AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\cos [\boldsymbol{2} \boldsymbol{\pi}] \boldsymbol{x}+\cos [-2 \boldsymbol{\pi}] \boldsymbol{x}, \) where
\( [x] \) stands for the greatest integer function, then

This question has multiple correct options
A. \( f(\pi / 2)=-1 \)
B. \( f(\pi)=+1 \)
c. \( f(-\pi)=0 \)
D. \( f(\pi / 4)=1 \)
Subject: Chemistry
The hybridization of iron in
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is?
A \( \cdot d s p^{2} \)
B \( \cdot s p^{3} \)
c. \( d^{2} s p^{3} \)
D. \( d^{2} s p^{2} \)
Subject: Physics
A circuit has a self-inductance of \( 1 \boldsymbol{H} \)
and carries a current of \( 2 A . \) To prevent sparking, when the circuit is switched off, a capacitor which can withstand
\( 400 V \) is used. The least capacitance of
the capacitor connected across the
switch must be equal to
A. \( 50 \mu F \)
B. \( 25 \mu F \)
c. \( 100 \mu F \)
D. \( 12.5 \mu F \)
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=\frac{x^{2}}{1+x^{2}} \forall x \in R \) is
A. one one but not onto
B. onto but not one one
c. a bijection
D. neither one one nor onto
Subject: Chemistry
Given below the phase diagram of
carbon, answer the following questions:
(a) How many triple points are there and
what are the phases that can co-exist at
each triple point?
(b) Which has a higher density, diamond?
A \( . \) (a) \( 1,(b) \) Diamond \( d \)
B. (a) 2, (b) Diamond
c. (a) \( 2, \) (b) Graphite
D. (a) \( 1, \) (b) Graphite
Subject: Chemistry
Which of the following homologous series has incorrect general formula?
A. Alkyne \( C_{n} H_{2 n-2} \)
B. Alkanol \( C_{n} H_{2 n+2} O \)
c. Alkanal \( C_{n} H_{2 n+1} O \)
D. carboxylic acid \( C_{n} H_{2 n} O_{2} \)
Subject: Chemistry
Select the correct IUPAC name from
following.
A. Diamminesilver (I) chloride: \( \left[\operatorname{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl} \)
B. Potassium cyanidoferrate (III) : K \( _{3} \) [Fe(CN) \( _{6} \) ]
C. Tetraamminecopper sulphate : [Cu(NHz),]SO
D. Hexamminecobalto
(III) chloride : [Co(NH_) \( \left._{6}\right] \) Сз \( _{3} \)
Subject: Physics
A point traversed half the distance with
a velocity \( v_{0} . \) The remaining part of the
distance was covered with velocity \( \boldsymbol{v}_{1} \)
for half the time, and with velocity \( v_{2} \) for the other half of the time. If the mean
velocity of the point averaged over the
whole time of motion is \( \langle\boldsymbol{v}\rangle= \)
\( \frac{\boldsymbol{x} \boldsymbol{v}_{0}\left(\boldsymbol{v}_{1}+\boldsymbol{v}_{2}\right)}{\mathbf{2} \boldsymbol{v}_{0}+\boldsymbol{v}_{1}+\boldsymbol{v}_{2}} . \) Find \( \boldsymbol{x} \)
Subject: Maths
\( f x \neq 0 \) and \( \left|\begin{array}{ccc}1 & x & 2 x \\ 1 & 3 x & 5 x \\ 1 & 3 & 4\end{array}\right|=0, \) then \( x= \)
\( A \)
B. -
\( c \cdot 2 \)
\( D \ldots-2 \)
Subject: Maths
The angles of the \( \Delta A B C \) and \( \Delta D E F \)
are given as follows; \( \boldsymbol{A}=\mathbf{9 0}^{\circ}, \quad \boldsymbol{B}=\mathbf{3 0}^{\circ}, \quad \boldsymbol{D}=\mathbf{9 0}^{\circ}, \) and \( \boldsymbol{E}= \)
\( \mathbf{3 0}^{\circ} \)
If the side \( B C \) is twice the side \( E F \)
which of the following statement is
true?
