AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c}, \) are unit vector such that \( \bar{a}+ \) \( \bar{b}+\bar{c}=\overline{0}, \) then the \( \bar{a} . \bar{b}+\bar{b} . \bar{c}+\bar{c} . \bar{a}= \)
\( A \cdot \frac{3}{2} \)
B. \( -\frac{3}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)
Subject: Maths
A suitcase with measures \( 80 \mathrm{cm}, 48 \mathrm{cm} \)
and \( 24 \mathrm{cm} \) is to be covered with a
tarpaulin cloth. How many metres of
tarpaulin of width \( 96 \mathrm{cm} \) is required to cover 100 such suitcases?
Subject: Maths
If \( M \) and \( N \) are any two events, the
probability that the exactly one of them
occurs is
This question has multiple correct options
A \( \cdot P(M)+P(N)-2 P(M \cap N) \)
B . \( P(M)+P(N)-P(M \cap N)^{c} \)
\( \mathbf{c} \cdot P\left(M^{c}\right)+P\left(N^{c}\right)-2 P\left(M^{c} \cap N^{c}\right) \)
D \( P\left(M \cap N^{c}\right)+P\left(M^{c} \cap N\right) \)
Subject: Maths
Find the unit vectors perpendicular to both \( \vec{a} \) and \( \vec{b}, \) when \( \vec{a}=3 \hat{i}+\hat{j}-2 \hat{k} \) and \( \overrightarrow{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
Subject: Chemistry
The correct IUPAC name of the
compound is:
A. 3,3 -dimethyl-3-cyclopentyl propanal
B. 3-Cyclopentyl-3-methyl butanal
C. \( 1-(1 \) -methyl-1-formyl to ethylcyclopropane
D. 3,3 -diethyl-3-cyclobutyl butanal
Subject: Chemistry
Out of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \) peroxy acids are:
A. \( H_{2} S_{2} O_{3}, H_{2} S_{2} O_{8} \)
в. \( H_{2} S O_{5}, H_{2} S_{2} O_{8} \)
c. \( H_{2} S_{2} O_{4}, H_{2} S O_{5} \)
D. \( H_{2} S_{2} O_{3}, H_{2} S_{2} O_{4} \)
Subject: Maths
The maximum value of function \( \boldsymbol{f}(\boldsymbol{x})= \) \( 3 x^{3}-18 x^{2}+27 x-40 \) on the \( \operatorname{set} S= \)
\( \left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\mathbf{3 0} \leq \mathbf{1 1} \boldsymbol{x}\right\} \) is:
A . 122
B . -222
c. -122
D. 222
Subject: Physics
White light is incident normally on a soap film of thickness \( 15 \times 10^{-5} \mathrm{cm} \)
and refractive index \( 1.33 . \) Which
wavelength is reflected maximum in the visible region?
A \( .26000 A^{\circ} \)
B. \( 8866 A^{\circ} \)
c. \( 5320 A^{\circ} \)
D. \( 3800 A^{\circ} \)
Subject: Physics
Two waves in a string (all in Sl units)
\( \operatorname{are} y_{1}=0.6 \sin (10 t-20 x) \) and \( y_{2}= \)
\( 0.4 \sin (10 t+20 x) \)
Statement-1: Stationary wave can be formed by their superposition but net energy transfer through any section will
be non-zero
Statement-2: Their amplitudes are
unequal.
\( A \). If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement- 2 is not the correct explanation of statement- 1
c. If statement-1 is true and statement-2 is false
D. If statement- 1 is false and statement- 2 is true
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a}_{5} \boldsymbol{x}^{5}+\boldsymbol{a}_{4} \boldsymbol{x}^{4}+\boldsymbol{a}_{3} \boldsymbol{x}^{3}+ \)
\( a_{2} x^{2}+a_{1} x, \) where \( a_{i}^{\prime} s \) are real and
\( f(x)=0 \) has a positive root \( \alpha_{0} . \) Then
This question has multiple correct options
A \( \cdot f^{\prime}(x)=0 \) has a root \( \alpha_{1} \) such that \( 0<\alpha_{1}<\alpha_{0} \)
B . \( f^{\prime}(x)=0 \) has at least one real root
C \( \cdot f^{\prime \prime}(x)=0 \) has at least one real root
D. All of the above
Subject: Maths
The equation of the straight line cutting off an intercept 8 on \( x \) -axis and making
an angle of \( 60^{\circ} \) with the positive
direction of \( y- \) axis is
A \( . x-\sqrt{3} y-8=0 \)
B. \( x+\sqrt{3} y=8 \)
c. \( y-\sqrt{3} x=8 \)
D. \( y+\sqrt{3} x=8 \)
Subject: Physics
A steamer is heading due North with
\( 20 m s^{-1} . \) The wind is blowing \( 10 m s^{-1} \) due west. In which direction the flag on the mast flutters?
