AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The mean square deviation of set of \( n \)
observations \( x_{1}, x_{2}, \ldots . . x_{n} \) about a point \( c \) is defined as \( \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-c\right)^{2} \)
The mean square deviation about -2 and 2 are 18 and 10 respectively, then standard deviation of this set of
observations is
A . 3
B. 2
c. 1
D. none of these
Subject: Maths
Solve \( : \frac{3}{x+y}+\frac{2}{x-y}=2 \) and
\( \frac{9}{x+y}-\frac{4}{x-y}=1 \)
A. \( x=\frac{2}{5} ; y=\frac{7}{2} \)
B. \( x=\frac{5}{2} ; y=\frac{1}{2} \)
c. \( x=\frac{6}{7} ; y=\frac{4}{3} \)
D. \( x=\frac{7}{3} ; y=\frac{1}{2} \)
Subject: Physics
The truth-table given below is for which gate?
\( \begin{array}{lll}A & B & C \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
A. xor
B. OR
c. AND
D. NAND
Subject: Maths
Consider \( \boldsymbol{a} \boldsymbol{z}^{2}+\boldsymbol{b} \boldsymbol{z}+\boldsymbol{c}=\mathbf{0}, \) where
\( a, b, c \in R \) and \( 4 a c>b^{2} \)
In the argand's plane. if \( A \) is the point
represnting \( z_{1} . \) B is the point representing \( z_{2} \) and \( z=\frac{\overrightarrow{O A}}{\partial B} \) then z is:
A. z is purely real
B. z is purely imaginary
c \( \cdot|z|=1 \)
D. \( \Delta A O B \) is a scalene triangle
Subject: Chemistry
A cylinder of gas is assumed to contains 14 kg of butane. If a normal family needs \( 20,000 \mathrm{kJ} \) of energy per day for cooking, The cylinder will last:
(Given : The enthalpy of combustion, \( -\Delta H=-2658 \mathrm{kJ} / \) mole for butane
A. 24.33 days
B. 28.44 days.
c. 29.33 days
D. 32 days.
Subject: Physics
The ratio of maximum to minimum
intensity due to superposition of two waves is \( \frac{49}{9} . \) Then the ratio of the
intensity of component waves is
A \( \cdot \frac{25}{4} \)
в. \( \frac{16}{25} \)
c. \( \frac{4}{49} \)
D. \( \frac{9}{49} \)
Subject: Physics
A system of three charges are placed as shown in the figure:
If \( D>>d \) the potential energy of the
system is best given by
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}-\frac{q Q d}{2 D^{2}}\right] \)
в. \( \frac{1}{4 \pi \varepsilon_{0}}\left[+\frac{q^{2}}{d}+\frac{2 q Q d}{D^{2}}\right] \)
c. \( \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}+\frac{q Q d}{D^{2}}\right] \)
D. \( \frac{1}{4 \pi \varepsilon_{0}}\left[-\frac{q^{2}}{d}-\frac{q Q d}{D^{2}}\right] \)
Subject: Maths
From \( 8-y+2 y^{2} \) take away
\( \left(y^{2}-7-2 y\right) \)
A \( \cdot y^{2}+y+15 \)
B. \( 5 y^{2}-1 \)
c. \( 3 y-7 y^{2}+11 \)
D. None of these
Subject: Physics
Find the circulation of the vector \( \vec{B} \)
around the square path \( \Gamma \) with side \( l \)
located as shown in the figure above.
\( \mathbf{A} \cdot \oint \vec{B} d r=2(1-\mu) B l \sin \theta \)
в. \( \oint \vec{B} d r=(1+\mu) B l \sin \theta \)
c. \( \oint \vec{B} d r=2(1-+\mu) B l \sin \theta \)
D. \( \oint \vec{B} d r=(1-\mu) B l \sin \theta \)
Subject: Maths
In which of the following situations, does the list of numbers involved make
an arithmetic progression, and why?
(i) The taxi fare after each \( \mathrm{km} \) when the
fare is Rs.15 for the first \( \mathrm{km} \) and Rs. 8
for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes
\( \frac{1}{4} \) of the air remaining in the cylinder at a time.
(iii) The cost of digging a well after every metre of digging, when it costs Rs.
150 for the first metre and rises by Rs.
50 for each subsequent metre.
(iv) The amount of money in the
account every year, when Rs. 10000 is deposited at compound interest at \( 8 \% \)
per annum.
