}<F^{-}<e n<C O \)
B . \( S C N^{-}<F^{-}<N H_{3}<e n<C O \)
c. \( S C N^{-}<F^{-}<e n^{-}<N H_{3}<C O \)
D. \( S C N^{-}<F^{-}<e n^{-}<C O^{-}<N H_{3} \)
Subject: Physics
Potentiometer wire of length \( 1 \mathrm{m} \) is connected in series with \( 490 \Omega \)
resistance and \( 2 \mathrm{V} \) battery. If \( 0.2 \mathrm{mV} / \mathrm{cm} \) is the potential gradient, then resistance of the potentiometer wire is?
A . \( 4.9 \Omega \)
B. \( 7.9 \Omega \)
\( c .5 .9 \Omega \)
D. \( 6.9 \Omega \)
Subject: Chemistry
Reaction; \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D}, \) follows
rate law; \( r a t e=k[A]^{2}[B]^{2} . \) Starting
with initial concentration of \( 1 M \) of \( A \)
and \( B \) each, what is the time taken for
concentration of \( A \) to become \( 0.25 M ? \)
Given: \( k=2.303 \times 10^{-2} s e c^{-1} \)
A . 300 sec
B. 600 sec
c. 900 sec
D. 1200sec
Subject: Chemistry
Which expression gives the correct
value for the standard potential for a
gold-rhodium voltaic cell?
Half-reaction \( \mathbb{E}^{\circ}(\mathbf{V}) \)
\( R h_{(q q)}^{+3}+3 e^{-} \rightarrow R h_{(s)} \)
\( A u_{(q q)}^{+}+e^{-} \rightarrow A u_{(s)} \)
A . \( 1.69 V+0.76 V \)
B . \( 1.69 V-0.76 V \)
c. \( 3(1.69) V+0.76 V \)
D. \( 3(1.69) V-0.76 V \)
Subject: Maths
The equation of the image of the circle \( x^{2}+y^{2}-6 x-4 y+12=0 \) by the
line mirror \( \boldsymbol{x}+\boldsymbol{y}-\mathbf{1}=\mathbf{0} \) is
A \( \cdot x^{2}+y^{2}+2 x+4 y+4=0 \)
B . \( x^{2}+y^{2}-2 x+4 y+4=0 \)
c. \( x^{2}+y^{2}+2 x+4 y-4=0 \)
D. \( x^{2}+y^{2}+2 x-4 y+4=0 \)
Subject: Physics
For two position of lens, the images are obtained on a fixed screen. If the size of
the object is \( 2 \mathrm{cm} \) and size of diminished image is \( 0.5 \mathrm{cm}, \) the size of the other image will be
A. \( 1 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)
Subject: Maths
State which of the following are infinite
sets
\( (i) A=\left\{x: x \in Z: x^{2} \text { is even }\right\} \)
\( (i i) B=\{x: x \in R:-4<x<-2\} \)
A . (i) only y
B. (ii) only
c. \( (i) \) and \( (i i) \) both
D. Neither \( (i) \) nor \( (i i) \)
Subject: Physics
Assertion
The electrostatic force on a charged
particle located on an equipotential surface is zero.
Reason
\( x \) component of electric field is given by,
\( \boldsymbol{E}_{\boldsymbol{x}}=-\frac{\boldsymbol{\delta} \boldsymbol{V}}{\boldsymbol{\delta} \boldsymbol{x}} \) and on equipotential
surface potential \( V \) is constant.
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 not correct but Reason is correct
Subject: Maths
From a circular sheet of paper with
radius \( 20 \mathrm{cm}, 4 \) circles of radius \( 5 \mathrm{cm} \)
each are cut out. Find the ratio of the
uncut to the cut portions.
\( \mathbf{A} \cdot 1: 3 \)
B. 4: 1
\( \mathbf{c} \cdot 3: 1 \)
D. 4: 3
Subject: Chemistry
The molality \( (\mathrm{m}) \) of each ion \( \left(\mathrm{N} \boldsymbol{H}_{4}^{+} \) and \right.