A \( \cdot \tan ^{-1} \frac{1}{2} \) west of north
B. \( \tan ^{-1} \frac{1}{2} \) east of north
c. \( \tan ^{-1} \frac{1}{2} \) north of east
D. \( \tan ^{-1} \frac{1}{2} \) north of west
Subject: Maths
A family has three children. Event \( A \) is
that family has at most one boy, Event
\( B^{\prime} \) is that family has at least one boy
and one girl, Event \( ^{\prime} C^{\prime} \) is that the family has at most one girl. Find whether
events \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \) are independent. Also find whether \( A, B, C \) are independent or
not
Subject: Maths
If \( A \) and \( B \) are independent events such that \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \) find
\( P(B) \)
Subject: Maths
Find the value of \( x \) if \( a \) and \( b \) are in
direct proportion
\( \begin{array}{ccccc}a & 2 & 3 & 4 & 5 \\ b & 14 & 21 & x & 35\end{array} \)
A . 16
в. 25
c. 27
D. 28
Subject: Physics
A \( 220 \mathrm{V} \) main supply is connected to a resistance of \( 100 \mathrm{k} \Omega \). The effective
current is?
A. \( 2.2 \mathrm{mA} \)
B. \( 2.2 \sqrt{2} \mathrm{mA} \)
c. \( \frac{2.2}{\sqrt{2}} \mathrm{m} \)
D. None of these
Subject: Maths
A straight line through origin 0 meets the lines \( 3 y=10-4 x \) and \( 8 x+6 y+ \)
\( 5=0 \) at points \( A \) and \( B \) respectively
Then 0 divides the segment \( A B \) in the
ratio:
A .2: 3
B. 1: 2
c. 4: 1
D. 3: 4
Subject: Maths
\( \vec{A} \) is a vector which when added to the resultant of vectors \( (2 \hat{i}-3 \hat{j}+4 \widehat{k}) \) and \( (\widehat{\boldsymbol{i}}+\boldsymbol{5} \widehat{\boldsymbol{j}}+\boldsymbol{2} \widehat{\boldsymbol{k}}) \) yields a unit vector along
the y-axis. Then vector \( \vec{A} \) is:
A . \( -3 \hat{i}-\widehat{j}-6 \widehat{k} \)
B. \( 3 \hat{i}+\widehat{j}-6 \widehat{k} \)
c. \( 3 \hat{i}-\widehat{j}+6 \widehat{k} \)
D. \( 3 \hat{i}+\widehat{j}+6 \widehat{k} \)
Subject: Physics
A particle is initially at rest, it is subjected to a linear acceleration \( a, \) as
shown in the figure. The maximum
speed attained by the particle is
A. \( 605 \mathrm{m} / \mathrm{s} \)
B. \( 110 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} .55 \mathrm{m} / \mathrm{s} \)
D. \( 550 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Consider the determinant \( \Delta= \)
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right| \)
\( M_{i j}= \) Minor of the element of \( i^{t h} \) row \&
\( j^{t h} \) column
\( C_{i j}= \) Cofactor of element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column.