Subject: Maths
If \( A \) and \( B \) are any two events such that \( P(A)=\frac{2}{5} \) and \( P(A \cap B)=\frac{3}{20}, \) then
the condition probability, \( \boldsymbol{P}\left(\boldsymbol{A} \mid \boldsymbol{A}^{\prime} \cup\right. \)
\( \left.B^{\prime}\right) \), where \( A^{\prime} \) denotes the complement
of \( A, \) is equal to:
A \( \cdot \frac{5}{17} \)
в. \( \frac{11}{20} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{8}{17} \)
Subject: Maths
Construct a \( \triangle A B C \) in which:
\( \boldsymbol{A B}+\boldsymbol{B C}+\boldsymbol{A C}=\mathbf{1 1 . 8 c m}, \angle \boldsymbol{B}= \)
\( 60^{\circ} \) and \( \angle C=45^{\circ} \)
Subject: Chemistry
For rusting of iron to take place
are required.
\( A \cdot O_{2} \) and \( C O_{2} \)
B. \( H_{2} O \) and \( N_{2} \)
\( \mathbf{c} \cdot H_{2} O \) and \( O_{2} \)
D. \( H_{2} O \) and \( H_{2} \)
Subject: Maths
In the circular lawn, there is a \( 16 \mathrm{m} \) long path in the form of a chord. If the path is \( 6 \mathrm{m} \) away from the centre of the lawn, then the radius of the circular lawn is
A. \( 16 \mathrm{m} \)
B. \( 6 \mathrm{m} \)
c. \( 10 \mathrm{m} \)
D. 8 m
Subject: Physics
A wave is represented by the equation \( \boldsymbol{y}=\boldsymbol{A} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) \) where \( \boldsymbol{x} \)
is in meters and \( t \) is in seconds. The
expression represents:
A. a wave travelling in the positive \( x \) -direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
B. a wave travelling in the negative \( x \) -direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
c. a wave travelling in the negative \( x \) -direction having a wavelength \( 0.2 m \)
D. a wave travelling in the positive \( x \) -direction having a wavelength \( 0.2 m \)
Subject: Maths
If \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{b}=\boldsymbol{a}+\mathbf{1}, \boldsymbol{a} \in \mathbb{Z}, \boldsymbol{0}< \)
\( a<5\} \) then find the range of \( R \)
Subject: Physics
The mean life time of a radionuclide, if
its activity decreases by \( 4 \% \) for every \( 1 h \) would be (product is non-radioactive,
i.e., stable)
A . \( 25 h \)
в. \( 1.042 h \)
\( c \cdot 2 h \)
D. \( 30 h \)
Subject: Maths
Let \( g:[1,3] \rightarrow Y \) be a function defined
\( \operatorname{as} g(x)=\ln \left(x^{2}+3 x+1\right) . \) Then
(a) Determine whether \( g(x) \) one-one or
many-one.
(b) Find the set \( Y \), so that \( g(x) \) is onto.
(c) Find \( g^{-1}(x) \), if it exists.
Subject: Maths
Construct a \( \triangle A B C, \) when \( A B= \)
\( \mathbf{5} . \mathbf{2} \mathbf{c m}, \angle \mathbf{A}=\mathbf{3 0}^{\circ} \) and \( \angle \mathbf{B}=\mathbf{7 5}^{\circ} \)
Subject: Physics
net acceleration of block \( \mathrm{B}, \) when
extension in the spring is \( \boldsymbol{x}=\frac{\boldsymbol{x}_{\boldsymbol{m}}}{\boldsymbol{4}} \)
A \( \cdot \frac{g}{2}(\text {downwards}) \)
B. \( \frac{g}{3}(\text {downwards}) \)
c. \( \frac{g}{4}(\text {downwards}) \)
D. \( \frac{g}{6}(\text {downwards}) \)
Subject: Physics
The adjoining diagram shows the
spectral energy density distribution \( \boldsymbol{E}_{\lambda} \)
of a black body at two different temperatures. If the areas under the curves are in the ratio \( 16: 1, \) the value
of temperature \( \boldsymbol{T} \) is :
A . \( 32,000 K \)
в. 16,000 К
c. \( 8,000 K \)
D. 4,000 К
Subject: Chemistry
\( \left(\boldsymbol{C O}+\boldsymbol{H}_{2}\right)+\boldsymbol{H}_{2}^{\boldsymbol{6} 73 \boldsymbol{k}, 300 a t \boldsymbol{m}, / C r_{2}} \overrightarrow{\boldsymbol{O}_{3}-\boldsymbol{Z} n \boldsymbol{O}} \)
The above shown reaction may by used for manufacture of:
A. \( H C H O \)
в. \( C H_{3} \) СООН
с. НСООН
D. \( C H_{3} O H \)
Subject: Physics
A solid cylinder of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is (h is the height of inclined plane) :
A. \( \sqrt{2 g h} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{\frac{3}{4} g h} \)
D. \( \sqrt{\frac{4 g}{h}} \)
Subject: Chemistry
Which represents one mole?