\( \left.C l^{-}\right), \) respectively, present in the
aqueous solution of \( 2 M N H_{4} C l \)
assuming \( 100 \% \) dissociation according to given reaction is,
\( N H_{4} C l(a q) \rightarrow N H_{4}^{+}(a q)+C l^{-}(a q) \)
Given that density of solution \( =3.107 \)
\( \mathrm{g} / \mathrm{ml} \)
A \( .0 .45 \mathrm{m}, 0.67 \mathrm{m} \)
в. \( 0.67 \mathrm{m}, 0.45 \mathrm{m} \)
\( c .0 .67 m, 0.67 m \)
\( m \)
D. \( 0.45 \mathrm{m}, 0.45 \mathrm{m} \)
Subject: Physics
Two objects that are moving along an xy-plane on a frictionless floor collide.
Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision.
What are the mission values \( (a, b) \)
After Before
collision collision
Object \( \mathrm{P}_{x} \) \( P_{x} \)
-2
A. 10,11
B. 1,11
\( c \cdot 5,7 \)
\( D \cdot 6,4 \)
Subject: Physics
The displacement of a particle executing simple harmonic motion is
given by \( \boldsymbol{y}=\boldsymbol{A}_{0}+\boldsymbol{A} \sin \omega \boldsymbol{t}+\boldsymbol{B} \cos \boldsymbol{\omega} \boldsymbol{t} \)
Then the amplitude of its oscillation is given by :
\( \mathbf{A} \cdot A_{0}+\sqrt{A^{2}+B^{2}} \)
B. \( \sqrt{A^{2}+B^{2}} \)
c. \( \sqrt{A_{0}^{2}+(A+B)^{2}} \)
D. \( A+B \)
Subject: Chemistry
Calculate the energy required for the
process:
\( \boldsymbol{H} \boldsymbol{e}^{+}(\boldsymbol{g}) \rightarrow \boldsymbol{H} \boldsymbol{e}^{2+}(\boldsymbol{g})+\boldsymbol{e}^{-} \)
If the ionisation energy for the H atom in the ground state is \( 2.18 \times 10^{-18} \)
J/atom.
Subject: Maths
Solve the following equations:
\( y+\sqrt{x^{2}-1}=2 \)
\( \sqrt{\boldsymbol{x}+\mathbf{1}}-\sqrt{\boldsymbol{x}-\mathbf{1}}=\sqrt{\boldsymbol{y}} \)
This question has multiple correct options
A. \( x=2 ; y=5 \)
в. \( x=1 ; y=2 \)
c. \( _{x}=\frac{5}{3} ; \frac{2}{3} \)
D. \( x=3 ; y=3 \)
Subject: Physics
A portion of a conductive wire is bent in
the form of a semicircle of radius r as
shown below in figure. At the centre of semicircle, the magnetic induction will
be:
A. zero
B. inifinite
C \( \cdot \frac{\mu_{0}}{4 \pi} \cdot \frac{\pi i}{2 r} \) tesla
D. \( \frac{\mu_{0}}{4 \pi} \cdot \frac{\pi i}{r} \) tesla
Subject: Maths
If \( a=\frac{1}{3-2 \sqrt{2}}, b=\frac{1}{3+2 \sqrt{2}}, \) then the
value of \( a^{3}+b^{3} \) is
A \( \cdot 194 \)
в. 196
\( c \cdot 198 \)
D. 200
Subject: Chemistry
Which of the following reactions does not involve oxidation-reduction?
This question has multiple correct options
A \( \cdot 2 R b+2 H_{2} O \rightarrow 2 R b O H+H_{2} \)
в. \( 2 C u I_{2} \rightarrow 2 C u I+I_{2} \)
c. \( N H_{4} C l+N a O H \rightarrow N a C l+N H_{3}+H_{2} O \)
D. \( _{4 K C N}+F e(C N)_{2} \rightarrow K_{4}\left[F e(C N)_{6}\right] \)
Subject: Physics
A sinusoidal voltage \( V=200 \sin 314 t \) is
applied to a \( 10 \Omega \) resistor. Find the peak
voltage
\( \mathbf{A} \cdot 200 V \)
B. \( 400 \mathrm{V} \)
\( \mathbf{c} .600 V \)
D. \( 800 \mathrm{V} \)
Subject: Physics
(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium
with speed of light in vacuum.
(b) The refractive indices of water and
glass with respect to air are \( 4 / 3 \) and \( 3 / 2 \) respectively. If the speed of light in
glass is \( 2 \times 10^{8} m s^{-1}, \) find the speed of
light in (i) air, (ii) water.
Subject: Physics
If universal gravitational constant \( (G) \) speed of light \( (c), \) and time (t) are base units then the dimensional formula of
mass can be represented as?