If all the elements of the determinant
are multiplied by 2, then the value of new determinant is
A . 0
B. \( 8 \Delta \)
\( c \cdot 2 \Delta \)
D. \( 2^{9} \Delta \)
Subject: Maths
Relation \( R \) in the set \( A \) of human beings
in a town at a particular time given by
\[
\boldsymbol{R}=
\]
\( \{(x, y): x \text { and } y \) work at the same plac
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only
4-Equivalence 5-None
Subject: Chemistry
Calculate EMF of \( \left.Z n\right|_{(0.01 M)} ^{Z n^{2+}} \|_{(0.1 M)}^{A g^{+}} \mid A g \)
\( E_{Z n / Z n^{+2}}^{0}=0.762 V E_{A g^{+} / A g}^{0}=+0.80 V \)
A. \( 1.56 v \)
B. 2.36V
c. \( 0.236 v \)
D. 0.118v
Subject: Maths
Let \( \bar{z}, \bar{w} \) be complex numbers such that
\( z+w \) purely imaginary and \( z-w \) is
purely real
\( \mathbf{A} \cdot z=w \)
в. \( z=-w \)
\( \mathbf{c} \cdot z=\bar{w} \)
D. \( z=-\bar{w} \)
Subject: Physics
What amount of heat must be supplied to \( 2.0 \times 10^{-2} k g \) of nitrogen (at room
temperature) to raise its temperature
by \( 45^{\circ} \mathrm{C} \) at constant pressure?
(Molecular mass of \( \boldsymbol{N}_{2}=\mathbf{2 8}: \boldsymbol{R}= \)
\( 8.3 m o l^{-1} K^{-1} . \)
Subject: Maths
Solve \( \int_{2}^{-13} \frac{d x}{\sqrt[5]{(3-x)^{4}}} \)
A \( \cdot-5(\sqrt[5]{16}-1) \)
B \( \cdot 5(\sqrt[3]{16}-1) \)
\( \mathbf{c} \cdot-5(\sqrt[5]{16}+1) \)
D. None of these
Subject: Physics
The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2}, \) where \( n_{1} \) and \( n_{2} \)
are the principal quantum numbers of the two states. Assume the Bohr model
as valid in this case. The frequency of the orbital motion of the electron in the
initial state is \( 1 / 27 \) of that in the final
state. The possible values of \( n_{1} \) and \( n_{2} \)
are
A \( \cdot n_{1}=6, n_{2}=3 \)
в. \( n_{1}=4, n_{2}=2 \)
c. \( n_{1}=8, n_{2}=1 \)
D. \( n_{1}=3, n_{2}=1 \)
Subject: Maths
\( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \Rightarrow x= \)
\( A \cdot-1 \)
B.
\( c \cdot c \)
D. \( \pi \sqrt{\frac{5}{8}} \)
Subject: Biology
Match the following:
\begin{tabular}{ccc|c} 
& LIST I & & LIST II \\
A & Family & 1 & Diptera \\
B & Order & 2 & Arthropoda \\
C & Class & 3 & Muscidae \\
D & Phylum & 4 & Insecta
\end{tabular}
\( A \cdot A-4, B-3, C-2, D- \)
B. \( A-3, B-2, C-1, D-4 \)
C. \( A-2, B-3, C-4, D-1 \)
D. \( A-3, B-1, C-4, D-2 \)
Subject: Chemistry
Assertion
The electrolysis of potassium iodide, \( \mathrm{K} \) I produces electrical energy.
Reason
Electrolytic cells convert chemical energy into electrical energy
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 \( A \) and \( B \) are two events such that
\( P(A)=\frac{3}{8}, P(B)=\frac{5}{8} \) and
\( P(A \cup B)=\frac{3}{4}, \) then \( P(A \cap \bar{B})= \)
\( A \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{1}{8} \)
D.
Subject: Chemistry
In which of the following reactions of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) sulphur retains its oxidation
state?