\( \mathbf{A} \cdot \sin B=2 \sin E \)
B. \( \sin E=2 \sin B \)
\( c \cdot \sin B=\sin E \)
\( \mathbf{D} \cdot \sin A=\sin B \)
Subject: Maths
If \( \boldsymbol{y}=\frac{1}{\mathbf{3 - 4 x}} \) then \( \boldsymbol{y}_{n}(1) \) equals
A .
B \( \cdot(-1)^{n+1} n ! \)
c. \( n ! 4^{n}(-1)^{n+1} \)
D. None of these
Subject: Maths
The degree of the differential equation \( \boldsymbol{y}(\boldsymbol{x})=\mathbf{1}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\mathbf{1}}{\mathbf{1 . 2}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+ \)
\( \frac{1}{1.2 .3}\left(\frac{d y}{d x}\right)^{3}+\dots . . \frac{1}{1.2 .3 \dots \dots . n}\left(\frac{d y}{d x}\right)^{n} \)
is.
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
\( D \)
Subject: Physics
Three Carnot engines operate in series
between a heat source at a temperature
\( T_{1} \) and a heat sink at temperature \( T_{4} \)
(see figure). There are two other
reservoirs at temperature \( T_{2}, \) and \( T_{3}, \) as
shown, with \( T_{2}>T_{2}>T_{3}>T_{4} . \) The
three engines are equally efficient
if \( _{--} \) ?
A \( \cdot T_{2}=\left(T_{1}^{2} T_{4}\right)^{1 / 3}: T_{3}=\left(T_{1} T_{4}^{2}\right)^{1 / 3} \)
B . \( T_{2}=\left(T_{1} T_{4}^{2}\right)^{1 / 3}: T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)
c. \( T_{2}=\left(T_{1}^{3} T_{4}\right)^{1 / 4}: T_{3}=\left(T_{1} T_{4}^{3}\right)^{1 / 4} \)
D. \( T_{2}=\left(T_{1} T_{4}\right)^{1 / 2}: T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)
Subject: Chemistry
Hydrolysis of one mole of
peroxydisulphuric acid produces:
A. two moles of sulphuric acid
B. two moles of peroxymonosulphuric acid
C. one mole of sulphuric acid and one mole of peroxymonosulphuric acid
D. one mole of sulphuric acid, one mole of peroxymonosulphuric acid, and one mole of hydrogen peroxide
Subject: Maths
Minimize and maximize \( \boldsymbol{z}=\mathbf{5} \boldsymbol{x}+\mathbf{1 0} \boldsymbol{y} \)
subject to the constraints \( x+2 y \leq 120 \)
\( \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{6 0} \)
\( x-2 y \geq 0 \) and \( x \geq 0, y \geq 0 \) by
graphical method.
Subject: Chemistry
A quantity of \( P C l_{5} \) was heated in
\( \mathbf{1 0} d \boldsymbol{m}^{3} \) vessel \( \mathbf{2 5 0}^{\mathbf{0}} \boldsymbol{C} \)
\( \boldsymbol{P C l}_{5} \) g) \( \square \boldsymbol{P} \boldsymbol{C l}_{3}(g)+\boldsymbol{C l}_{2}(g) \)
At equilibrium the vessel contains \( 0 . \)
mole of \( P C l_{5} \) and 0.2 mole of \( C l_{2} \). The
equilibrium constant of the reaction is
\( ? \)
A. 0.05
B. 0.02
c. 0.025
D. 0.04
Subject: Biology
If due to some injury, the chordae tendinae of the tricuspid valve of the human heart partially becomes nonfunctional, what will be the immediate
effect?
A. The flow of blood into the pulmonary artery will be reduced
B. The flow of blood into the aorta will be slowed down
c. The pacemaker will stop working.
D. The blood will tend to flow back into the left atrium.
Subject: Maths
Munnabhai had 4 crates, with 24 eggs
in each crate costing \( R s .4 .50 \) per egg. On his bicycle. while cycling to his shop with three crates he went over a big pothole. On reaching his shop he found
that 33 eggs were broken. If he sold the remaining eggs at 6.00 per each, What loss per cent did he suffer?
