AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Complete the following statements with an appropriate word /term be filled in
the blank space(s).

The equivalent capacitance \( C \) for the series combination of three
capacitance \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( \frac{1}{C}= \)
A. \( C_{1}+C_{2}+C_{3} \)
\( ^{\text {В }} \cdot\left(\frac{1}{C_{1}+C_{2}+C_{3}}\right) \)
\( \left(\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}}\right) \)
D \( \cdot\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\right) \)
Subject: Chemistry
\( \boldsymbol{S b F}_{5} \) reacts with \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) and \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) to
form ionic compounds \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}\right]^{-} \boldsymbol{a n d}\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}^{-}\right] \)
The geometry of \( X e F_{3}^{+} \) ion and \( X e F_{5}^{+} \) ion, respectively, is :
A. sqare pyramidal, T-shaped
B. bent T-shaped, square pyramidal
c. see-saw, square pyramidal
D. square pyramidal, see-saw
Subject: Biology
Select the correct matches.
(a) Nitrosomonas - nitrite to nitrate
(b) Thiobacillus - denitrification
(c) Nostoc - free-living nitrogen fixer
(d) Azotobacter - anaerobic nitrogen fixer
A. a and
B. b and c
\( c . \) a and \( c \)
D. c and d
E. b and d
Subject: Physics
The imaging drum of a photocopier is positively charged to attract negatively
charged particles of toner. Near the surface of the drum, its electric field
has magnitude \( 1.4 \times 10^{5} N C^{-1} . \) A toner
particle is to be attached to the drum with a force that is 10 times the weight of the particle. Assume toner particles are made of carbon \( _{6}^{12} C \) Find charge to mass ratio of the charged toner particle :
A \( \cdot 7.0 \times 10^{-4} \mathrm{Ckg}^{-1} \)
В. \( 7.0 \times 10^{-3} \mathrm{Ckg}^{-1} \)
C. \( 7.0 \times 10^{-5} \mathrm{Ckg}^{-1} \)
D. \( 7.0 \times 10^{-6} \mathrm{Ckg}^{-1} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{D}-\boldsymbol{A} \)
Subject: Maths
A balloon is pumped at the rate of a cm \( ^{3} \) /minute. The rate of increase of its
surface area when the radius is \( b \mathrm{cm} \), is
A \( \cdot \frac{2 a^{2}}{b^{4}} \mathrm{cm}^{2} / \mathrm{min} \)
B. \( \frac{a}{2 b} \mathrm{cm}^{2} / \mathrm{min} \)
c. \( \frac{2 a}{b} \mathrm{cm}^{2} / \mathrm{min} \)
D. none of these
Subject: Maths
The mean deviation about median from
the data
\( \mathbf{3 4 0}, \mathbf{1 5 0}, \mathbf{2 1 0}, \mathbf{2 4 0}, \mathbf{3 0 0}, \mathbf{3 1 0}, \mathbf{3 2 0} \) is
\( \mathbf{A} .50 \)
B. 52.8
c. 55
D. 45
Subject: Physics
Two wires of the same material but of
different diameters carry the same current I. If the ratio of their diameters
is \( 2: 1, \) then the corresponding ratio of their mean drift velocities will be
\( A \cdot 4: \)
B. 1: 1
\( c \cdot 1: 2 \)
\( D \cdot 1: 4 \)
Subject: Maths
The plane \( a x+b y+c z+(-3)=0 \)
meet the co-ordinate axes in \( A, B, C \)
The centroid of the triangle is
B \( \cdot\left(\frac{3}{a} \cdot \frac{3}{b}, \frac{3}{c}\right) \)
c. \( \left(\frac{a}{3} \cdot \frac{b}{3}, \frac{c}{3}\right) \)
D. \( \left(\frac{1}{a} \cdot \frac{1}{b}, \frac{1}{c}\right) \)
Subject: Chemistry
Assertion
Propyne is more reactive than propene
towards electrophilic addition of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
Reason

Propyne has greator electron density avaliable for electrophile due to two pibonds, therefore more electrophilic
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
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Subject: Maths
Using the property of determinants and with out expanding prove that \( \left|\begin{array}{lll}\boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} \\ \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}\end{array}\right|=\mathbf{0} \)
Subject: Maths
The length of the latus rectum of the \( \operatorname{conic} \frac{5}{r}=3-2 \cos \theta \) is
A \( \cdot \frac{3}{5} \)
B. \( \frac{5}{3} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{10}{3} \)
Subject: Maths
\( f\left(\begin{array}{ccc}-1 & -3 & -3 \\ 3 & 1 & -3 \\ 3 & -3 & 1\end{array}\right] \) then adj \( (A) \) is
A.
