AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
In the reaction \( \boldsymbol{B C l}_{3}+\boldsymbol{P H}_{3} \rightarrow \)
\( \left[\boldsymbol{C l}_{3} \boldsymbol{B} \leftarrow \boldsymbol{P} \boldsymbol{H}_{3}\right] \) the Lewis base is:
\( \mathbf{A} \cdot B C l_{3} \)
в. \( P H_{3} \)
c. both
D. none of them
Subject: Chemistry
Assertion
If two half reaction with electrode
potential \( E_{1}^{o} \) and \( E_{2}^{o} \) gives a third half
reaction, then \( \Delta G_{3}^{o}=\Delta G_{1}^{o}+\Delta G_{2}^{o} \)
Reason
\( \boldsymbol{E}_{\mathbf{3}}^{\boldsymbol{o}}=\boldsymbol{E}_{\mathbf{1}}^{\boldsymbol{o}}+\boldsymbol{E}_{\mathbf{2}}^{\boldsymbol{o}} \)
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
A box contains \( b \) blue balls and \( r \) red
balls. A ball is drawn randomly from the box and is returned to the box with
another ball of the same colour. The
probability that the second ball drawn from the box is blue is
A \( \cdot \frac{b}{r+b} \)
в. \( \frac{b^{2}}{(r+b)^{2}} \)
c. \( \frac{b+1}{r+b+1} \)
D. \( \frac{b(b+1)}{(r+b)(r+b+1)} \)
Subject: Physics
A container with rigid walls is covered with perfectly insulating material. The container is divided into two parts by a partition. One part contains a gas while the other is fully evacuated (vacuum). The partition is suddenly removed. The gas rushes to fill the entire volume and
comes to equilibrium after a little time. If the gas is not ideal. Choose the
correct option:
A. The initial internal energy of the gas equals its final internal energy
B. The initial temperature of the gas equals its final temperature.
C. The initial pressure of the gas equals its final pressure
D. The initial entropy of the gas equals its final entropy
Subject: Chemistry
toppr
Q Type your question
inspection should convince you that they are indeed different. Now, how their
physical and chemical properties differ? Generally,
i) Cis-isomer has more dipole moment than trans-isomer.
ii) Cis is less stable than trans.
iii) The boiling points of cis isomers are more than those of trans isomers
(remember boiling points are directly related to polarity which is determined by dipole moment).
iv) Chemical reactivities of cis and
trans also differ from each other.
Which of the following statements best explain(s) the relationship between two
isomers of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} ? \)
You are given two compounds
This question has multiple correct options
A. They are diastereomers
B. They are enantiomers.
C. They are geometrical isomers.
D. Their melting points are same.
Subject: Chemistry
The degree of dissociation of
\( \boldsymbol{C a}\left(\boldsymbol{N O}_{3}\right)_{2} \) in a dilute aqueous
solution containing \( 7 g \) of the salt per \( 100 g \) of water at \( 100^{\circ} C \) is \( 70 \% \). If the vapour pressure of water at \( 100^{\circ} \mathrm{C} \) is
\( \mathbf{7 6 0} \boldsymbol{m m}, \) calculate the vapour pressure of the solution.
\( \mathbf{A} .378 .5 \mathrm{mm} \)
В. \( 492.8 \mathrm{mm} \)
c. \( 746.10 m m \)
D. \( 985.6 \mathrm{mm} \)
Subject: Maths
Find the equation of a circle.
(i) Which touches both the axes at a
distance of 6 units from the origin.
(ii) Which touches x-axis at a distance
5 from the origin and radius 6 units.
(iii) Which touches both the origin,
radius 17 and ordinate of the centre is
-15
(iv) Passing through the origin, radius
17 and ordinate of the centre is -15
Subject: Physics
Nuclei A and B convert into a stable
nucleus C. Nucleus A is converted into C
by emitting \( 2 \alpha- \) particles and \( 3 \beta- \) particles. Nucleus B is converted into \( C \) by emitting one \( \alpha- \) particle and \( 5 \beta- \)
particles. At time \( t=0, \) nuclei of A are
\( 4 N_{0} \) and nuclei of \( B \) are \( N_{0} . \) Initially,
number of nuclei of \( C \) are zero. Half-life
of \( A \) (into conversion of \( C \) ) is 1 min and
that of \( \mathrm{B} \) is 2 min. Find the time (in
minutes) at which rate of disintegration of \( A \) and \( B \) are equal
Subject: Maths
If \( 1<x<\sqrt{2}, \) the number of solutions of
the equation \( \tan ^{-1}(x-1)+\tan ^{-1} x+ \)
\( \tan ^{-1}(x+1)=\tan ^{-1} 3 x \) is
A.
B.
\( c \cdot 2 \)
D.