Subject: Physics
An equilateral triangle has been constructed with an uniform wire whose
resistance per unit length is 4 ohm
\( c m^{-1} . \) If the length of each side of the
triangle is \( 10 c, \) the resistance across any side will be
A. 80 ohm
B. 40 ohm
c. \( \frac{80}{3} \) onm
D. \( \frac{40}{3} \) ohm
Subject: Chemistry
Assertion
Statement \( 1: H g C l_{2} \) and \( S n C l_{2} \) exist
together in an aqueous solution.
Reason

Statement \( 2: S n C l_{2} \) is a strong
reducing agent.
A. Statement 1 is true, Statement 2 is true and Statement 2 is correct explanation for Statement
B. Statement 1 is true, Statement 2 is true and Statement 2 is not the correct explanation for Statement
c. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Subject: Maths
\( \boldsymbol{I}=\int_{0}^{1} x^{2} e^{-x} d x \)
A \( \cdot_{I=1-\frac{1}{e}} \)
B \( \cdot \quad I=2-\frac{1}{e} \)
C \( \cdot \quad I=2-\frac{1}{2 e} \)
D \( \quad I=2-\frac{1}{e^{2}} \)
Subject: Maths
Find the expression equivalent to \( \frac{1}{2} y^{2}(6 x+2 y+12 x-2 y) \)
A \( \cdot 9 x y^{2} \)
\( \begin{array}{ll}2 & 2 \\ 2 & 2\end{array} \)
в. \( 18 x y \)
c. \( 3 x y^{2}+12 x \)
D. \( 9 x y^{2}-2 y^{3} \)
E \( .3 x y^{2}+12 x-y^{3}-2 y \)
Subject: Maths
The intercept made by the plane \( \vec{r} \cdot \vec{n}= \) \( q \) on the \( x \) -axis is
A \( \cdot \frac{q}{\hat{i} \cdot \vec{n}} \)
в. \( \frac{\hat{i} \cdot \vec{n}}{q} \)
\( c \cdot \frac{\hat{i} \cdot q}{n} \)
D. \( \frac{q}{|\vec{n}|} \)
Subject: Chemistry
If the energy difference between the
electronic states is \( 214.68 \mathrm{kJ} \mathrm{mol}^{-1} \)
calculate the frequency of light emitted when an electron drops form the higher to the lower state Plank's constant?
\( h=39.79 \times k J \mathrm{mol}^{-1} \)
A \( \cdot 5.39 \times 10^{14} \) cps
B. \( 5.99 \times 10^{15} \) cps
C. \( 5.99 \times 10^{14} \) cps
D. 5.39 \( \times 10^{15} \mathrm{cps} \)
Subject: Physics
A particle of mass M moves along the \( x \)
axis with speed \( V_{0} \) and collides and
sticks to a particle of mass \( m \) moving
with a speed \( V_{0} \) along y-axis. The velocity of the combined particle after the collision:
\( ^{\mathbf{A}} \cdot \frac{M \hat{i}+m \hat{j}}{(M+m)} V_{0} \)
B. \( \frac{m \hat{i}+M \hat{j}}{(M+m)} V_{0} \)
c. \( (m \hat{i}+M \hat{j}) V_{0} \)
D. Zero
Subject: Maths
Solve:
\( \int \log \left(1+x^{2}\right) d x \)
A \( \cdot x \log \left(1+x^{2}\right)-2 x+2 \tan ^{-1} x+c \)
B \( \cdot x \log \left(1+x^{2}\right)-2 x-2 \tan ^{-1} x+c \)
C \( \cdot \log \left(1+x^{2}\right)-2 x+2 \tan ^{-1} x+c \)
D. \( \log \left(1+x^{2}\right)+2 x-2 \tan ^{-1} x+c \)
Subject: Maths
If \( z \) satisfies \( |z+1|<|z-2|, \) and \( \omega= \)
\( \mathbf{3} z+\mathbf{2}+\mathbf{i}, \) then
\( \mathbf{A} \cdot|\omega+1|<|\omega-8| \)
B . \( |\omega+1|<|\omega-7| \)
c. \( \omega+\bar{\omega}>7 \)
D \( \cdot|\omega+5|<\mid \omega-4 \)
Subject: Physics
There is an electric field E in x-direction.