This question has multiple correct options
\( \mathbf{A} \cdot 22.4 L H e \) at \( S T P \)
\( \mathbf{B} \cdot 16 g O_{2} \)
\( \mathbf{c} \cdot 158 g K M n O_{4} \)
D. \( 392 g \) FeSO\( _{4} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot 6 H_{2} O \)
Subject: Maths
The inverse of statement" If a
quadrilateral is a rectangle,then it has two pairs of parallel sides."
A. If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides.
B. If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
C. If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle.
D. None of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log \left(2 \boldsymbol{x}-\boldsymbol{x}^{2}\right)} . \) Then, dom
\( (f)=? \)
A \( .(0,2) \)
B. [1,2]
\( c \cdot(-\infty, 1] \)
D. None of these
Subject: Physics
If \( \bar{A} \times \bar{B}=\bar{C} \) which of the following
statement is not correct?
A. \( \bar{C} \) T \( \bar{A} \)
в. \( \bar{C} \) Т \( \bar{B} \)
c. \( \bar{C} \) T \( \bar{A} \times \bar{B} \)
D. \( \bar{C} \top \bar{A}+\bar{B} \)
Subject: Chemistry
Which of the following can show coordination isomerism?
(i) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t C l}_{4}\right] ; \) (ii)
\( \left[\boldsymbol{F e}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]_{2}\left[\boldsymbol{P t}(\boldsymbol{C N})_{6}\right]_{3} \quad ; \) (iii)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] ; \) (iv)
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{3}\right]\left(\boldsymbol{S O}_{4}\right)_{2} \)
Subject: Chemistry
Which one of the following statements
İs incorrect?
A. All halogens have weaker \( X \) -X bond than \( X \) - X' bond, in interhalogens (except F-F bond in fluorine)
B. Radius ratio between iodine and fluorine (among halogens) is maximum
C. Interhalogen compounds are more reactive than halogen compounds
D. Among interhalogen compounds, maximum number of atoms are present in iodine fluoride
Subject: Maths
If \( L_{1} L_{2} \) is the latusrectum of \( y^{2}=12 x \)
\( P \) is any point on the directrix then the
\( \operatorname{area~of} \Delta P L_{1} L_{2}= \)
\( A \cdot 32 \)
B . 18
\( c .36 \)
D. 16
Subject: Physics
Point out the wrong statement about the magnetic properties of soft iron and
steel
A. Retentivity of soft iron is more than retentivity of steel
B. Coercivity of soft iron is less than coercivity of steel.
c. Area of B-H loop in soft iron is smaller than the area of B-H loop for steel
D. Area of B-H loop in soft iron is greater than the area of B-H loop for steel
Subject: Chemistry
Assertion
\( \mathbf{\Psi} \) indicates the amplitude of electron -
wave
Reason
\( \mathbf{\Psi}^{2} \) denotes the probability of finding an
electron in the space around the
nucleus.
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: Chemistry
\( S b F_{5} \) reacts with \( X e F_{4} \) and \( X e F_{6} \) to
form ionic compounds \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}\right]\left[\boldsymbol{S} \boldsymbol{b} \boldsymbol{F}_{6}^{-}\right] \)
and \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}^{-}\right] . \) The geometry of
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+},\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right] \) ion respectively is:
A. square pyramidal, T-shaped
B. bent T-shaped, square pyramidal
c. see-saw, square pyramidal
D. square pyramidal, see saw
Subject: Chemistry
The metabolism of an antibiotic, \( ^{\prime} \boldsymbol{A}^{\prime} \) is
first-order rate process. The rate constant 'K' for this process depends on temperature and body weight but for a
70 kg man at \( 37^{\circ} \mathrm{C} \) its value is \( \boldsymbol{K}= \) \( 3.0 \times 10^{-5} \mathrm{sec}^{-1} . \) How long after taking
the first pill containing \( 400 \mathrm{mg} \) of antibiotic must this man take the
second pill to keep the concentration at
200 mg per 100 kg body weight? (Assume instantaneous uniform distribution of the antibiotic
throughout the body?
