AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In a Young's double slit experiment, let
\( A \) and \( B \) be the two slits. A thin film of
thickness \( t \) and refractive index \( \mu \) is
placed in front of \( \boldsymbol{A} \). Let \( \boldsymbol{\beta}= \) fringe width The central maximum will shift
This question has multiple correct options
A. towards \( A \)
B. towards \( B \)
\( c \cdot \operatorname{byt}(\mu-1) \frac{\beta}{\lambda} \)
D. by \( \mu t \frac{\beta}{\lambda} \)
Subject: Chemistry
Arrange the following molecules in the
increasing order of \( \alpha \) to \( \pi \) bond ratio?
(1)
(2)
(3)
(4)
\( A \cdot(2)<(3)<(4)<(1) \)
B. \( (2)<(4)<(3)<(1) \)
\( c \cdot(3)<(2)<(1)<(4) \)
\( D \cdot(2)<(3)<(1)<(4) \)
Subject: Chemistry
Which of the following reactions are
possible?
This question has multiple correct options
\( \mathbf{A} \cdot 3 M g+2 A l^{3+} \rightarrow 2 A l+3 M g^{2+} \)
B \( \cdot C l_{2}+2 I^{-} \rightarrow I_{2}+2 C l^{-} \)
\( \mathbf{c} \cdot K^{+}+N a \rightarrow K+N a^{+} \)
\( \mathbf{D} \cdot K+N \rightarrow K^{-}+N^{+} \)
Subject: Physics
A ball is projected from the ground with a speed of \( 20 m / s \) at an angle of 45 with
horizontal. There is a wall of \( 25 m \) height
at a distance of \( 10 m \) from the
projection point. The ball will hit the wal at a height of
\( A \cdot 5 m \)
в. \( 7.5 m \)
c. \( 10 m \)
D. \( 12.5 m \)
Subject: Chemistry
Some statements about heavy water are given below.
(i) Heavy water is used as moderator in nuclear reactors
(ii) Heavy water is more associated then ordinary water
(iii) Heavy water is more effective solvent than ordinary water Which of the above statements are
correct?
A \( \cdot \) (i) and (ii)
B. (i), (ii) and (iii)
c. (ii) and (iii)
D. (i) and (iii)
Subject: Maths
If \( \boldsymbol{y}=\cos ^{-1}(\cos \boldsymbol{x}), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}= \)
\( \frac{5 \pi}{4} \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B . -
c. \( \frac{1}{\sqrt{2}} \)
D. \( -\frac{1}{\sqrt{2}} \)
Subject: Maths
f \( a \neq b \neq c \) such that
\( \left|\begin{array}{ccc}\boldsymbol{a}^{3}-\mathbf{1} & \boldsymbol{b}^{\mathbf{3}}-\mathbf{1} & \boldsymbol{c}^{\mathbf{3}}-\mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{\mathbf{2}} & \boldsymbol{b}^{\mathbf{2}} & \boldsymbol{c}^{\mathbf{2}}\end{array}\right|=\mathbf{0} \) ther
A \( . a b+b c+c a=0 \)
B . \( a+b+c=0 \)
\( c \cdot a b c=1 \)
D. \( a+b+c=1 \)
Subject: Maths
\( \left(\left[\begin{array}{ll}\mathbf{8} & \mathbf{4} \\ \boldsymbol{x} & \mathbf{8}\end{array}\right]\right)=\mathbf{4}\left(\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2}\end{array}\right]\right) \) then the value
of \( x \) is
A .