Subject: Maths
A bank offers \( 5 \% \) cash back on petrol
purchase up to \( \$ 1500 \) and \( 2 \% \)
on amount spent on petrol thereafter, in
a calendar year. If functions \( g(x) \) and
\( e(x) \) represents cash back earned on
petrol purchases up to \( \$ 1,500 \) and in
excess of \( \$ 1,500, \) respectively, then the sets of functions that could be used to
determine the amount of cash back
earned is
\( \mathbf{A} \cdot g(x)=0.05 x, 0 \leq x<1,500 ; e(x)= \)
\[
0.02(x-1,500), x \geq 1,500
\]
B \cdot \( g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)=0.02 x, x>1,500 \)
C \( \cdot g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)= \)
\[
0.02(x-1,500), x>1,500
\]
D \( \cdot g(x)=0.05 x, 0 \leq x \leq 1,500 ; e(x)= \)
\[
0.02(1,500-x), x>1,500
\]
Subject: Maths
If \( y=\frac{x}{|n| c x \mid} \) (where \( c \) is an arbitrary
constant) is the general solution of the differential equation \( \frac{d y}{d x}=\frac{y}{x}+\phi\left(\frac{x}{y}\right) \)
then the function \( \phi\left(\frac{x}{y}\right) \)
A \( \cdot \frac{x^{2}}{y^{2}} \)
в. \( -\frac{x^{2}}{y^{2}} \)
c. \( \frac{y^{2}}{x^{2}} \)
D. \( -\frac{y^{2}}{x^{2}} \)
Subject: Physics
In Millikan's oil drop experiment, a charged drop of mass \( 1.8 \times 10^{-14} k g \) is
stationary between the plates. The distance between the plates is \( 0.90 \mathrm{cm} \) and potential difference between them is \( 2.0 \mathrm{kV} \). The number of electrons on the
drop is
A. 500
B. 50
\( c \cdot 5 \)
D.
Subject: Maths
The P.M.F of a r.v. \( \boldsymbol{X} \) is \( \boldsymbol{P}(\boldsymbol{x})=\frac{1}{5} \) for \( \boldsymbol{x}= \)
\( 1,2,3, \dots 14,15 ; P(x)=0 \) otherwise
Find (i) \( \boldsymbol{E}(\boldsymbol{X})(\text { ii) } \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{X}) \)
Subject: Biology
Match following.
1.Kidneys
(a) Air
2.Heart
(b) Food
3.Lungs
(c) Blood
4.Stomach
(d) Wastes
A \( \cdot 1-a, 2-c, 3-d, 4-d \)
B. \( 1-d, 2-c, 3-a, 4-b \)
\( c \cdot 1-c, 2-d, 3-b, 4-a \)
D. \( 1-d, 2-c, 3-b, 4-a \)
Subject: Chemistry
Ten milliliters of a gaseous hydrocarbon
was burnt completely in \( 80 \mathrm{ml} \) of \( \mathrm{O}_{2} \) at STP. The Volume of the remaining gas is 70 ml. The volume became \( 50 \mathrm{ml} \) on
treatment with NaOH. The formula of
the hydrocarbon is :
A \( \cdot C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{6} \)
Subject: Physics
The far point of a myopic person is 40 cm. To see the distant objects clearly, the focal length and the power of the
lens used should be:
A. \( -40 \mathrm{cm},-2.5 \mathrm{D} \)
B. \( -25 \mathrm{cm},-4.0 \mathrm{D} \)
\( c \cdot+40 \mathrm{cm},+2.5 \mathrm{D} \)
D. \( -40 \mathrm{cm},+2.5 \mathrm{D} \)
Subject: Chemistry
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}, \quad \boldsymbol{E}^{o}=\boldsymbol{x}_{1} \) volt
\( \boldsymbol{C u}^{2+}+\mathbf{2} e^{-} \longrightarrow \boldsymbol{C u}, \quad \boldsymbol{E}^{o}=\boldsymbol{x}_{2} \) volt
then for
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}^{+}, \quad \boldsymbol{E}^{o}(\text { volt }) \) will be
A. \( x_{1}-2 x_{2} \)
В. \( x_{1}+2 x_{2} \)
c. \( x_{1}-x_{2} \)
D. \( 2 x_{2}-x_{1} \)
Subject: Physics
Assertion
Paramagnetic substances get poorly attracted in magnetic field.
Reason
Because magnetic dipoles are aligned along external magnetic field weakly.