If the work done on moving a charge of \( 0.2 \mathrm{C} \) through a distance of \( 2 \mathrm{m} \) along a
line making an angle \( 60^{\circ} \) with \( x \) -axis is
4 J, then what is the value of E?
A. \( \sqrt{3} \) N/C
B. 4 N/C
c. \( 5 \mathrm{N} / \mathrm{c} \)
D. 20 N/C
Subject: Chemistry
Assertion
The \( S-S-S- \) bond angle in \( S_{8} \)
molecule is \( 107.8^{\circ} \)
Reason
\( S_{8} \) has a \( V \) -shape.
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 \( \theta \) is the angle between the lines whose vector equations are \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{3} \overrightarrow{\boldsymbol{i}}+\boldsymbol{2} \overrightarrow{\boldsymbol{j}}+ \)
\( 4 \vec{k}+\lambda(\vec{i}+2 \vec{j}+2 \vec{k}) \) and \( \vec{r}=5 \vec{i} \)
\( 2 \vec{k}+\mu(3 \vec{i}+2 \vec{j}+6 \vec{k}) ; \lambda \) and \( \mu \) being
parameters, then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \cos \theta=\frac{19}{21} \)
B. \( \sin \theta=\frac{19}{21} \)
\( ^{\mathbf{C}} \sin \theta=\frac{4 \sqrt{5}}{21} \)
D. \( \cos \theta=\frac{4 \sqrt{5}}{21} \)
Subject: Physics
Charges of \( +\frac{10}{3} \times 10^{-9} C \) are placed at each of the four corners of a square of
side \( 8 \mathrm{cm} . \) The potential at the intersection of the diagonals is
A. \( 150 \sqrt{2} \) volt
в. \( 1500 \sqrt{2} \) volt
c. \( 900 \sqrt{2} \) volt
D. 900 volt
Subject: Chemistry
A colorless gas ' \( x \) ' forms a brown colored
gas ' \( \boldsymbol{y}^{\prime} \) when mixed with air. \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
could be:
A. \( N O, N O_{2} \)
в. \( N O, O_{2} \)
c. \( N O_{2}, N_{2} O_{4} \)
D. \( N O, N_{2} O_{4} \)
Subject: Chemistry
Which of the following statements in
relation to the hydrogen atom is
correct?

This question has multiple correct options
A. \( 3 s \) -orbital is lower in energy than \( 3 p \) -orbital
B. \( 3 p \) -orbital is lower in energy than \( 3 d \) -orbital
C. \( 3 s \) -and \( 3 p \) -orbitals are of lower energy than \( 3 d \) -orbital
D. \( 3 s, 3 p \) -and \( 3 d \) -orbitals all have the same energy
Subject: Maths
Points \( A \& B \) are in the first
quadrant:Point 'o' isthe origin. If the slope of \( \mathrm{OA} \) is \( 1, \) slope of \( \mathrm{OB} \) is 7 and OA=OB, then the slope of AB is-
A. \( -1 / 5 \)
B . \( -1 / 4 \)
c. \( -1 / 3 \)
D. \( -1 / 2 \)
Subject: Physics
A series LCR circuit contains
inductance \( 5 m H, \) capacitance \( 2 \mu F \) and resistance \( 10 \Omega \). If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?
\( ^{\mathbf{A}} \cdot \frac{10^{5}}{\pi} H z \)
в. \( \frac{10^{-5}}{\pi} H z \)
c. \( \frac{2}{\pi} \times 10^{5} H z \)
D. \( \frac{5}{\pi} \times 10^{3} H z \)
Subject: Physics
A body initially at \( 60^{\circ} \mathrm{C} \) cools to \( 50^{\circ} \mathrm{C} \) in
10 min. What will be it's temperature at the end of the next 10 min. if the roc
temperature is \( 20^{\circ} \) C.Assume newton's
law of cooling.