\[
=4\left[\begin{array}{ccc}-2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & 3 & 2\end{array}\right]
\]
B. \( \quad\left[\begin{array}{ccc}-2 & 3 & 3 \\ 3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right] \)
C.
\[
=4\left[\begin{array}{ccc}-2 & -3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right]
\]
D.
\[
=4\left[\begin{array}{ccc}-2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2\end{array}\right]
\]
Subject: Physics
A student very cautiously traces the
path of a ray through a glass slab for
different values of the angle of
incidence \( (\angle i) . \) He then measures the
corresponding values of the angle of
refraction \( (\angle r) \) and the angle of
emergence \( (\angle e) \) for every value of the
angle of incidence. On analysing these
measurements of angles, his conclusion would be
A. \( \angle i>\angle r>\angle e \)
B. \( \angle i=\angle e>\angle r \)
\( \mathbf{c} \cdot \angle i, \angle r, \angle e \)
D. \( \angle i=\angle e, \angle r \)
Subject: Chemistry
Match List-I (species) with List-II
(Hybrid orbitals used by the central atom in their formation) and select the
correct answer:
List-I
\( s p^{3} \) \( N i(C N)_{5}^{3-} \)
(A) 's
(B) \( \mathrm{CuCl}_{5}^{3-} \)
(2) \( d s p^{2} \)
(c)
(3) \( s p^{3} d_{z^{2}} \) \( A u C l_{4}^{-} \) ( )
(D) \( \mathrm{ClO}_{4}^{-} \) ) \( d_{x^{2}-y^{2}} s p^{3} \)
\( ^{3} \) (4)
A \( \cdot(A)-1,(B)-3,(C)-2,(D)-4 \)
B. \( (A)-3,(B)-4,(C)-2,(D)-1 \)
c. \( (A)-4,(B)-2,(C)-1,(D)-3 \)
D. \( (A)-4,(B)-3,(C)-2,(D)-1 \)
Subject: Chemistry
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{P b C l}_{2} \) is \( \mathbf{1 0}^{-13} \cdot\left[\boldsymbol{P b}^{2+}\right] \) in solution
prepared by mixing \( 100 m L \) of \( 0.1 M \)
\( P b\left(N O_{3}\right)_{2} \) and \( 1 m L \) of \( 1 M H C l \) will
be:
\( \mathbf{A} \cdot\left[P b^{2+}\right]=9.4 \times 10^{-2} \) mollitre \( ^{-1} \)
B . \( \left[P b^{2+}\right]=8.4 \times 10^{-2} \) mollitre \( ^{-1} \)
C \( \cdot\left[P b^{2+}\right]=9.0 \times 10^{-2} \) mollitre \( ^{-1} \)
D \( \cdot\left[P b^{2+}\right]=9.2 \times 10^{-2} \) mollitre \( ^{-1} \)
Subject: Physics
A uniform rod \( A B \) of length \( l \) and mass
\( m \) hangs from point \( A \) in a car moving
with velocity \( v_{0} \) on an inclined plane as
shown in the figure. The rod can rotate
in vertical plane about the axis at point
A. If the car suddenly stops, the angular
speed with which the rod starts rotating
is :
A \( \cdot \frac{3}{2} \frac{v_{0}}{l} \cos \theta \)
B. \( \frac{v_{0}}{2} \frac{\cos \theta}{l} \)
c. \( \frac{3}{2} \frac{v_{0}}{l} \sin \theta \)
\( D \)
Subject: Chemistry
The hybridization of carbon atoms in \( C \) -
C single bond of \( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
is :
B. \( s p^{2}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p^{2} \)
D. \( s p^{3}-s p \)
Subject: Physics
The magnetic field at the centre of a circular loop of area \( A \) is \( B \). The
magnetic moment of the loop is
A \( \cdot \frac{B A^{2}}{\mu_{0} \pi} \)
B. \( \frac{B A \sqrt{A}}{\mu} \)
\( ^{\mathrm{c}} \cdot \frac{B A \sqrt{A}}{\mu_{0} \pi} \)
D. \( \frac{2 B A \sqrt{A}}{\mu_{0} \sqrt{\pi}} \)
Subject: Chemistry
Select the intramolecular redox
reaction(s) among the following.