B. 2
\( c \cdot \frac{1}{4} \)
\( D \)
Subject: Physics
Three identical batteries each emf 4 V
and zero of negligible internal
resistance are connected as shown
in figure below. The potential difference
between the poilints \( A \) and \( G\left(V_{A}-V_{G}\right) \)
A . 4 v
B . \( -4 V \)
\( c \cdot 8 v \)
\( \mathbf{D} \cdot-8 V \)
Subject: Physics
An electron moving with a velocity of \( 5 \times 10^{4} m s^{-1} \) enters into a
uniform electric field and acquires a
uniform acceleration of \( 10^{4} m s^{-2} \) in the
direction of its initial motion. Calculate
the time(in \( s \) ) in which the electron
would acquire a velocity double of its initial velocity
A . 10
B. 8
\( c \cdot 5 \)
\( D \)
Subject: Physics
Equal volume of two immiscible liquids
of densities \( \rho \) and \( 2 \rho \) are filled in a
vessel as shown in the figure. Two smal
holes are punched at depths h/2 and 3h/2 from the surface of lighter liquid. If
\( v_{1} \) and \( v_{2} \) are the velocities of efflux at
these two holes, then \( v_{1} / v_{2} \) is:
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
For the reaction of one mole zinc dust
with one mole sulphuric acid in a bomb calorimeter, \( \triangle \boldsymbol{U} \) and \( \mathbf{w} \) correspond to?
A. \( \triangle U<0, w=0 \)
в. \( \triangle U<0, w<0 \)
\( \mathbf{c} . \triangle U>0, w=0 \)
D. \( \Delta U>0, w>0 \)
Subject: Physics
Let two mirrors \( A \) and \( B \) be separated by a distance of \( 10 \mathrm{m} \). Let object 0 be
placed at midpoint of the mirrors. Let \( \boldsymbol{I}_{1} \) be the first image in mirror \( A \) and \( I_{2} \) be the second image in mirror B. What is
the distance between \( I_{1} \) and \( I_{2} ? \)
A . \( 10 m \)
B. \( 20 m \)
\( c .30 m \)
D. \( 40 m \)
Subject: Chemistry
The hybridization associated with the central atom of a molecule in which all
the bond angles are \( 120^{\circ} \) is
\( \mathbf{A} \cdot s p \)
в. \( S p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)
E \( \cdot s p^{3} d^{2} \)
Subject: Maths
The value of \( x \) between 0 and \( 2 \pi \) which
satisfy the equation \( \sin x \sqrt{8 \cos ^{2} x}=1 \)
are in A.P. The common difference of the
A.P. is
A \( \cdot \frac{\pi}{8} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{3 \pi}{8} \)
D. \( \frac{5 \pi}{8} \)
Subject: Chemistry
Which of the following pairs of carbonyl compounds and Grignard reagent should be chosen as reactants to
prepare 2,4 -dimethyl-3-pentanol?
A. \( C H_{3} C H_{2} C H_{2} C H O \) and \( C H_{3} C H_{2} C H_{2} M g B r \)
в. \( \left(C H_{3}\right)_{2} C H C H O \) and \( \left(C H_{3}\right)_{2} C H M g B r \)
c. \( C H_{3} C H_{2} C O C H_{3} \) and \( \left(C H_{3}\right)_{2} C H M g B r \)
D. \( \left(C H_{3}\right)_{2} C H C H O \) and \( C H_{3} C H_{2} C H_{2} M g B r \)
Subject: Chemistry
Among \( \boldsymbol{C a} \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{a} \boldsymbol{H}_{2}, \) the order
of ionic character is
A. \( B e H_{2}<B a H_{2}<C a H_{2} \)
в. \( B e H_{2}<C a H_{2}<B a H_{2} \)
c. \( B a H_{2}<B e H_{2}<C a H_{2} \)
D. \( C a H_{2}<B e H_{2}<B a H_{2} \)
Subject: Maths
let \( \boldsymbol{f}(\boldsymbol{\theta})=\frac{1}{1+(\tan \theta)^{2013}} \) then value of
\( \sum_{\theta=1^{0}}^{89^{\circ}} f(\theta) \) equals
A . 45
B. 44
c. \( 89 / 2 \)
D. \( 91 / 2 \)
Subject: Chemistry
The standard EMF of quantity electrode is \( 0.699 V . \) The EMF of the
quinhydrone electrode dipped in a solution with \( \mathrm{pH}=10 \) is:
A \( .0 .109 V \)
\( V \)
B. \( -0.109 V \)
c. \( 1.289 V \)
D . \( -1.289 V \)
Subject: Maths
Let \( \overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=10 \vec{a}+2 \vec{b} \) and
\( \overrightarrow{O C}=\vec{b}, \) where \( O, A \) and \( C \) are non
collinear points. Let \( p \) denote the area of
quadrilateral \( O A B C, \) and \( q \) denote the
area of the parallelogram with \( O A \) and \( O C \) as adjecent sides, then \( \frac{p}{q} \) is equal
to
A. 4
в. 6
\( ^{\mathrm{c}} \frac{1}{2} \frac{|\vec{a}-\vec{b}|}{\vec{a}} \)
D. None of these
Subject: Physics
\( \alpha- \) particles of 6 MeV energy is
scattered back from a silver foil.