This question has multiple correct options
A. Reaction of dilute \( H_{2} S O_{4} \) with sulphur
B. Reaction of conc. \( H_{2} S O_{4} \) with sulphur
c. Reaction of conc. \( H_{2} S O_{4} \) with glucose
D. Reaction of dilute \( H_{2} S O_{4} \) with zinc
Subject: Physics
A ball is vertically downwards with a speed of \( 6 \mathrm{m} / \mathrm{s} \) from a hight of \( 3.2 \mathrm{m} . \) It strikes a horizontal floor and rebounds
back to the same height. The value of corfficient of restitutions
\( (e) \) is :
A. 0.5
B. 0.6
\( c .0 . \)
D. 0.8
Subject: Chemistry
\( N O_{2} \) required for a reaction is produced
by the decomposition of \( N_{2} O_{5} \) in \( C C l_{4} \) as per the equation \( \mathbf{2} N_{2} O_{5}(g) \rightarrow 4 N O_{2}(g)+O_{2}(g) \)
The initial concentration of \( N_{2} O_{5} \) is
3.00 mol \( L^{-1} \) and it is 2.75 mol \( L^{-1} \)
after 30 minute. The rate of formation of
\( N O_{2} \) is :
в. \( 4.167 \times 10^{-3} \) mol \( L^{-1} \) min \( ^{-1} \)
c. \( 8.333 \times 10^{-3} \) mol \( L^{-1} \min ^{-1} \)
D. \( 1.667 \times 10^{-2} \) mol \( L^{-1} \min ^{-1} \)
Subject: Maths
Let \( \mathbf{P} \) and \( \mathbf{Q} \) be \( \mathbf{3} \times \mathbf{3} \) matrices with
\( \boldsymbol{P} \neq \boldsymbol{Q} . \) If \( \boldsymbol{P}^{3}=\boldsymbol{Q}^{3} \) and \( \boldsymbol{P}^{2} \boldsymbol{Q}=\boldsymbol{Q}^{2} \boldsymbol{P} \)
then determinant of \( \left(P^{2}+Q^{2}\right) \) is equal
to:
A . -2
B.
\( c \cdot 0 \)
D. -
Subject: Chemistry
Which of the following elements shown as pairs with their atomic numbers
belong to the same period?
A. \( Z=19 \) and \( z=38 \)
B. \( Z=12 \) and \( Z=17 \)
C \( . \quad Z=11 \) and \( Z=21 \)
D. \( z=16 \) and \( z=35 \)
Subject: Maths
The points \( A(2 a, 4 a), B(2 a, 6 a) \) and
\( C(2 a+\sqrt{3} a, 5 a)(\text { when } a>0) \) are
vertices of
A. an obtuse angled triangle
B. an equilateral triangle
c. an isosceles obtuse angled triangle
D. a right angled triangle
Subject: Maths
Two triangular walls of a flyover have been used for advertisements from both
sides. The sides of each wall are \( 120 \mathrm{m} \)
\( 110 \mathrm{m} \) and \( 20 \mathrm{m} . \) The advertisements
yield an earning of R.s 100 per \( m^{2} \) per
year. Find the amount of revenue earned
in one year. (Take \( \sqrt{7}=2.65) \)
A. Rs. 3,97,500
B. Rs. 3,47,500
c. Rs. 5,73,300
D. Rs. 4,73,500
Subject: Maths
\( f(x)=\cot ^{-1}\left(\frac{x^{x}-x^{-x}}{2}\right) \) then \( f^{1}(1)= \)
\( \mathbf{A} \cdot-\log 2 \)
B. \( \log 2 \)
\( c \cdot 1 \)
D. -
Subject: Physics
Match List - I (Mixture to be separated) with the List - II (Method used) and
select the correct option using the
codes given below.

List -I (mixture to be \( \quad \) List - II (Method separated) used)
\( (I) \)
(A) Petroleum products \( \quad \) Chromatography
\( (B) \) Camphor and rock salt
\( (I I) \) Centrifugation
\( (C) \) Cream from milk
\( (I I I) \) Sublimation
\( (D) \) Coloured components
\( (I V) \) Fractional in a dye distillation
\( \mathbf{A} \cdot A-I, B-I I, C-I I I, D-I V \)
B . \( A-I I, B-I V, C-I I I, D-I \)
c. \( A-I V, B-I I I, C-I, D-I I \)
D. \( A-I V, B-I I I, C-I I, D-I \)
Subject: Chemistry
The rate of a certain reaction at different times are as follows:
\( \begin{array}{ll}\text { Time } & \text { rate }\left(\text { mole } l i t^{-1} \sec ^{-1}\right) \\ \text {1) } 0 & \text { a) } 2.8 \times 10^{-2}\end{array} \) ") 10 \( \quad \) b) \( 2.78 \times 10^{-2} \) -2 A
\( \begin{array}{ll}\text { III) } 20 & \text { с) } 2.81 \times 10^{-2}\end{array} \) -2
\( \begin{array}{ll}\text { ।V) } 30 & \text { d) } 2.79 \times 10^{-2}\end{array} \) \( j \) \( ^{2} \)
The correct matching is:
A. zero order
B. first order
c. second order
D. third order
Subject: Physics
The motion of a particle is described by
\( \boldsymbol{x}=\mathbf{3 0} \sin (\boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{6}), \) where \( \boldsymbol{x} \) is in \( \boldsymbol{c m} \)
and \( t \) in sec. Potential energy of the
particel is twice of kinetic energy for the first time after \( t=0 \) when the particle
is at position after
time.