This question has multiple correct options
A \( .2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
B. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)
\( c \cdot C l_{2} \rightarrow C l^{-}+C l O_{3} \)
D. \( N H_{4} N O_{2} \rightarrow N_{2}+2 H_{2} O \)
Subject: Chemistry
For the reaction \( : 2 N O C l(g) \longrightarrow \)
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) The equilibrium
constant at \( 400 \mathrm{K}, \) if \( \Delta \boldsymbol{H}^{o}= \)
\( 77.18 k J m o l^{-1} \) and \( \Delta S^{o}= \)
\( \mathbf{0 . 1 2 2 k J K}^{-1} \mathbf{m o l}^{-\mathbf{1}} \mathbf{i s} \)
A \( \cdot 1.97 \times 10^{-3} \)
В. \( 1.97 \times 10^{-2} \)
c. \( 1.97 \times 10^{-4} \)
D. \( 1.97 \times 10^{-1} \)
Subject: Physics
A ray of light travelling in water is
incident on its surface open to air. The
angle of incidence \( \theta \), which is less than
the critical angle. Then there will be:
A. only a reflected ray and no refracted ray
B. only a refracted ray and no reflected ray
C . a reflected ray and a refracted ray and the angle between them would be less than \( 180^{\circ}-2 \theta \)
D. a reflected ray and a refracted ray and the angle between them would be greater than \( 180^{\circ}-2 \theta \)
Subject: Chemistry
What is \( \left[\boldsymbol{S O}_{4}^{2-}\right] \) when first solid gets precipitated?
A \( \cdot\left[S O_{4}^{2-}\right]=1.0 \times 10^{-8} M \)
B . \( \left[S O_{4}^{2-}\right]=1.1 \times 10^{-8} M \)
\( \mathbf{C} \cdot\left[S O_{4}^{2-}\right]=1.2 \times 10^{-8} M \)
D. None of these
Subject: Physics
A small steel ball falls through a syrup
with a speed of \( 10 \mathrm{cm} \mathrm{s}^{-1} . \) If the steel ball is given an upward force equal to its effective weight, it would move upward with a speed of
A \( \cdot 10 \mathrm{cm} \mathrm{s}^{-1} \)
B . \( 20 \mathrm{cm} \mathrm{s}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{cm} \mathrm{s}^{-1} \)
D. \( 10 \sqrt{3} \mathrm{cms}^{-1} \)
Subject: Physics
For a moving particle doing round trip which of the following options may be
correct? Here, \( V_{a v} \) is average velocity
and \( u_{a v} \) the average speed.
A \( \cdot\left|V_{a v}\right|<u_{a v} \)
В . \( \left|V_{a v}\right|>u_{a v} \)
C \( \cdot V_{a v}=0 \) but \( u_{a v} \neq 0 \)
D. \( V_{v v} \neq 0 \) but \( u_{a v}=0 \)
Subject: Physics
A charge q is situated at the centre of a square of side d. The electric field
intensity at the midpoint of a side is \( \mathrm{E}_{1} \)
and at one corner of the square is \( \mathrm{E}_{2} \)
Then, the ratio of \( E_{1} / E_{2} \) is :
A . 0.5
в. 0.7
c. 1
D.