Calculate the maximum volume where
the entire charge of the atom is
supposed to be accumulated.
\( [Z \text { for silver }=47] \)
A . \( 3.6 \times 10^{-28} \mathrm{m}^{3} \)
В. \( 5.97 \times 10^{-42} \mathrm{m}^{3} \)
c. \( 6.55 \times 10^{-71} m^{3} \)
D. \( 48 \times 10^{-42} m^{3} \)
Subject: Maths
The area common to the circle \( x^{2}+ \)
\( y^{2}=16 a^{2} \) and the parabola \( y^{2}=6 a x \) is
A \( \cdot 4 a^{2}(8 \pi-\sqrt{3}) \)
B. \( \frac{4 a^{2}(4 \pi+\sqrt{3})}{3} \)
c. \( \frac{8 a^{2}(4 \pi-\sqrt{3})}{5} \)
D. none of these
Subject: Physics
There are two concentric metal shells of
radii \( r_{1} \) and \( r_{2}\left(>r_{1}\right) . \) If the outer shell
has a charge \( q \) and the inner shell is grounded, the charge on the inner shell is
A. zero
B. \( -\left(r_{1} / r_{2}\right) \) q
c. \( r_{1} r_{2} \) q
D. None of thee
Subject: Maths
f \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y})|\boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{7}| \text { , where } \boldsymbol{x} \in \boldsymbol{R} \)
and \( -5 \leq x \leq 5\} \) is relation, find the
domain of \( \boldsymbol{R} \)
Subject: Physics
The wavelength of maximum intensity
of emission of solar radiation is \( \lambda_{m}= \)
\( 4753 A^{\circ} \) and from moon it is \( 14 \mu \mathrm{mm} \)
The surface temperature of sun and
moon are \( \left(\operatorname{given} b=2.898 \times 10^{-3}\right. \)
meter-kelvin)
A. 6097 К. 207К
в. 8097 К, зот к
c. 10000 К, \( 400 \mathrm{k} \)
D. 3000 К, 100 к
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right] \) and
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=\boldsymbol{k}\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) then the value of
\( k \) is
\( \mathbf{A} \cdot \sin x \cos x \)
B.
c.
D.
Subject: Chemistry
Statement 1: Isotopes of a particular element have nearly identical chemical behavior.
Statement 2: They have identical electron configurations.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct
Subject: Physics
f a satellite is revolving around a planet of mass \( \mathrm{M} \) in an elliptical orbit of semimajor axis a. Show that the orbital speed of the satellite when it is at a distance r from the focus will be given by \( \boldsymbol{v}^{2}=\boldsymbol{G} \boldsymbol{M}\left[\frac{\boldsymbol{2}}{\boldsymbol{r}}-\frac{\mathbf{1}}{\boldsymbol{a}}\right] \)
Subject: Biology
Assertion
Tracheids and the tracheae, the dead tissues are chief conducting tissues and their death is of great advantage to
plants.