Subject: Chemistry
Calculate the percent of hydrolysis in a \( \mathbf{0 . 0 6} M \) solution of \( \boldsymbol{K} \boldsymbol{C} \boldsymbol{N} \)
Use \( :\left[\boldsymbol{K}_{a(\boldsymbol{H} C N)}=\boldsymbol{6} \times \mathbf{1 0}^{-\mathbf{1 0}}\right] \)
A . \( 1.667 \% \)
B . \( 7.45 \% \)
c. \( 34.67 \% \)
D. None of these
Subject: Chemistry
The incorrect IUPAC name is:
\( \mathbf{A} \cdot C H_{3}-C O-C H\left(C H_{3}\right)-C H_{3}: 2- \) methyl-3-butanone
\( \mathbf{B} \cdot C H_{3}-C H\left(C H_{3}\right)-C H\left(C H_{2} C H_{3}\right)-C H_{3}: 2,3 \)
dimethylpentane
\( \mathbf{c} \cdot C H_{3}-C \equiv C-C H\left(C H_{3}\right) \quad \) 2,4-Methyl-2-pentyne
D. \( C H_{3}-C H(C l)-C H(B r)-C H_{3}: 2- \) bromo-3
chlorobutane
Subject: Chemistry
Calculate the rate constant of a
reaction at \( 293 K \) when the energy of
activation is \( 103 k J \) mol\( ^{-1} \) and the rate
constant at \( 273 K \) is \( 7.87 \times 10^{-7} s^{-1} \)
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{k J} \mathbf{m o l}^{-\mathbf{1}} \mathbf{K}^{-1}\right) \)
Subject: Chemistry
Two moles of a perfect gas undergo the following process:
(a) A reversible isobaric expansion from
\( (1 \operatorname{atm} \operatorname{to} 20 L) \) to \( (1 \operatorname{atm} \operatorname{to~} 40 L) \)
(b) A reversible isochoric change of
state from \( (1 \text { atm to } 40 L) \) to \( (0.5 \) atm to
\( 40 L) \)
(c) A reversible isothermal
compression from \( (0.5 \text { at } m \text { to } 40 L) \) to
\( 1 \text { atm to } 20 L) \)
(i) Sketch with labels each of the
process on the same P-V diagram.
(ii) Calculate the total work \( (w) \) and the
total change \( (q) \) involved in the above
process
(iii) What will be the value of
\( \Delta U, \Delta H, \Delta S \) for the overall process?
Subject: Physics
A trolley of mass \( 20 \mathrm{kg} \) is attached to a
block of mass \( 4 \mathrm{kg} \) by a massless string passing over a frictionless pulley as
shown in the figure. If the coefficient of
kinetic friction between trolley and the surface is \( 0.02, \) then the acceleration of
the trolley and block system is:
(Take \( \left.g=10 m s^{-2}\right) \)
\( A \cdot 1 m s^{-2} \)
B. \( 2 m s^{-2} \)
\( \mathbf{C} \cdot 1.5 \mathrm{ms}^{-2} \)
D. \( 2.5 \mathrm{ms}^{-2} \)
Subject: Maths
Let \( k \) be a positive real number and let
\[
\begin{array}{l}
\boldsymbol{A}=\left[\begin{array}{ccc}
2 \boldsymbol{k}-\mathbf{1} & \mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{2} \sqrt{\boldsymbol{k}} \\
\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{1} & -\mathbf{2} \boldsymbol{k} \\
-\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{2} \boldsymbol{k} & \mathbf{1}
\end{array}\right] \\
\boldsymbol{B}=\left[\begin{array}{ccc}
\mathbf{0} & \mathbf{2} \boldsymbol{k}-\mathbf{1} & \sqrt{\boldsymbol{k}} \\
\mathbf{1}-\mathbf{2} \boldsymbol{k} & \mathbf{0} & \mathbf{2} \sqrt{\boldsymbol{k}} \\
-\sqrt{\boldsymbol{k}} & -\mathbf{2} \sqrt{\boldsymbol{k}} & \mathbf{0}
\end{array}\right] \\
\text { If det }(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A}))+\operatorname{det}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{B}))=\mathbf{1 0}^{\boldsymbol{o}}
\end{array}
\]
then \( [k] \) is equal to
4
3.6
\( c \)
\( D \)
Subject: Physics
A car is travelling along a circular curve that has a radius of \( 50 \mathrm{m} \). If its speed is
\( 16 \mathrm{m} / \mathrm{s} \) and is incrcasing uniformly at \( 8 m / s^{2} . \) Determine the magnitude of its acceleration at this instant.