A \( \cdot\left[G^{1} c^{3} t^{1}\right] \)
\( \mathbf{B} \cdot\left[G^{-1} c^{3} t^{1}\right] \)
C. \( \left[G^{-1} c^{-2} t^{-1}\right] \)
\( \mathbf{D} \cdot\left[G^{1} c^{-3} t^{-1}\right] \)
Subject: Physics
An object A is moving with \( 5 \mathrm{m} / \mathrm{s} \) and \( \mathrm{B} \) is moving with \( 20 \mathrm{m} / \mathrm{s} \) in the same direction. (positive \( \mathbf{x} \) -axis). Find velocity of B with respect to A.
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot-15 m / s \)
D. -20 m/s
Subject: Maths
The cosine of the angle \( A \) of the triangle with vertices
\( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{6}, \mathbf{1 1}, \mathbf{2}), \boldsymbol{C}(\mathbf{1}, \mathbf{2}, \boldsymbol{6}) \) is
\( ^{\text {A }} \cdot \frac{63}{65} \)
в. \( \frac{36}{65} \)
c. \( \frac{16}{65} \)
D. \( \frac{13}{64} \)
Subject: Maths
Find the mean deviation about the
median for the following continuous distribution:
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 20- & 30- \\ \text { obtained } & 10 & 20 & 30 & 40\end{array} \)
No. of
body 6
\( 8 \quad 14 \)
Subject: Maths
Find the intersection of \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) and
represent it by Venn diagram:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{5}, \boldsymbol{4}, \mathbf{7}\} \)
Subject: Physics
Two particles \( A \) and \( B \) are placed as
shown in Fig. A.12. The particle \( A \), on the top of tower, is projected horizontally with a velocity \( u \) and particle \( B \) is projected along the surface towards the
tower, simultaneously. If both particles
meet each other, then the speed of projection of particle \( \boldsymbol{B} \) is [ignore any friction]
A \( \cdot d \sqrt{\frac{g}{2 H}} u \)
в. \( d \sqrt{\frac{g}{2 H}} \)
\( c \)
\[
d \sqrt{\frac{g}{2 H}}-u
\]
D.
Subject: Maths
Area bounded by the curve \( y^{2}(2 a- \)
\( x)=x^{3} \) and the line \( x=2 a \) is:
\( A \cdot 3 \pi a^{2} \)
B. \( 2 \pi \)
c. \( 2 \pi a \)
D. \( 3 \pi \)
Subject: Chemistry
Which is not a redox reaction?
A. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
в. \( 2 B a O_{+} O_{2} \rightarrow 2 B a O_{2} \)
c. \( 4 K C l O_{3} \rightarrow 4 K C l O_{2}+2 O_{2} \)
D. \( S O_{2}+2 H_{2} S \rightarrow 2 H_{2} O+3 S \)
Subject: Maths
Evaluate :
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}+\boldsymbol{3}} \)
Subject: Chemistry
For a system \( C(s)+O_{2}(g)=C O_{2}(g) \)
which of the following is correct?
\( \mathbf{A} \cdot \Delta H=\triangle E \)
в. \( \triangle H>\triangle E \)
c. \( \triangle H<\triangle E \)
D. \( \triangle H=0 \)
Subject: Chemistry
With respect to the figure which of the
following statement is correct?
\( A \cdot E_{A} \) for forward reaction is \( E_{A}-E_{B} \)
B. \( E_{A} \) for forward reaction is \( E_{C}-E_{A} \)
\( \mathrm{c} \cdot E_{A} \) for reverse reaction is greater than \( E_{A} \) for forward reaction
D. \( E_{A} \) for forward reaction is greater than \( E_{A} \) for
backward reaction
Subject: Maths
The maximum value of \( a^{2} b^{3} c^{4} \) subject
\( \operatorname{to} a+b+c=18 \) is
\( \mathbf{A} \cdot 4^{2} 6^{3} 8^{4} \)
В \( \cdot 4^{3} 6^{2} 8^{4} \)
c. \( 4^{4} 6^{2} 8^{3} \)
D \( \cdot 4^{2} 6^{4} 8^{3} \)
Subject: Maths
Let \( f(x) \) satisfy the requirements of Lagrange's mean value theorem in [0,1] \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \leq \mathbf{1}-\boldsymbol{x}, \forall \boldsymbol{x} \boldsymbol{\epsilon}(\mathbf{0}, \mathbf{1}) \)
then
A. \( f(x) \geq x \)
в. \( |f(x)| \geq 1 \)
C \( . f(x) \leq x(1-x) \)
D. \( f(x) \leq \frac{1}{4} \)
Subject: Chemistry
Identify A to in the following sequence of reaction. \( \boldsymbol{N} \boldsymbol{a}+\boldsymbol{O}_{2} \rightarrow(\boldsymbol{A}) \stackrel{\boldsymbol{H} C l}{\rightarrow} \)
\( (B) \frac{e t h e r}{H^{+} / K_{2} C r_{2} O_{7}} C \)
\( C \) is forms blue colour in ethereal
solution.