A \( \cdot 0.7 \times 10^{4} \sec \)
B. \( 1.5 \times 10^{4} \) sec
c. \( 1.4 \times 10^{4} \) sec
D. \( 3.6 \times 10^{4} \) sec
Subject: Maths
For each graph given below, four linear equations are given. Out of these find the equation that represents the given
graph.Equations are
A) \( y=x \)
B) \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \)
C) \( y=2 x \)
D) \( 2+3 y=7 x \)
Subject: Chemistry
The electron revolves only in the orbits
in which
A \( \cdot m v r=\frac{n h}{2 \pi} \)
B. \( m v r \geq \frac{n h}{2 \pi} \)
c. \( m v r>\frac{n h}{2 \pi} \)
D. \( _{m v r}<\frac{n h}{2 \pi} \)
Subject: Physics
another prism of refractive index \( n_{2} \) are
struck together without a gap as shown,
\( \boldsymbol{n}_{1} \) and \( \boldsymbol{n}_{2} \) depend upon \( \boldsymbol{\lambda} \) the wave
length of light according ton \( _{1}=1.2+ \) \( \frac{10.8 \times 10^{4}}{\lambda^{2}} \) and \( n_{2}=1.45+\frac{1.8 \times 10^{4}}{\lambda^{2}} \)
where \( \lambda \) is in nanometer.
(a)Calculate the wave length \( \lambda_{0} \) for
which rays incident at any angle on the
interface pass through without bending
a the interface.
(b)For light of wave length \( \lambda_{0} \) for which
rays incident on the face \( A C \) such that
the deviated produced by the
combination of the prism is minimum.
Subject: Physics
Assertion
Kepler's second law can be understood by conservation of angular momentum principle.
Reason
Kepler's second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as \( (\boldsymbol{d A} / \boldsymbol{d t})=\left(\boldsymbol{r}^{2} \boldsymbol{\omega}\right) / 2 \)
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
In the figure shown in thin parallel beam of light is incident on a plane
mirror \( \boldsymbol{m}_{1} \) at small angle \( ^{\prime} \boldsymbol{\theta}^{\prime} \boldsymbol{m}_{2} \) is a
concave mirror of focal length ' \( f^{\prime} \). After
three successive reflections of this
beam the \( x \) and \( y \) coordinates of the
image is:
A \( . x=f-d, y=f \theta \)
B. \( x=f+d, y=f \)
c. \( x=f-d, y=-f \theta \)
D. \( x=d-f, y=-f \theta \)
Subject: Maths
If \( \vec{b}=3 \hat{i}+4 \hat{j} \) and \( \vec{a}=\hat{i}-\hat{j}, \) the vector
having the same magnitude as that of \( \vec{b} \) and parallel to \( \vec{a} \) is
A \( \cdot \frac{5}{\sqrt{2}}(\hat{i}-\hat{j}) \)
B. \( \frac{5}{\sqrt{2}}(\hat{i}+\hat{j}) \)
c. \( 5(\hat{i}-\hat{j}) \)
D. \( 5(\hat{i}+\hat{j}) \)
Subject: Maths
Solution of \( (x+y)^{2} \frac{d y}{d x}=a^{2}\left(^{\prime} a^{\prime} \) being a \right.
constant) is:
A \( \cdot \frac{(x+y)}{a}=\tan \frac{y+c}{a}, c \) is an arbitrary constant
B. \( x y=a \tan c x, c \) is an arbitrary constant
c. \( \frac{x}{a}=\tan \frac{y}{c}, c \) is an arbitrary constant
D. \( x y=\tan (x+c), c \) is an arbitrary constant
Subject: Maths
The following table shows the number of workers in a factory and their daily wages. Find the median of the daily
wages.
\( \begin{array}{llll}\text { Daily } & \mathbf{1 0 0}- & \mathbf{1 1 0}- & \mathbf{1 2 0}- \\ \text { wages(Rupees) } & \mathbf{1 1 0} & \mathbf{1 2 0} & \mathbf{1 3 0}\end{array} \)
No. of workers 37
38
Subject: Biology
Which of the following layers you will find in the body wall of earthworm (from outside to inside)?
A. Non-cellular cuticle, epidermis, circular muscles longitudinal muscles, coelomic epithelium
B. Cuticle, epidermis, longitudinal muscles, circular muscles, coelomic epithelium
c. Non-cellular cuticle, epidermis, coelomic epithelium, circular muscles, longitudinal muscles
D. Cuticle, epidermis, peritoneal muscles
Subject: Maths
Heights of the pupils of a particular school are given. Draw greater than cumulative curve and find the median
height from it.