Reason
In the dead tissues, the water and
solutes move freely and have not to diffuse through any differentially
permeable membranes, making conduction rapid and efficient.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Calculate the flux through the base of
the cone of radius \( r \)
\( \mathbf{A} \cdot 2 \pi r^{2} E \)
\( \mathbf{B} \cdot 4 \pi r^{2} E \)
\( \mathbf{c} \cdot 0.5 \pi r^{2} E \)
\( \mathbf{D} \cdot \pi r^{2} E \)
Subject: Chemistry
The velocities of two particles \( A \) and \( B \) are 0.05 and \( 0.02 m s^{-1} \) respectively.
The mass of \( B \) is five times the mass of
A. The ratio of their de-Broglie's wavelength is :
A .2: 1
B. 1: 4
\( c \cdot 1: 1 \)
D. 4: 1
Subject: Chemistry
formula \( \left(C_{8} H_{10}\right) .(A) \) is oxidized by a strong oxidizing agent to (B). (B) on dehydration and subsequent reaction with ammonia forms an imide, (C). (C) is then reacted with a strong inorganic
base to form a compound that undergoes Hoffman bromamide reaction to give (D). (D) is treated with sodium nitrite in an ice cold acidic
solution to form the product (E). (E) is a
steam volatile compound and on nitration gives two mononitro derivatives. (E) is treated with sodium
hydroxide to form the salt (F). On heating a solution of (F), bubble are
formed due to release of gas. This gas does not burn. On analysis it was found
that the gas has two components, one
lighter than air and one heavier than air.
Compound \( (B) \) is :
A. Phthalic acid
B. Isophthalic acid
c. Terephthalic acid
D. Benzoic acid
Subject: Physics
A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the \( n^{t h} \) second to
distance covered in \( n \) seconds is
A \( \cdot \frac{2}{n}-\frac{1}{n^{2}} \)
B. \( \frac{1}{n^{2}}-\frac{1}{n} \)
c. \( \frac{2}{n^{2}}-\frac{1}{n} \)
D. \( \frac{2}{n}+\frac{1}{n^{2}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}| . \) Find
\( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})\left(-\frac{\boldsymbol{5}}{\boldsymbol{3}}\right)-(\boldsymbol{f o g})\left(-\frac{\boldsymbol{5}}{\boldsymbol{3}}\right) \)
\( A \)
B . 2
\( c .3 \)
\( D \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \)
Complete the reaction.
Subject: Physics
A coil of inductive reactance \( 1 / \sqrt{3} \Omega \) and resistance \( 1 \Omega \) is connected to
\( 200 V, 50 H z \) A.C. supply. The time lag
between maximum voltage and current
is
A \( \cdot \frac{1}{600} s \)
в. \( \frac{1}{200} s \)
c. \( \frac{1}{300} s \)
D. \( \frac{1}{500} s \)
Subject: Biology
Assertion
All pteridophytes have originated from
Rhynia.
Reason
It is a living fossil fern.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.
Subject: Maths
The line \( y=x \) is a tangent at (0,0) to a
circle of radius is \( 1, \) then centre of the
circle is
\( ^{\mathbf{A}} \cdot\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)
B \( \cdot\left(\frac{1}{2 \sqrt{2}}-\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)
D. \( \left(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right) \)
Subject: Chemistry
The correct balanced equation from the
following is:
A. \( P b O+N H_{3} \rightarrow P b+H_{2} O+N_{2} \)
B. \( P b O+2 N H_{3} \rightarrow P b+H_{2} O+N_{2} \)
c. \( P b O+2 N H_{3} \rightarrow 3 P b+3 H_{2} O+N_{2} \)
D. \( 3 P b O+2 N H_{3} \rightarrow 3 P b+3 H_{2} O+N_{2} \)
Subject: Maths
I : Number of partial fractions of \( \frac{x^{3}+x^{2}+1}{x^{4}+x^{2}+1} \) is 4
II : Number of partial fractions of \( \frac{3 x+5}{(x-1)^{2}\left(x^{2}+1\right)^{3}} \) is 5
Which of the above statement is true.