A \( \cdot 42.50^{\circ} \mathrm{C} \)
B. \( 45^{\circ} \mathrm{C} \)
c. \( 40.46^{\circ} \mathrm{C} \)
D. \( 44.23^{\circ} \mathrm{C} \)
Subject: Physics
Find out the velocity of the centre of mass of two \( 1 k g \) masses moving toward
each other, one mass with velocity \( \boldsymbol{v}_{1}= \)
\( \mathbf{1 0 m} / \boldsymbol{s}, \) the other with velocity \( \boldsymbol{v}_{\mathbf{2}}= \)
\( 20 m / s \)
A. \( 0 m / s \)
B. \( 5 m / s \) to the left
c. \( 10 m / s \) to the left
D. \( 15 \mathrm{m} / \mathrm{s} \) to the left
E . \( 20 \mathrm{m} / \mathrm{s} \) to the left
Subject: Physics
The Sl unit of the universal gravitational
constant \( G: \)
\( \mathbf{A} \cdot N m K g^{-2} \)
B. \( N m^{2} K g^{-2} \)
c. \( N m^{2} K g^{-1} \)
D. \( N m K g^{-1} \)
Subject: Physics
The velocity-time graphs of a car and a
scooter are shown in the figure. (i) the difference between the distance
travelled by the car and the scooter in
\( 15 s \) and (ii) the time at which the car
will catch up with the scooter are,
respectively
A \( .337 .5 m \) and \( 25 s \)
B. \( 225.5 m \) and \( 10 s \)
c. \( 112.5 m \) and \( 22.5 s \)
D. \( 11.2 .5 m \) and \( 15 s \)
Subject: Chemistry
Arrange the acids \( C H_{3} C H_{2} C O O H \) (I) \( C H_{2}=C H-C O O H \) (II) and \( H C \equiv \)
\( C-C O O H \) (III) in order of decrease in
acidity
A . ।>॥>॥
в. ॥॥>॥>
c. ॥>1>॥||
D. ॥ᅵ>1>1
Subject: Chemistry
Sea water is \( 3.5 \% \) by mass of common
salt and has a density \( 1.04 g \mathrm{cm}^{-3} \) at \( 298 K . \) Assuming the salt to be sodium chloride, then osmotic pressure of sea water will be: (assume complete
ionisation of the salt)
A . 25.45 atm
B. \( 11.56 a t m \)
c. \( 15.13 a t m \)
D. \( 30.40 a t m \)
Subject: Chemistry
If \( \Delta E \) is the heat of reaction for
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( 2 C O_{2}(g)+3 H_{2} O(l) \)
at constant volume, the \( \Delta \boldsymbol{H} \) (heat of
reaction at constant pressure), at constant temperature is:
A. \( \Delta H=\Delta E+R T \)
B. \( \Delta H=\Delta E-R T \)
c. \( \Delta H=\Delta E-2 R T \)
D. \( \Delta H=\Delta E+2 R T \)
Subject: Chemistry
Which of the following is chloroprene?
\( \mathbf{A} \cdot C H_{2}=C H-C H=C H_{2} \)
B.
\[
\begin{array}{c}
C H_{2}=C-C H=C H_{2} \\
C_{1}
\end{array}
\]
\( c \)
\[
C H_{3}-C=C=C H_{2}
\]
\[
C l
\]
D.
\[
C H_{3}-C=C H_{2}-C H_{3}
\]
\( C \)
Subject: Maths
In the adjoining figure, it is given that
\( A B \| C D, \angle B A O=108^{\circ} \) and
\( \angle O C D=120^{\circ}, \) then \( \angle A O C= \)
\( \mathbf{A} \cdot 120 \)
B. 72
\( c \cdot 132^{\circ} \)
D. 150
Subject: Biology
Consider the following statements:
A. Condom, diaphragm and cervical caps ate the common barriers used to
prevent pregnancy.
B. Oral pills and vaginal pills are the chemical method practiced for the
prevention of pregnancy.
C. Intra-Uterine Contraceptive Devices (IUCDs) prevent implantation in the
uterus.
D. Vasectomy and tubectomy are the surgical methods practiced for birth
control.