A \( \cdot \) A: \( N a_{2} O_{2}, \) B \( : H_{2} O, c: C r O_{3} \)
B. A: \( N a O_{2}, \) В \( : H_{2} O_{2}, \mathrm{C}: C r_{2} O_{7} \)
c. \( A: N a_{2} O_{2}, B: H_{2} O_{2}, c: C r O_{3} \)
D. A: \( N a O, \) В \( : H_{2} O, c: C r O_{3} \)
Subject: Physics
If for hydrogen \( S_{p}-S_{v}=a \) and for
oxygen, \( S_{p}-S_{v}=b \) where \( S_{p} \) and \( S_{v} \)
are specific heat at constant pressure and at constant volume, then
\( \mathbf{A} \cdot a=b \)
в. \( a=16 b \)
c. \( b=16 a \)
D. \( a \) and \( b \) are not pressures
Subject: Chemistry
For which of the following reactions,
\( \Delta H=\Delta E+2 R T ? \)
A \( \cdot N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
B. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) \)
C \( . N H_{4} H S(s) \rightarrow N H_{3}(g)+H_{2} S(g) \)
D. \( P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)
Subject: Maths
The Geometric mean of \( 4,4^{2}, 4^{3}, \cdots, 4^{n} \)
is
A. \( 2^{\frac{2}{2}} \)
\( \frac{2}{2} \)
B. \( 2^{\frac{n-1}{2}} \)
c. \( 4^{n+1} \)
D. \( 2^{n+1} \)
Subject: Biology
What is the basic difference between
binary fission and budding?
A. In budding, the parents identity is lost, while in binary fission, it is maintained.
B. In binary fission, the parents identity is lost, while it is maintained in budding
C. There is a fusion of daughter cells in binary fission while in budding, genetically non-identical daughter cells are produced.
D. In binary fission, two dissimilar individuals (daughter cells) are formed while in budding, daughter and parent cells are similar.
Subject: Chemistry
Suppose an electron is attracted towards the origin by a force \( \frac{\mathbf{k}}{\mathbf{r}} \) where \( \mathbf{k}^{\prime} \) is a constant and \( \mathbf{r}^{\prime} \) is the distance of
the electron from the origin. By applying Bohr model to this system, the radius of the \( n^{\text {th }} \) orbital of the electron is found to
be \( \mathbf{r}_{\mathbf{n}}^{\text {' and the kinetic energy of the }} \)
electron to be' \( \mathbf{T}_{\mathbf{n}} . \) Then which of the
following is true?
A \( \cdot \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n} \)
B. \( \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^{2} \)
\( c \cdot \mathrm{T}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^{2}}, \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^{2} \)
D. \( T_{n} \) independent of \( n, r_{n} \propto n \)
Subject: Chemistry
The oxidation potential of hydrogen
electrode at \( \mathrm{pH}=10 \) and \( \mathrm{P}_{H_{2}}=1 \) atm is
A . \( 0.51 V \)
в. \( 0.00 \mathrm{V} \)
\( \mathbf{c} .+0.59 V \)
D. \( -0.059 V \)
Subject: Maths
If
\( \mathbf{3}\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{z} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{cc}\boldsymbol{x} & \boldsymbol{6} \\ -\mathbf{1} & \boldsymbol{2} \boldsymbol{w}\end{array}\right]+ \)
\( \left[\begin{array}{cc}\mathbf{4} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{z}+\boldsymbol{w} & \mathbf{3}\end{array}\right], \) find the values of
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \& \boldsymbol{w} \)
Subject: Maths
If \( \mathbf{x} \in \mathbf{R} \) and the numbers \( \mathbf{5}^{(1-x)}+\mathbf{5}^{(x+1)} \)
a/2, \( \left(25^{x}+25^{-x}\right) \) form an A. P. then a
must lie in the interval
\( A \cdot[12, \infty] \)
в. [-5,5]
D. \( [8, \infty] \)
Subject: Physics
Two cells of unequal e.m.fs. \( E_{1} \) and \( E_{2} \)
and internal resistance \( r_{1} \) and \( r_{2} \) are
joined as shown. \( V_{A} \) and \( V_{B} \) are the
potentials at \( A \) and \( B \) respectively:
This question has multiple correct options
A. one cell will continuously supply energy to the other
B. the potential difference across both the cells will be equal
c. the potential difference across one cell will be greater than its e.m.f.