A. onlyı
B. Only II
c. Both I and II
D. Neither I nor II
Subject: Chemistry
The radius of an orbit in hydrogen atom is 52.9 A. The angular momentum of the electron in the orbit could be:
A \( \cdot \frac{5 h}{\pi} \)
в. \( \frac{5 h}{4 \pi} \)
\( c \cdot \frac{4 h}{2 \pi} \)
D. \( \frac{4 h}{\pi} \)
Subject: Maths
\( \int \frac{5 x+4}{\sqrt{x^{2}+3 x+2}} d x= \)
\( A \sqrt{x^{2}+3 x+2} \)
\( \boldsymbol{B} \ln \left[\left(\boldsymbol{x}+\frac{\boldsymbol{3}}{\mathbf{2}}\right)+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}}\right]+\boldsymbol{C} \)
Then \( A+2 B=? \)
\( A \cdot 9 \)
B . 10
c. 11
D. 12
Subject: Chemistry
Assertion
Statement-I: Lead, tin and bismuth are purified by liquation method.
Reason
Statement- -II : Lead, tin and bismuth
have low m.p. as compared to impurities.
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
The points \( O, A, B, C, D \) are such that \( \boldsymbol{O A}=\boldsymbol{a}, \boldsymbol{O B}=\boldsymbol{b}, \boldsymbol{O C}=\boldsymbol{2} \boldsymbol{a}+\boldsymbol{3 b} \) and
\( \boldsymbol{O} \boldsymbol{D}=\boldsymbol{a}-\boldsymbol{2 b} . \) If \( |\boldsymbol{a}|=\boldsymbol{3}|\boldsymbol{b}|, \) then the
angle between \( B D \) and \( A C \) is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. None of these
Subject: Chemistry
Which of the following statements is
not true about \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot \) It is a tribasic acid
B. One mole of it is neutralised by 0.5 mole of \( C a(O H)_{2} \)
C \( . N a H_{2} P O_{2} \) is not an acidic salt
D. It disproportionates to \( H_{3} P O_{3} \) and \( P H_{3} \) on heating
Subject: Chemistry
Bleaching powder dissolves in water to
form:
A \( \cdot C a(O H)_{2}, C l_{2} \)
B. \( \mathrm{Ca}^{+2}, \mathrm{Cl}^{-}, \mathrm{ClO}_{2}^{-} \)
c. \( \mathrm{Ca}^{2+}, \mathrm{Cl}^{-}, \mathrm{ClO}_{3} \)
D. \( \mathrm{Ca}^{2+}, \mathrm{C} 1^{-}, \mathrm{ClO}_{4}^{-} \)
Subject: Maths
Find the slope and \( y \) -intercept of the
line \( -\mathbf{5 x}+\boldsymbol{y}=\mathbf{5} \)
A. slope \( =5, y \) -intercept \( =-5 \)
B. slope \( =5, y \) -intercept \( =-4 \)
c. slope \( =5, y \) -intercept \( =5 \)
D. slope \( =5, y \) -intercept \( =-1 \)
Subject: Chemistry
The signs of \( \Delta \mathrm{H}, \Delta \mathrm{S} \) and \( \Delta \mathrm{G} \) for a non
spontaneous reaction at all temperatures would be:
\( A \cdot+,+, \)
\( B .+. .,+ \)
\( c \ldots- \)
D. \( +,+,+ \)
Subject: Biology
Which one of the following conditions correctly describes the manner of determining the sex in the given example?
A. Homozygous sex chromosomes (XX) produce male in Drosophila.
B. Homozygous sex chromosomes (ZZ) determine female sex in birds
c. xo type of sex chromosomes determine male sex in grasshopper.