The correct ones are given in
\( A \cdot A, B, C \) and \( D \)
B. \( B, c \) and \( D \)
c. A and D
D. \( c \) and \( D \)
Subject: Chemistry
Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)
A. Cylic process : \( q=-w \)
B. Isothermal process : \( q=-w \)
c. Adiabatic process: \( \Delta U=-w \)
D. Isochoric process: \( \Delta U=q \)
Subject: Maths
Prove by method of induction, for all
\( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{2}+\mathbf{4}+\mathbf{6}+\ldots+\mathbf{2} \boldsymbol{n}=\boldsymbol{n}(\boldsymbol{n}+\mathbf{1}) \)
Subject: Physics
n Fig. (i), a metre stick, half of which is
wood and the other half steel is pivoted at the wooden end at \( a \) ' and a Force \( \mathrm{F} \) is
applied to the steel end a. In Fig(ii) the stick is pivoted at the steel end at a and
the same force \( F \) is applied at the wooden end at \( a^{\prime} . \) The angular acceleration
A \( . \) In (i) is greater than in (ii)
B. In (ii) is greater than in (i)
c. Is equal both in (i) and (ii)
D. None of the above
Subject: Chemistry
The following table shows the electronic configuration of the elements \( \boldsymbol{W}, \boldsymbol{X}, \boldsymbol{Y}, \boldsymbol{Z} \)
\[
\begin{array}{lllll}
\text { Element } & \mathrm{w} & \mathrm{x} & \mathrm{Y} & \mathrm{z} \\
\begin{array}{l}
\text { Electronic } \\
\text { configuration }
\end{array} & \begin{array}{l}
2, \\
8,1
\end{array} & \begin{array}{l}
2, \\
8,
\end{array} & \begin{array}{l}
2, \\
7
\end{array} & 5
\end{array}
\]
Answer the following questions based on the table above:
(i) What type of Bond is formed between
1. \( W \) and \( X \)
2. \( Y \) and \( Z \)
(ii) What is the formula of the
compound formed between:
1. \( X \) and \( Z \)
2. \( W \) and \( X \)
Subject: Physics
Q Type your question
through the side, along the diameter of
a cross section of the coil. From out
point of view, we are looking straight through the coil.
We can see from the diagram that from
out perspective, the coil carries a clockwise conventional current, and the straight wire carries a conventional
current to the right. From our perspective, what is the
direction of the force on the segment of straight wire in the coil, due to the magnetic field produced by the coil?
A. Away from us
B. Toward us
\( c \cdot u p \)
D. Down
E . Right
Subject: Chemistry
Assertion
To overcome electrostatic force of
attraction between electrons and
nucleus, they revolve around the
nucleus
Reason
Mass of the atom is almost due to its
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. Both Assertion and Reason are incorrect
Subject: Maths
The set of values of \( ^{\prime} x^{\prime} \) which
satisfies the inequation \( \sqrt{x^{2}-18 x+72}<(x-1) \) is
\( A \cdot \phi \)
B \( \cdot[1,2) \)
\( \mathrm{c} \cdot[12, \infty) \)
D・(1,2)
Subject: Chemistry
During sodium extract preparation for Lassaigne's test both \( N \) and \( S \) present
in an organic compound change to:
A. \( N a C N \) and \( N a_{2} S \)
В. \( \operatorname{NaNH}_{2} \) and \( N a_{2} S O_{4} \)
c. \( N a S C N \)
D. \( N a N O_{3} \) and \( N a_{2} S \)
Subject: Chemistry
Match the column I with column II and
mark the appropriate choice.
Column I
(i) Saturated
(A) Liquid \( \leftrightarrow \) Vapour
(B) Solid \( \leftrightarrow \) Liquid
(ii) Boiling point
(C) Solid \( \leftrightarrow \)
(iii) Sublimation vapour \( \quad \) point
(D) Solute
\( (s) \leftrightarrow \)
(iv) Melting point Solute(solution)
\( A \cdot(A)-(i),(B)-(i i i),(C)-(i i),(D)-(i v) \)
B. (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i)
C. \( (A)-(i v),(B)-(i i),(C)-(i),(D)-(i i i) \)
D. (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i)
Subject: Maths
If \( \lim _{n \rightarrow \infty} \frac{1^{a}+2^{a}+3^{a}+\dots+n^{a}}{n^{a+1}}=\frac{1}{5} \)
\( (w h e r e a>-1) \) then the value of \( a \) is
A .2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
Assertion
Generally, covalent compounds are gases, liquids or soft solids at room temperature.