Subject: Physics
The ends of a circular coil of radius \( r \)
and number of turns \( n \) is connected to
the two terminals of a cell. The
magnetic field at the centre of the coil is \( B \). If the number of turns be made \( 2 n \)
keeping the radius same, the magnetic field at the centre of the coil will be:
A. \( B \)
в. \( 2 B \)
\( c .3 B \)
D. \( 4 B \)
Subject: Biology
Study the following statements about chordate.
A) Columella auris present in the middle ear of amphibians is modified hyomandibula of fishes.
B) Reptiles lay cledoic egg.
C) Sphenodon is a connecting link between amphibians and reptiles.
D) Panthera tigris is an extinct animal of
India.
From the above identify the incorrect
statement or statements.
\( A \cdot A, C \)
B. Only A
c. only D
D. B,
Subject: Maths
The value of the determinant
\[
\left|\begin{array}{ccc}
\mathbf{1} & \cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{c o s} \boldsymbol{\alpha} \\
\cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{1} & \cos \beta \\
\cos \boldsymbol{\alpha} & \cos \beta & \mathbf{1}
\end{array}\right|
\]
A \( \cdot \alpha^{2}+\beta^{2} \)
B \( \cdot \alpha^{2}-\beta^{2} \)
\( c .1 \)
\( D \)
Subject: Maths
Solve \( \int x^{3} \log x d x \)
A \( \frac{x^{4} \log x}{4}+C \)
B. \( I=\frac{x^{4}}{4} \log x-\frac{x^{4}}{16}+C \)
c. \( \frac{1}{8}\left[x^{4} \log x-4 x^{2}\right]+C \)
D \( \cdot \frac{1}{16}\left[4 x^{4} \log x+x^{4}\right]+C \)
Subject: Physics
toppr OG
Q Type your question_
sphere has the same amount of charge.
Assume each pair is isolated.

For which pair is there a point between
them on the dotted line where the
electric field magnitude is zero and a
point between them on the dotted line
where the electric potential is zero?
A . 1
B. 2
\( c \cdot 3 \)
\( \mathbf{D} \cdot 4 \)
E. None of the pairs has points that meet these conditions
Subject: Chemistry
The molar conductivities \( \wedge^{0}_{N a} O A c \) and
\( \wedge^{0}_{H C l} \) at infinite dilution in water at \( 25^{0} \)
\( \mathrm{C} \) are 91.0 and \( 426.2 \mathrm{Scm}^{2} / \mathrm{mol} \)
respectively. To calculate \( \wedge^{0}_{H O A c} \), the additional
value required is :
\( \mathbf{A} \cdot \wedge^{0} H_{2} O \)
B . \( \wedge^{0} \)кСl
c. \( \wedge_{N a O H}^{0} \)
D. \( \wedge^{0} \)Nacl
Subject: Physics
A molecule of gas in a container hits one wall (1) normally and rebounds back. It suffers no collision and hits the
opposite wall (2) which is at an angle of
\( 30^{\circ} \) with wall 1
Assuming the collisions to be elastic
and the small collision time to be the
same for both the walls, the magnitude
of average force by wall 2. \( \left(F_{2}\right) \) provided the molecule during collision satisfy
\( \mathbf{A} \cdot F_{1}>F_{2} \)
B. \( F_{1}<F_{2} \)
C \( \cdot F_{1}=F_{2}, \) both non-zero
D. \( F_{1}=F_{2}=0 \)
Subject: Chemistry
The approximate concentration of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in perhydrol is :
A. 30 gm/litre
B. \( 300 \mathrm{gm} / \mathrm{ml} \)
c. \( 10 \mathrm{gm} / \) /litre
D. 300 gm/litre
Subject: Chemistry
Which of the following complex ions, which is diamagnetic in nature?