D. xo condition in humans as found in Turner Syndrome determines female sex
Subject: Physics
In the figure shown, the friction force
between the bead and the light string is
\( m g / 4, \) find the time which the bead
loses contact with string after the
system is released:
A. \( \sqrt{\frac{2 l}{7 a}} \)
в. \( \sqrt{\frac{4 l}{7 q}} \)
c. \( \sqrt{\frac{8 l}{7 q}} \)
D. \( \sqrt{\frac{7 l}{7 g}} \)
Subject: Physics
The magnetic induction at a distance d
from the magnetic pole of the unknown strength \( m \) is \( B \). If an identical pole is now placed at a distance of \( 2 \mathrm{d} \) from the first pole, the force between the two poles is
A. ms
B. \( \frac{m B}{2} \)
\( \mathbf{c} \cdot \frac{m B}{4} \)
D. 2mB
Subject: Physics
A wooden plank of length 1 m and
uniform cross section is hinged at one
end to the bottom of a tank as shown in
the figure. The tank is filled with water
up to a height of 0.5 m. The specific
gravity of the plank is \( 0.5 . \) If the angle \( \theta \) by the inclination of that the plank
makes with the vertical in the
equilibrium position (exclude the case
\( \theta=0 \) ). Find the value of \( \frac{1}{\cos ^{2} \theta} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{\log \left(1+\boldsymbol{x}+\boldsymbol{x}^{2}+\boldsymbol{x}^{3}+\cdots\right)}, \) where \( |\boldsymbol{x}|<\mathbf{1} \)
then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{-1}{(1-x)^{2}} \)
B. \( \frac{1}{(1-x)^{2}} \)
c. \( \frac{1}{(1+x)^{2}} \)
D. None of these
Subject: Physics
A boat covers a certain distance
between two spots in a river taking \( t_{1} \)
hrs going downstream and \( t_{2} \) hrs going upstream. What time will be taken by boat to cover same distance in still
water?
A \( \cdot \frac{t_{1}+t_{2}}{2} \)
B \( .2\left(t_{2}=t_{1}\right) \)
c. \( \frac{2 t_{1} t_{2}}{t_{1}+t_{2}} \)
D. \( \sqrt{t_{1} t_{2}} \)
Subject: Maths
The equation of the latus rectum of the parabola \( \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is -
\( A \cdot 3 y=2 \)
B. \( 2 y+3=0 \)
c. \( 2 y=3 \)
D. \( 3 y+2=0 \)
Subject: Physics
A ray of light travels from air to glass at
an angle of incidence of \( 37^{\circ}, \) the angle
of refraction is \( 24^{\circ} . \) What is the
refractive index of glass? (Given: \( \left.\sin 37^{\circ}=0.60, \sin 24^{\circ}=0.40\right) \)
A . 0.66
B. 0.133
\( c .1 .5 \)
D. None
Subject: Maths
Two circles with centres \( A \) and \( B \) of
radii \( 3 \mathrm{cm} \) and \( 4 \mathrm{cm}, \) respectively
intersect at two points \( C \) and \( D \) such that \( A C \) and \( B C \) are tangents to the
two circles. Find the 10 times length of
the common chord \( C D \)
A .48
B. 58
\( c \cdot 56 \)
D. 54
Subject: Physics
In a n-p-n transistor, the collector current is \( 10 \mathrm{mA} \). If \( 10 \% \) of the electrons
are lost in the base, then the emitter current is:
A . \( 10 \mathrm{mA} \)
B. \( 0.9 \mathrm{mA} \)
c. \( 0.09 \mathrm{mA} \)
D. \( 11.1 \mathrm{m} \)
Subject: Physics
A wire of length \( 44 \mathrm{cm} \) is bent into a
circle and a current of \( 9.8 A \) is passed through it. The intensity of magnetic induction at the centre of the circle is
\( \mathbf{A} \cdot 8.8 \times 10^{-6} T \)
B . \( 8.8 \times 10^{-5} T \)
c. \( 8.4 \times 10^{-6} T \)
D. \( 61.5 \times 10^{-5} T \)
Subject: Physics
A rod lies across frictionless rails in a