Reason
Between covalent compounds Vander
Waals forces of attractions exists
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 \( \boldsymbol{x} \sqrt{\boldsymbol{y}}+\boldsymbol{y} \sqrt{\boldsymbol{x}}=1, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) equals
\( \mathbf{A} \cdot-\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}} \)
B. \( -\sqrt{\frac{x}{y}}\left(\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}}\right) \)
\( \mathbf{c} \cdot-\sqrt{\frac{y}{x}}\left(\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}}\right) \)
D. None of these
Subject: Physics
Two long conductors, separated by a
distance d carry current \( I_{1} \) and \( I_{2} \) in the
same direction. They exert a force \( F \) on
each other. Now the current in one of
them is increased to two times and its
direction is reversed. the distance is
also increased to 3 d. The new value of
the force between them is
A \( \cdot-\frac{2 F}{3} \)
B. \( \frac{F}{3} \)
c. \( -2 F \)
D. \( -\frac{F}{3} \)
Subject: Maths
A sum of Rs. 18750 is left by will by a father to be divided between two sons,
12 and 14 years of age, so that when they attain maturity at \( 18, \) the amount received by each of them at 5 per cent simple interest will be the
same. Find the sum allotted at present
to each son?
A. Rs. 9500 , Rs. 9250
B. Rs. 8000, Rs. 1750
c. Rs. \( 9000, \) Rs. 9750
D. Rs. 10000, Rs. 8750
Subject: Chemistry
A gas occupies volume of \( 0.35 d m^{3} \) at
\( 290 \mathrm{K} \) and \( 92.458 \mathrm{K} \mathrm{Nm}^{-2} \) pressure.
Calculate the volume of gas at STP (Ans
\( \left.0.3 d m^{3}\right) \)
Subject: Chemistry
For the reaction, \( \left[A g\left(C N_{2}\right)\right]^{-} \rightleftharpoons \)
\( A g^{+}+2 C N^{-} \) the equilibrium constant
at \( 298 \mathrm{K} \) is \( 4.0 \times 10^{-10} . \) The silver ion
concentration in a solution which was
originally 0.12 molar \( n K C N \) and 0.04
molar in \( A g N O_{3}, \) is:
A \( \cdot 1 \times 10^{-10} \mathrm{M} \)
В. \( 1 \times 10^{-8} M \)
c. \( 1 \times 10^{-12} M \)
D. \( 1 \times 10^{-4} M \)
Subject: Chemistry
Write IUPAC names of the following coordination compounds.
a) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
b) \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( \boldsymbol{c} \boldsymbol{K}_{2}\left[\boldsymbol{P} \boldsymbol{d}(\boldsymbol{C l})_{4}\right. \)
d) \( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{o})_{4}\right] \)
Subject: Maths
Let the eccentricity of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) be reciprocal to that of the
ellipse \( x^{2}+4 y^{2}=4 . \) If the hyperbola
passes through a focus of the ellipse, then
This question has multiple correct options
A the equation of the hyperbola is \( \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 \)
B. a focus of the hyperbola is (2,0)
c. the eccentricity of the hyperbola is \( \sqrt{\frac{5}{3}} \)
D. the equation of the hyperbola is \( x^{2}-3 y^{2}=3 \)
Subject: Maths
Solve the inequality and represent the
solution graphically on number line. \( \mathbf{2}(\boldsymbol{x}-\mathbf{1})<\boldsymbol{x}+\mathbf{5}, \boldsymbol{3}(\boldsymbol{x}+\mathbf{2})>\mathbf{2}-\boldsymbol{x} \)
Subject: Maths
\( \int \frac{3+4 \sin x+2 \cos x}{3+2 \sin x+\cos x} d x \)
A \( \cdot 2 x+3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
B . \( 2 x-3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
c. \( 2 x-6 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)
D・ \( x-3 \tan ^{-1}\left(\tan \frac{x}{2}+1\right)+c \)