A \( \cdot 7.5 m s^{-2} \)
B. \( 8.5 m s^{-2} \)
c. \( 9.5 m s^{-2} \)
D. \( 9.8 m s^{-2} \)
Subject: Physics
The de Broglie wavelength of an electron
accelerated by an electric field of \( V \) volt is given by:
A \( \cdot \lambda=\frac{1.23}{\sqrt{m}} \)
в. \( \lambda=\frac{1.23 m}{\sqrt{h}} m \)
c. \( \lambda=\frac{1.23}{\sqrt{V}} n m \)
D. \( \lambda=\frac{1.23}{V} \)
Subject: Maths
Mean of 10 observations is 50 and their
standard deviation is \( 10 . \) If each
observation is subtracted by 5 and then
divided by \( 4, \) then the new mean and standard deviation are
A \( .22 .45,2.5 \)
В. 11.25,2.5
c. 11.5,2.5
D. 11,2.5
E . 11.75,2.5
Subject: Maths
Equation of the ellipse whose axes are the axes of coordinates and which
passes through the point (-3,1) and has eccentricity \( \sqrt{\frac{2}{5}} \) is
A \( \cdot 5 x^{3}+3 y^{2}-48=0 \)
B . \( 3 x^{2}+5 y^{2}-15=0 \)
c. \( 5 x^{2}+3 y^{2}-32=0 \)
D. \( 3 x^{2}+5 y^{2}-32=0 \)
Subject: Chemistry
Two iron rod \( A \) and \( B \) are taken. \( A \) is
dipped in dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \boldsymbol{B} \) is first
dipped in conc. \( H N O_{3} \) and later in
dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) What will be the status
of iron rods after some time? Justify
Subject: Physics
A loaded spring gun of mass \( M \) fires a bullet of mass \( m \) with a velocity \( v \) at an
angle of elevation \( \theta \). The gun is initially at rest on a horizontal smooth surface.
After firing, the centre of mass of the
gun and bullet system
A . Moves with velocity \( \frac{v}{M} \) m
B. Moves with velocity \( \frac{v m}{M \cos \theta} \) in the horizontal direction
c. Does not move in horizontal direction
D. Moves with velocity \( \frac{v(M-m)}{M+m} \) in the horizonta direction
Subject: Physics
A point mass \( m_{0} \) is placed at a distance \( \boldsymbol{R} \)
\( \frac{n}{3} \) from the centre of a spherical shell of mass \( M \) and radius \( R \). The
gravitational force on the point mass
\( \boldsymbol{m}_{0} \) is:
\( ^{\mathrm{A}} \cdot \frac{9 G M m_{0}}{R^{2}} \)
в. \( \frac{G M m_{0}}{R^{2}} \)
c. zero
D. \( \frac{4 G M m_{0}}{R^{2}} \)
Subject: Physics
Two convex lens of focal lengths \( f_{1} \) and
\( f_{2} \) form images with magnification \( m_{1} \)
and \( m_{2}, \) when used individually for an object kept at the same distance from
the lenses. Then \( \boldsymbol{f}_{1} / \boldsymbol{f}_{2} \)
A \( \cdot \frac{m_{1}\left(1+m_{1}\right)}{m_{2}\left(1+m_{2}\right)} \)
в. \( \frac{m_{1}\left(1-m_{2}\right)}{m_{2}\left(1-m_{1}\right)} \)
c. \( \frac{m_{2}\left(1+m_{1}\right)}{m_{1}\left(1+m_{2}\right)} \)
D \( \cdot \frac{m_{2}\left(1+m_{2}\right)}{m_{1}\left(1+m_{1}\right)} \)
Subject: Maths
Fo parabola \( 3 y^{2}=16 x, \) equation of
directrix and length of latus rectum is
A \( \cdot x=\frac{-4}{3}, \frac{3}{4} \)
B. \( x=\frac{4}{3}, \frac{4}{3} \)
c. \( y=\frac{-4}{3}, \frac{4}{3} \)
D. \( x=\frac{-4}{3}, \frac{16}{3} \)
Subject: Biology
During lactic acid fermentation
A. \( O_{2} \) is used and \( C O_{2} \) is liberated
B. Neither \( O_{2} \) is used, nor \( C O_{2} \) is liberated
\( \mathrm{c} \cdot O_{2} \) is used, but \( C O_{2} \) is not liberated