\( 110-\quad 120 \)
\( \begin{array}{ll}90- & 100- \\ 100 & 110\end{array} \) Height
(in \( \mathrm{cm} \) ) 120 13.
Number of pupils
Subject: Maths
If \( C_{0} . C_{1}, C_{2}, \dots, C_{n} \) are the coefficients
of the expansion of \( (1+x)^{n}, \) then the value of \( \sum_{0}^{n} \frac{C_{k}}{k+1} \) is
A .
в. \( \frac{2^{n}-1}{n} \)
c. \( \frac{2^{n+1}-1}{n+1} \)
D. None of these
Subject: Physics
A particle starts moving rectilinearly at time \( t=0 \) such that its velocity \( v \)
changes with time \( t \) according to the equation \( \boldsymbol{v}=\boldsymbol{t}^{2}-\boldsymbol{t}, \) where \( \boldsymbol{t} \) is in
seconds and \( v \) is in \( m s^{-1} \). The time
interval for which the particle retards (i.e., magnitude of velocity decreases) is:
A. \( t<1 / 2 \)
B. \( 1 / 2<t<1 \)
\( c \cdot t>1 \)
D. \( t<1 / 2 \) and \( t>1 \)
Subject: Physics
Given below are some functions of \( x \) and
\( t \) to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these
represent (i) a travelling wave (ii) a stationary wave or (iii) none at all:
(a) \( y=2 \cos (3 x) \sin (10 t) \)
(b) \( y=2 \sqrt{x-v t} \)
(c) \( y=3 \sin (5 x-0.5 t)+4 \cos (5 x- \)
\( \mathbf{0 . 5 t} \)
(d) \( y=\cos x \sin t+\cos 2 x \sin 2 t \)
Subject: Physics
A particle executes simple harmonic oscillation with an amplitude \( a \). The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
A \( \cdot \frac{T}{4} \)
в. \( \frac{T}{8} \)
c. \( \frac{T}{12} \)
D. \( \frac{T}{2} \)
Subject: Chemistry
Statement \( 1: A \) 0.2 \( M \) solution of
carbonic Acid is a weaker conductor of
electricity than a \( 0.2 \mathrm{M} \) solution of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
Statement 2: In solutions with the
same concentration of solute
molecules, \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) is less dissociated
than \( H B r \)
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and 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.
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
In a room where the temperature is
\( 30^{\circ} \mathrm{C}, \) a body cools from \( 61^{\circ} \mathrm{C} \) to \( 59^{\circ} \mathrm{C} \)
in 4 min. The time (in min) taken by the
body to cool from \( 51^{\circ} \mathrm{C} \) to \( 49^{\circ} \mathrm{C} \) will be:
A . 4
B. 6
c. 5
D.
Subject: Chemistry
When chlorine reacts with a gas \( X, \) an explosive inorganic compound Y is formed. Then X and Y will be:
A. \( X=O_{2} \) and \( Y=N C l_{3} \)
B. \( X=N H_{3} \) and \( Y=N C l_{3} \)
c. \( X=O_{2} \) and \( Y=N H_{4} C l \)
D. \( X=N H_{3} \) and \( Y=N H_{4} C l \)
Subject: Maths
Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop
harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
Subject: Physics
A light spring of force constant \( \boldsymbol{K} \) is
held between two blocks of masses \( m \)
and \( 2 m . \) The two blocks and the spring system rests on a smooth horizontal
floor. Now the blocks are moved towards
each other compressing the spring by \( x \) and then they are suddenly released. The relative velocity between the blocks when the spring attains its natural length will be
\( ^{\mathrm{A}} \cdot(\sqrt{\frac{3 K}{2 m}}) x \)
\( ^{\mathrm{B}} \cdot(\sqrt{\frac{2 K}{3 m}}) x \)
\( ^{c \cdot}(\sqrt{\frac{K}{3 m}}) x \)
\( ^{\mathrm{D} \cdot}(\sqrt{\frac{K}{2 m}}) x \)
Subject: Chemistry
Which of the following is correct increasing order of molecular mass?