A \( \cdot\left[C c F_{6}\right]^{3-} \)
B. \( \left[N i C l_{4}\right]^{2-} \)
c. \( \left[N i(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[C u C l_{2}\right]^{2} \)
Subject: Chemistry
The increasing order of the strength of hydrogen bond in the following mentioned linkages is:
(i) \( \boldsymbol{O} \boldsymbol{H}-\boldsymbol{S} \)
(II) \( \boldsymbol{S} \boldsymbol{H}-\boldsymbol{O} \)
(iii) \( \boldsymbol{F} \boldsymbol{H}-\boldsymbol{F} \)
(iv) \( \boldsymbol{F H}-\boldsymbol{O} \)
\( A \cdot(\text { i) }<(\text { ii })<(\text { iv })<(\text { iii }) \)
B. (ii) < (i) < (iv) < (iii)
c. (i) \( < \) (ii) \( < \) (iii) \( < \) (iv)
D. (ii) < (i) < (iii) < (iv)
Subject: Physics
A wire elongates by 1 m \( m \) when a load
\( W \) is hung from it. If the wire goes over
a pulley and the two weights \( W \), each are hung at the two ends, then the elongation of the wire will be:
A. \( 0.5 m m \)
в. \( 1 \mathrm{mm} \)
\( \mathbf{c} \cdot 2 m m \)
D. \( 4 m m \)
Subject: Chemistry
A solution of \( (R)-2- \) iodobutane,
\( [\alpha]=15.9^{\circ} \) in acetone is treated with
radioactive iodied, until 1.0\% of
iodobutane contain radioactive iodine, the specific rotation of recovered
iodobutane is found to be \( -15.58^{\circ} \) which statement is correct about above information?
This question has multiple correct options
A. It has optical purity \( 96 \% \)
B. \% of R in solution is \( 99 \% \)
c. Racemic mixture is \( 2 \% \)
D. Final solution is dextrorotatory
Subject: Chemistry
In the reaction \( \rightarrow \)
\( M N O_{2}+4 H C L \rightarrow M n C l_{2}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{l}_{2} \)
(a) name the compound (i) oxidised
(ii) reduced
(b) define oxidation of reduction on its
basis.
Subject: Physics
single Correct Answer Type
f a stone has to hit at a point which is
at a distance \( d \) away and at a height \( h \)
above the point from where the stone starts, then what is the value of initial
speed \( u \) if the stone is thrown at an
angle \( \theta ? \)
A \( \cdot \frac{g}{\cos \theta} \sqrt{\frac{d}{(2(d \tan \theta-h)}} \)
в. \( \frac{d}{\cos \theta} \sqrt{\frac{g}{(2(d \tan \theta-h)}} \)
c. \( \sqrt{\frac{g d^{2}}{h \cos ^{2} \theta}} \)
D. \( \sqrt{\frac{g d^{2}}{(d-h)}} \)
Subject: Maths
In a group of 10 people, \( 70 \% \) take vitamins. If you randomly choose 2 of them, what is the probability
that neither person selected takes vitamins?
A \( . . .0677 \)
в \( \ldots .09 \)
\( c \ldots 30 \)
D \( \ldots 4 \)
\( E \ldots .49 \)
Subject: Physics
The power of the heater is \( 1000 W \) at
\( 1000^{\circ} \mathrm{C} . \) What will be its power at
\( 4000^{\circ} \mathrm{C} ? \)
Given, temperature coefficient of resistance of heater-wire is \( 1.4 \times \)
\( 10^{-40} C^{-1} \)
A \( .1 .42 \times 10^{3} W \)
в. \( 1.3 \times 10^{3} \mathrm{W} \)
c. \( 9.68 \times 10^{3} W \)
D . \( 1.08 \times 10^{3} W \)
Subject: Chemistry
Which reaction shows oxidising nature
of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. \( A g_{2} O+H_{2} O_{2} \rightarrow A g+H_{2} O+O_{2} \)
в. \( M n O_{2}+H_{2} O_{2}+H_{2} S O_{4} \rightarrow M n S O_{4}+2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
D. \( K_{2} C r_{2} O_{7}+H_{2} S O_{4}+4 H_{2} O_{2} \rightarrow K_{2} S O_{4}+2 C r O_{5}+ \)
\( 5 H_{2} O \)