D. None of the above
Subject: Chemistry
For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \) the correct
choice is:
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing
B. \( H_{3} P O_{3} \) is dibasic and non-reducing
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic and reducing
D. \( H_{3} P O_{3} \) is tribasic and non-reducing
Subject: Physics
The pressure that has to be applied to
the ends of a steel wire of length \( 10 c m \)
to keep its length constant when its
temperature is raised by \( 100^{\circ} \mathrm{C} \) is:
(For steel Young's modulus is \( 2 \times \)
\( 10^{11} N m^{-2} \) and coefficient of thermal
expansion is \( 1.1 \times 10^{-5} K^{-1} \) )
A \( \cdot 2.2 \times 10^{7} \) Ра
B . \( 2.2 \times 10^{6} \) ра
c. \( 2.2 \times 10^{8} \) Pa
D. \( 2.2 \times 10^{9} \) pa
Subject: Physics
A pyramid has a square base of side \( a \) and four faces which are equilateral triangles. A charge \( Q \) is placed on the centre of the base of the pyramid. What is the net flux of electric field emerging from one of the triangular faces of the
pyramid?
A. 0
в. \( \frac{Q}{8 \epsilon_{0}} \)
c. \( \frac{Q a^{2}}{8 \epsilon_{0}} \)
D. \( \frac{Q}{2 \epsilon_{0}} \)
Subject: Maths
In the given figure, 0 is the centre of the
circle and XOY is a diameter. If \( X Z \) is
any other chord of the circle, then which
of the following is correct?
\( A \cdot X Z<O Z \)
8. \( x y>x z \)
\( c \cdot 0 x+0 z \)
D. zX + ZY
Subject: Maths
Stat whether the following pairs of sets
are equal or not
(I) \( A=\{x: x \text { is a letter of the world 'paper' }\} \) and \( A=\operatorname{set} \) of digits in the number 59672
(ii) \( A=\{x: x \text { is a letter of the world 'pepar' }\} \) and \( \mathrm{B}=\operatorname{set} \) of digits in the number 756889
Subject: Physics
toppr
Q Type your question
Thumbtacks were fixed with wax on
each material and then the materials
were fixed to a trough containing hot water as shown in the diagram. Vijay tabulated his results as shown here.
Time taken for thumbtacks to Material drop(minutes)
5
0
6
2
What can be inferred from his
experiment?
A. Material R is a better conductor of heat than material
\( S \)
B. Material S is a better conductor of heat than material
\( \mathrm{R} \)
C. Material Q is a better conductor of heat than material
\( P \)
D. Materials \( \mathrm{P}, \mathrm{Q}, \mathrm{R} \) and \( \mathrm{S} \) are equally good conductors of heat.
Subject: Physics
A wire of initial length \( L \) and radius \( r \) is
stretched by a length \( l \). Another wire of same material but with initial length \( 2 L \) and radius \( 2 r \) is stretched by a
length \( 2 l \). The ratio of stored elastic
energy per unit volume in the first and
second wire is:
A .1: 4
B. 1: 2
c. 2: 1
D. 1: 1
Subject: Physics
Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of
\( 3 m s^{-1} \) and \( 2 m s^{-1} \) respectively. They collide with each other. After collision,
glass sphere of mass 10 g moves with a velocity of \( 2.5 m s^{-1} . \) Find the velocity of the second ball after collision.
A \( .2 .25 m s^{-1} \)
B. \( 5.5 m s^{-1} \)
\( \mathbf{c} \cdot 2.75 m s^{-1} \)
D. \( 7.5 m s^{-1} \)