A. \( H_{2} O<H C l<H_{2} S<C O_{2} \)
в. \( H_{2} O<H_{2} S<H C l<C O_{2} \)
c. \( H_{2} O<C O_{2}<<H C l<H_{2} S \)
D. \( H C l<H_{2} S<H_{2} O<C O_{2} \)
Subject: Maths
The direction angles of the line \( x= \)
\( \mathbf{4} z+\mathbf{3}, \boldsymbol{y}=\mathbf{2}-\mathbf{3} z \) are \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma, \) then
\( \cos \alpha+\cos \beta+\cos \gamma= \)
A \( \cdot \frac{2}{\sqrt{26}} \)
B. \( \frac{8}{\sqrt{26}} \)
c. 1
D. 2
Subject: Physics
Three variable Boolean expression \( \boldsymbol{P Q}+\boldsymbol{P Q R}+\overline{\boldsymbol{P}} \boldsymbol{Q}+\boldsymbol{P} \overline{\boldsymbol{Q}} \boldsymbol{R} \operatorname{can} \mathrm{be} \)
written as
A. \( \bar{Q}+\bar{P} R \)
в. \( \bar{P}+\bar{Q} R \)
c. \( Q+P R \)
D. \( Q+\sqrt{P} R \)
E . \( P+Q R \)
Subject: Chemistry
Which is true for the combustion of
\( \operatorname{sucrose}\left(C_{12} H_{22} O_{11}\right) \) at \( 25^{\circ} C ? \)
\( \mathbf{A} \cdot \Delta H>\Delta E \)
в. \( \Delta H<\Delta E \)
c. \( \Delta H=\Delta E \)
D. None
Subject: Chemistry
Assertion
Ethanol boils at lower temperature than
ethane.
Reason
The molecular weight of ethanol is
higher than that of ethane.
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
The amplitude of simple harmonic motion represented by the displacement equation \( y(c m)=4(\sin 5 \) \( \pi t+\sqrt{2} \cos 5 \pi t) \) is :
\( A \cdot 4 \mathrm{cm} \)
B. \( 4 \sqrt{2} \mathrm{cm} \)
c. \( 4 \sqrt{3} \mathrm{cm} \)
D. \( 4(\sqrt{2}+1) \) cm
Subject: Chemistry
Which molecule pair do not have
identical structure
\( \mathbf{A} \cdot I_{3}^{-}, B e F_{2} \)
в. НС го\( , \) \( , \)О О\( _{2} \)
\( \mathbf{c} \cdot B F_{3}, I C l_{3} \)
D. \( B r F_{4}^{-}, X e F_{4} \)
Subject: Chemistry
Among the following complexes, the diamagnetic complexes are
\( (\boldsymbol{K}): \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( (L):\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
\( (M): N a_{3}\left[C o(\text {oxalate})_{3}\right] \)
\( (N):\left[N i\left(H_{2} O\right)_{6}\right] C l_{2} \)
\( (\boldsymbol{O}): \boldsymbol{K}_{2}\left[\boldsymbol{P} \boldsymbol{t}(\boldsymbol{C} \boldsymbol{N})_{4}\right. \)
\( (\boldsymbol{P}):\left[\boldsymbol{Z n}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
A. \( K, L, M, N \)
в. \( K, M, O, P \)
c. \( L, M, O, P \)
D. \( L, M, N, O \)
Subject: Chemistry
Which of the following salts when dissolved in water will produce an
acidic solution?
\( \mathbf{1} \cdot \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{C l} \)
2. \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4} \)
3. \( \boldsymbol{N a C N} \)
A .2 and 3
B. 1 and 2
c. only 3
D. 2 and 4
Subject: Physics
Positive and negative point charges of equal magnitude are kept at \( \left(0,0, \frac{a}{2}\right) \) and \( \left(0,0, \frac{-a}{2}\right) \)
respectively. The work done by the electric field when another positive
point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is
A. Positive
B. Negative
c. zero
D. Depends on the path connecting the initial and final positions
Subject: Maths
Let \( [x] \) be the greatest integer function
\( f(x)=\frac{\sin \frac{1}{4} \pi[x]}{[x]} \) is-
This question has multiple correct options
A. not continuous at any point
B. continuous at \( \frac{3}{2} \)
c. discontinuous at 2
D. differentiable at \( \frac{4}{3} \)
Subject: Physics
Two equal drops are falling through air
with a steady velocity of \( 5 \mathrm{cm} s^{-1} . \) If the drop coalesces, the new terminal velocity will become:
A. \( 5 \times 2 c m s^{-1} \)
B . \( 5 \times \sqrt{2} \mathrm{cms}^{-1} \)
C \( .5 \times(4)^{\frac{1}{3}} \mathrm{cm} s^{-1} \)
D. \( \frac{5}{\sqrt{2}} c m s^{-1} \)