Subject: Maths
The value of \( f(0) \) so that the function \( f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \) is continuous at
each point in its domain, is equal to
A . 2
в. \( \frac{1}{3} \)
c. \( \frac{2}{3} \)
D. \( \frac{-1}{3} \)
Subject: Maths
What is the Cartesian product of \( \boldsymbol{A}= \)
\{1,2\} and \( B=\{a, b\} ? \)
A \( \cdot\{(1, a),(1, b),(2, a),(b, b)\} \)
B - \( \{(1,1),(2,2),(a, a),(b, b)\} \)
c. \( \{(1, a),(2, a),(1, b),(2, b)\} \)
D \cdot \( \{(1,1),(a, a),(2, a),(1, b)\} \)
Subject: Physics
A boat is sailing at a velocity \( 3 \hat{i}+4 \hat{j} \) with respect to ground and water in river is flowing with a velocity \( -3 \hat{i}-4 \hat{j} \)
Relative velocity of the boat with respect to water is :-
\( A \cdot 8 \hat{3} \)
B . \( 5 \sqrt{2} \hat{j} \)
c. \( 6 \hat{i}+8 \hat{j} \)
D. \( -6 \hat{i}-8 \hat{j} \)
Subject: Physics
If the angle of incidence is twice the angle of refraction in a medium of refractive index \( \mu, \) then the angle of
incidence is :
A \( \cdot 2 \cos ^{-1} \frac{\mu}{2} \)
B \( \cdot 2 \sin ^{-1} \frac{\mu}{2} \)
\( \mathrm{c} \cdot 2 \cos ^{-1} \mu \)
D. \( 2 \sin ^{-1} \mu \)
Subject: Biology
Ram was going through a forest and found many similar plants. What
amongst the given below could be
reason for the observed phenomenon?
The plants are
A. Of many genera
B. Of only one species
C. Capable of interbreeding
D. Capable of crossbreeding. Select the correct alternative from the
following.
A. A and B
B. B and C
c. \( c \) and \( D \)
D. A and D
Subject: Maths
\( \boldsymbol{A}(\mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{B}(\mathbf{5},-\mathbf{2}) \) are two given
points. If \( \boldsymbol{A P}=\boldsymbol{P B} \) and area of
\( \triangle P A B=10, \) then \( P \) is
A. (7,1)
()
B. (7,2)
c. (-7,2)
D. (-7,-1)
Subject: Maths
Find graphically, the maximum value of \( z=2 x+5 y, \) subject to constraints
given below:
\( 2 x+4 y \leq 8 \)
\( \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{6} \)
\( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4} \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \leq \mathbf{0 . 6} \)
Subject: Physics
A body dropped from the top of the tower covers a distance \( 7 x \) in the last second
of its journey, where \( x \) is the distance
covered in first second. How much time
does it takes to reach the ground?
A . \( 3 s \)
B. \( 4 s \)
\( c .5 s \)
D. \( 6 s \)
Subject: Maths
The particular solution of the differential equation
\( \left[\boldsymbol{x} \sin ^{2}\left(\frac{y}{x}\right)-\boldsymbol{y}\right] \boldsymbol{d} \boldsymbol{x}+\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
satisfying the condition \( y=\frac{\pi}{4}, \) when
\( \boldsymbol{x}=\mathbf{1}, \) is
\( \mathbf{A} \cdot \tan \left(\frac{y}{x}\right)=\log (e x) \)
B \( \cdot \tan \left(\frac{x}{y}\right)=\log (e x) \)
C \( \cdot \cot \left(\frac{y}{x}\right)=\log \left(\frac{e}{x}\right) \)
D \( \cdot \cot \left(\frac{y}{x}\right)=\log (e x) \)
Subject: Physics
For an \( L-R \) circuit, the inductive
reactance is equal to the resistance \( \boldsymbol{R} \)
of the circuit. An emf \( \boldsymbol{E}=\boldsymbol{E}_{0} \cos (\boldsymbol{w} \boldsymbol{t}) \) is
applied to the circuit. Then, the power consumed in the circuit is :
A \( \cdot \frac{E_{0}}{R} \)