\( V_{A}-V_{B}=\frac{\left(E_{1} R_{2}+E_{2} R_{1}\right)}{\left(r_{1}+r_{2}\right)} \)
Subject: Physics
A body performs harmonic oscillations along the straight line \( A B C D E \) with \( C \) as a mid-point. of \( A E . \) Its kinetic
energies at \( B \) and \( D \) are each onefourth of its maximum value. If \( \boldsymbol{A} \boldsymbol{E}= \)
\( 2 R, \) the distance between \( B \) and \( D \) is:
Subject: Maths
A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}4 \boldsymbol{x}^{2}-\mathbf{1} ; & -\mathbf{3} \leq \boldsymbol{x}<\mathbf{2} \\ \mathbf{3} \boldsymbol{x}-\mathbf{2} ; & \mathbf{2} \leq \boldsymbol{x} \leq \mathbf{4} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} ; & \mathbf{4}<\boldsymbol{x} \leq \mathbf{6}\end{array}\right. \)
Find:
\( \frac{\boldsymbol{f}(\boldsymbol{3})+\boldsymbol{f}(-1)}{2 \boldsymbol{f}(\boldsymbol{6})-\boldsymbol{f}(1)} \)
Subject: Physics
A body is projected with an initial
velocity \( 20 \mathrm{m} / \mathrm{s} \) at \( 60^{\circ} \) to the horizontal. Its initial velocity vector is
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
B. \( 10 \sqrt{3 i}+10 j \)
c. \( 10 i+10 \sqrt{3} j \)
D. \( 5 i+5 \sqrt{3} j \)
Subject: Physics
A triangle has sides of length 13,30 and
\( 37 . \) If the radius of the inscribed circle is
\( \frac{p}{q}(\text { where } p \text { and } q \text { are coprime }) \),then the value of \( \boldsymbol{q}^{\boldsymbol{p}+\mathbf{3}} \) is
A . 2048
в. 4096
c. 1024
D. 512
Subject: Physics
A light of wavelength \( \lambda \) is incident on
a metal sheet of work function \( \phi=2 e V \)
The wavelength \( \lambda \) varies with time as
\( \lambda=3000+40 t, \) where \( \lambda \) is in and \( t \) is in
second. The power incident on metal sheet is constant at 100 W. This signal is switched on and off for time intervals
of 2 minutes and 1 minute respectively.
Each time the signal is switched on, the
\( \lambda \) start from an initial value of \( 3000 . \) The
metal plate is grounded and electron clouding is negligible. The efficiency of photoemission is \( 1 \%(h c=12400 e V) \)
The time after which photo-emission will stop is
A. 79 s
B. 80 s
c. \( 81 \mathrm{s} \)
D. 78 s
Subject: Biology
Assertion
Dolly was a female domestic sheep, and the first mammal cloned by somatic
cell nuclear transfer
Reason
Cell nucleus from an adult somatic cell
is transferred into an unfertilized oocyte
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
In circular motion if \( \bar{v} \) is velocity vector,
\( \bar{a} \) is acceleration vector, \( \bar{r} \) is
instantaneous position vector, \( \bar{p} \) is momentum vector and \( \bar{\omega} \) is angular velocity of particle, then:
This question has multiple correct options
A \( . \bar{v}, \bar{\omega}, \bar{r} \) are mutually perpendicular
B . \( \bar{p}, \bar{v}, \bar{\omega} \) are mutually perpendicular
c. \( \bar{r} \times \bar{v}=0 \) and \( \bar{r} \times \bar{\omega}=0 \)
D. \( \bar{r} . \bar{v}=0 \) and \( \bar{r} . \bar{\omega}=0 \)
Subject: Chemistry
In which of the following cases, change of colour can be an indication of extent
of the reaction?