uniform magnetic field \( \vec{B} \) as shown in
figure. The rid moves to the right with speed \( V . \) In order to make the induced
emf in the circuit to be zero, the
magnitude of the magnetic field should
A. not change
B. increase linearly with time
c. decrease linearly with time
D. decrease nonlinearly with time
E. answer required
Subject: Physics
Four charges \( 10^{-8} ;-2 \times 10^{-8} ;+3 \times 10^{-8} \)
and \( 2 \times 10^{-8} \) coulombs are placed at the
four corners of a square of side \( 1 \mathrm{m} \). The
potential at the centre of the square is
A . zero
B. 360volt
c. \( 180 v o l t \)
D. \( 360 \sqrt{2} \) volt
Subject: Maths
A window is in the shape of a rectangle surmounted by a semi circle. If the perimeter of the window is of fixed
length I then the maximum area of the window is
A \( \cdot \frac{I^{2}}{2 \pi+4} \)
B. \( \frac{I^{2}}{\pi+8} \)
c. \( \frac{I^{2}}{2 \pi+8} \)
D. \( \frac{I^{2}}{8 \pi+4} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{I} \boldsymbol{R} \rightarrow \boldsymbol{I} \boldsymbol{R} \quad \) be defined as
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+\left|\boldsymbol{x}^{2}-1\right| . \) The total number
of points at which \( f \) attains either a
local maximum or local minimum is
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{3} \cot ^{3} \boldsymbol{x}-\cot \boldsymbol{x}+ \)
\( \int \cot ^{4} x d x \) and \( f\left(\frac{\pi}{2}\right)=\frac{\pi}{2}, \) then
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \mathbf{A} \cdot \pi-x \)
B. \( x-\pi \)
c. \( \frac{\pi}{2}-x \)
D. \( x \)
Subject: Maths
You enter a chess tournament where
your probability of winning a game is 0.3 against half the players (call them
type 1 ), 0.4 against a quarter of the players (call them type 2 ), and 0.5 against the remaining quarter of the
players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning?
A. 0.375
в. 0.986
\( c \cdot 0.236 \)
D. 0.135
Subject: Physics
In a metre bridge experiment null point is obtained at \( 40 \mathrm{cm} \) form one end of the
wire when resistance \( X \) is balanced
against another resistance Y. If \( \mathrm{X}<\mathrm{Y} \) then the new position of the null point from the same end, if one decides to
balance a resistance of \( 3 \mathrm{X} \) against \( \mathrm{Y} \) will be close to
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 75 \mathrm{cm} \)
\( c \cdot 67 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)
Subject: Physics
The acceleration of an electron in the
first orbit of the hydrogen atom \( (\boldsymbol{n}=\mathbf{1}) \)
is :
A \( \cdot \frac{h^{2}}{\pi^{2} m^{2} r^{3}} \)
B. \( \frac{h^{2}}{8 \pi^{2} m^{2} r^{3}} \)
c. \( \frac{h^{2}}{4 \pi m^{2} r^{3}} \)
D. \( \frac{2 \pi^{2} k m e^{2} Z}{\eta h} \)
Subject: Maths
Unit vector perpendicular to the plane passing through the points \( \hat{\mathbf{i}}-\hat{\mathbf{j}}+ \) \( 2 \hat{k}, 2 \hat{i}-\hat{k} \) and \( 2 \hat{j}+\hat{k} \) is
A \( \cdot \frac{2 \hat{i}-\hat{j}+\hat{k}}{\sqrt{6}} \)
\( ^{\text {В } \cdot \frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}} \)
c. \( \frac{2 \hat{i}+\hat{j}-\hat{k}}{\sqrt{6}} \)
D. None of these
Subject: Maths
Given a function \( f \) such that \( f(4)=5 \)
then which of the following is/are true
for \( \boldsymbol{f} ? \)
A \( . f(x) \neq x+1 \)
в. \( f(x) \neq 2 x-3 \)
c. \( f(x) \neq 3 x-2 \)
D. \( f(x) \neq 4 x-11 \)