в. \( \frac{E_{0}^{2}}{4 R} \)
c. \( \frac{4 R}{E_{0}} \)
D. \( \frac{R}{E_{0}} \)
Subject: Maths
The median of the observations,
arranged in increasing order is \( 26 . \) Find
the value of \( \boldsymbol{x} . \mathbf{1 0}, \mathbf{1 7}, \mathbf{2 2}, \boldsymbol{x}+\mathbf{2}, \boldsymbol{x}+ \)
4,30,36,40
Subject: Maths
The range of \( f(x)=\cos [x],-\frac{\pi}{4}<x< \)
\( \frac{\pi}{4}, \) where \( [ \) represent greatest integer
function less than or equal to \( x \) is
\( A \cdot\{0\} \)
B . [-1,1]
\( \mathbf{c} \cdot\{\cos 1,1\} \)
D \( \cdot\{-1,1\} \)
Subject: Physics
A uniform wire of length \( l \) is bent into
the shape \( V \) as shown in the figure. The
distance of its center of mass from the
vertex \( \boldsymbol{A} \) is \( (\text { in } \boldsymbol{m}) \)
A. \( l / 2 \)
\( B \cdot \frac{1 \sqrt{3}}{1} \)
\( c \cdot \frac{1 \sqrt{3}}{0} \)
D. none of thes
Subject: Chemistry
\( 100 \mathrm{mL} \) of a solution contains \( 2 \mathrm{g} \) of acetic acid and 3 g of sodium acetate providing \( K_{a}=1.8 \times 10^{-5} . \) Choose the
correct option.
A. This solution is basic in nature
B. This solution is acidic in nature
c. This solution is amphoteric in nature
D. This solution is neutral in nature
Subject: Physics
Electric field due to a point charge \( \boldsymbol{q} \) at
distance \( r \) has magnitude:
A \( \cdot \frac{q}{4 \pi \varepsilon_{0} r^{3}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} r^{2}} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} r} \)
D. \( \frac{q^{2}}{4 \pi \varepsilon_{0} r^{2}} \)
Subject: Physics
A circular disc of radius \( \boldsymbol{R} \) and
thickness \( \frac{R}{6} \) has moment inertia \( I \) about an axis passing through its
centre perpendicular to its plane. lt is
melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is
A. \( I \)
B. \( \frac{2 I}{8} \)
c. \( \frac{1}{5} \)
D. \( \frac{I}{10} \)
Subject: Chemistry
\( \mathbf{A} \cdot-62.7 k J m o l^{-1} \)
\( \mathbf{B} \cdot-31.4 k J m o l^{-1} \)
\( \mathbf{c} \cdot-15.7 k J m o l^{-1} \)
D. \( -3.14 k J \) mol\( ^{-1} \)
Subject: Maths
For any two complex numbers \( z_{1}, z_{2} \) and any two real numbers a, b show that
\( \left|\boldsymbol{a} \boldsymbol{z}_{1}-\boldsymbol{b} \boldsymbol{z}_{2}\right|^{2}+\left|\boldsymbol{b} \boldsymbol{z}_{1}+\boldsymbol{a} \boldsymbol{z}_{2}\right|^{2}= \)
\( \left(a^{2}+b^{2}\right)\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
Subject: Maths
Show that the point whose distance from \( y-a x i s \) is thrice its distance
from (1,2,-1) satisfies the equation
\( 8 x^{2}+9 y^{2}+8 z^{2}-18 x-36 y+18 z+ \)
\( \mathbf{5 4}=\mathbf{0} \)
Subject: Biology
A bacterium divides every 35 minutes. If
a culture containing \( 10^{5} \) cells/ml is
grown in 175 minutes, what will be cell
concentration after that period
A \( \cdot 175 \times 10^{5} \)
В. \( 35 \times 10^{5} \)
c. \( 5 \times 10^{5} \)
D. \( 32 \times 10^{5} \)
Subject: Maths
let ABCD is trapezium such that \( \overrightarrow{A B}=3 \overrightarrow{D E}, \) E divides line segement
AB internally in the ratio 2: 1 and \( F \) is mid point of DC. if position vector of \( A, B \) and \( \mathrm{C} \) are \( \vec{a}, \vec{b} \) and \( \vec{c} \) respectively then find the vector \( \overrightarrow{\boldsymbol{F E}} \).