\( ^{\mathrm{A}} \cdot_{S O_{2}(g)+\frac{1}{2}} O_{2}(g) \leftrightharpoons S O_{3}(g) \)
B. \( N_{2}(g)+3 H_{2}(g) \leftrightharpoons 2 N H_{3}(g) \)
c. \( 2 H I(g) \leftrightharpoons H_{2}(g)+I_{2}(g) \)
D. \( C(\text { graphite })+C O_{2}(g) \leftrightharpoons 2 C O(g) \)
Subject: Chemistry
The average velocity of an ideal gas
molecule at \( 27^{\circ} C \) is \( 0.3 m / \) sec. The
average velocity at \( 927^{\circ} \mathrm{C} \) will be:
A. \( 0.6 m / s e c \)
в. \( 0.3 m / \)sec
\( \mathbf{c} \cdot 0.9 m / \)sec
D. \( 3.0 m / s e c \)
Subject: Physics
Two particles are projected under
gravity with speed \( 4 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \) simultaneously from same point and at
angles \( 53^{\circ} \) and \( 37^{\circ} \) with the horizontal
surface respectively as shown in figure.
Then:
This question has multiple correct options
A. Their relative velocity is along vertical direction.
B. Their relative acceleration is non-zero and it is along vertical direction.
C. They will hit the surface simultaneously
D. Their relative velocity is constant and has magnitude \( 1.4 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A body is sliding down an inclined plane (fixed plane) under its own weight at constant speed.If the inclination of the
plane to the horizontal is \( 30^{\circ} . \) the angle
of friction is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 15^{\circ} \)
Subject: Physics
Find the moment of inertia of a hollow
sphere about a chord that is at a distance of \( 3 \mathrm{m} \) from the centre of the
sphere. The radius of the sphere is \( 5 \mathrm{m} \) and mass \( =10 \mathrm{kg} \)
A. \( 257 k g-m^{2} \)
B . \( 57 k g-m^{2} \)
c. \( 27 k g-m^{2} \)
D. \( 157 k g-m^{2} \)
Subject: Maths
If \( 3 \vec{a}+4 \vec{b}-7 \vec{c}=0 \) then the ratio in
which \( C(\vec{c}) \) divides the join of \( \boldsymbol{A}(\overrightarrow{\boldsymbol{a}}) \) and \( B(\vec{b}) \) is
A .1: 2
B. 2: 3
\( c \cdot 3: 2 \)
D. 4: 3
Subject: Maths
Which of the following pairs is pair of interior formed by two parallel lines and on the same side of the transversal?
A \( \cdot 30^{\circ}, 60^{\circ} \)
\( ^{0}, 66,6^{\circ} \)
В. \( 30^{0}, 150^{0} \)
c. \( 60^{\circ}, 130^{\circ} \)
D. \( 50^{\circ}, 120^{0} \)
Subject: Chemistry
Baking powder used to make a cake is a
mixture of \( \operatorname{starch}, N a H C O_{3} \) and
\( \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} . \) The function of
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) is:
A \( \cdot \) to slow down the release of \( C O_{2} \)
B. being acidic in nature and give \( C O_{2} \) when moistened with \( N a H C O_{3} \)
\( c . \) to act as a fille
D. none of these
Subject: Chemistry
Which of the following will result in the
formation of an ether?
This question has multiple correct options
A \( \cdot\left(C H_{3}\right)_{3} C \bar{O} \stackrel{+}{N} a+C H_{3} C H_{2} B r \longrightarrow \)
В \( \cdot\left(C H_{3}\right)_{3} C B r+C_{2} H_{5} \bar{O} \dot{N} a \longrightarrow \)
c. \( C_{6} H_{5} \) ONa \( +C H_{3} B r \longrightarrow \)
D. \( C_{6} H_{5} B r+C H_{3} \bar{O}_{N a} \rightarrow \)
Subject: Maths
If matrix \( \mathbf{A}=[\boldsymbol{a} \boldsymbol{i} \boldsymbol{j}]_{3 \times 2}, \) and \( \boldsymbol{a} \boldsymbol{i} \boldsymbol{j}=(\boldsymbol{3} \boldsymbol{i}- \)
\( 2 j)^{2}, \) then find the matrix \( A \)