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: Physics
A small body of mass \( m \) tied to a non-
stretchable thread moves over a smooth
horizontal plane. The other end of the
thread is being drawn into a hole \( \boldsymbol{O} \)
(figure shown above) with a constant velocity. Find the thread tension as a
function of the distance \( r \) between
the body and the hole if at \( r=r_{0} \) the
angular velocity of the thread is equal to
\( \omega_{0} \)
Subject: Physics
The number of turns in the primary and secondary of a transformer are, respectively 100 and \( 50 . \) If the input power and input current are, respectively \( 60 \mathrm{W} \) and \( 1 \mathrm{A} \), and the efficiency of the transformer is
\( 0.95, \) then, the output power and the output current will be, respectively
\( A \cdot 60 \mathrm{W}, 2 \mathrm{A} \)
B. \( 60 \mathrm{W}, 1 \mathrm{A} \)
c. \( 57 \mathrm{w} \), 2 \( \mathrm{A} \)
D. 57 W, 1.9 A
Subject: Maths
Find the length of a chord that is at a distance of \( 5 \mathrm{cm} \) form the centre of a
circle of radius \( 13 \mathrm{cm} \)
\( A \cdot 20 \mathrm{cm} \)
B . \( 24 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)
Subject: Physics
\( \boldsymbol{F}=\boldsymbol{G} \frac{\boldsymbol{m}_{1} \times \boldsymbol{m}_{2}}{\boldsymbol{R}^{2}} \) is the formula to prove
A. Newton's First law of motion
B. Newton's Second law of motion
C. Newton's Third law of motion
D. Newton's law of Gravitation
Subject: Physics
If the earth is one-fourth of its present distance from the sun, the duration of
the year will be changed to :
A. half of the present year
B. \( \frac{1}{4} t h \) of the present year
c. \( \frac{1}{8} t h \) of the present year
D. \( \frac{7}{8} t h \) of the present year
E \( \cdot \frac{1}{16} t h \) of the present yea
Subject: Physics
\( \lambda_{a} \) and \( \lambda_{m} \) are the wavelengths of a
beam of light in air and medium respectively. If \( \theta \) is the polarising angle, the correct relation between \( \lambda_{a}, \lambda_{m} \) and
\( \boldsymbol{\theta} \) is:
A \( \cdot \lambda_{a}=\lambda_{m} \tan ^{2} \theta \)
B \( \cdot \lambda_{m}=\lambda_{a} \tan ^{2} \theta \)
\( \mathbf{c} \cdot \lambda_{a}=\lambda_{m} \cot \theta \)
D. \( \lambda_{m}=\lambda_{a} \cot \theta \)
Subject: Physics
In a double-slit experiment, instead of taking slits of equal width, one slit is made twice as wide as the other. Then
in the interference pattern
A. the intensities of both the maxima and the minima increase
B. the intensity of the maxima increases and the minima has zero intensity
c. the intensity of the maxima decreases and that of the minima increases
D. the intensity of the maxima decreases and the minima has zero intensity
Subject: Chemistry
In the complexes \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+},\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{3-},\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)\right. \)
and \( \left[\boldsymbol{F} e \boldsymbol{C l}_{6}\right]^{3-}, \) more stability is shown
by :
\( \mathbf{A} \cdot\left[F e C l_{6}\right]^{3-} \)
B . \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right]^{3}\right. \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3+} \)
D. \( \left[F e(C N)_{6}\right]^{3-} \)
Subject: Maths
The number of intersection points of diagonals of 2009 sides polygon, which lie inside the polygon.
A \( .^{2009} \mathrm{C}_{4} \)
В. \( 2009 \mathrm{C}_{2} \)
c. \( 2008 C_{4} \)
D. \( 2008 \mathrm{C}_{2} \)
Subject: Maths
\( \boldsymbol{n} \stackrel{\boldsymbol{L} t}{\rightarrow} \infty \sum_{r=0}^{\boldsymbol{n}-1} \frac{1}{\sqrt{\boldsymbol{n}^{2}-\boldsymbol{r}^{2}}} \)
\( A \)
B . \( \pi / 2 \)
c. \( \pi / 3 \)
D . \( \pi / 6 \)
Subject: Chemistry
Which of the one is true for this
reaction:
\( 2 F e C l_{3}+S n C l_{2} \rightarrow 2 F e C l_{2}+S n C l_{4} \)
A \( \cdot F e^{+3} \) reduced to \( F e^{+2} \)
B. \( S n^{+2} \) is reduced to \( S n^{+4} \)
\( c \cdot S n^{+2} \) oxidized to sn
D. \( F e^{+3} \) gains two electrons
Subject: Physics
An inductor L of inductance \( \boldsymbol{X}_{\boldsymbol{L}} \) is
connected in series with a bulb \( \mathrm{B} \) and
an ac source. How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an
iron rod is inserted in the inductor and
(iii) a capacitor of reactance \( \boldsymbol{X}_{\boldsymbol{C}}=\boldsymbol{X}_{\boldsymbol{L}} \)
is inserted in series in the circuit.
Justify your answer in each case.
Subject: Maths
\( \int x \sqrt{x} d x= \)
A \( \cdot \frac{3}{2} x^{3 / 2}+c \)
B \( \cdot \frac{2}{5} x^{5 / 2}+c \)
c. \( \frac{5}{2} x^{5 / 2}+c \)
D. \( \frac{3}{2} \sqrt{x}+c \)
Subject: Maths
\( \frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+. . n \) terms \( = \)
A \( \cdot \frac{3 n}{2(3 n+2)} \)
B. \( \frac{3 n}{3 n+2} \)
c. \( \frac{n}{2(3 n+2)} \)
D. \( \frac{n}{3 n+2} \)
Subject: Physics
Two liquids \( A \) and \( B \) are \( a t 30^{\circ} C \) and
\( 20^{\circ} \mathrm{C} \) respectively. When they are mixed in equal masses, the temperature of the
mixture is found to be \( 26^{\circ} \mathrm{C} \). The ratio of
specific heat is :
\( A \cdot 4: 3 \)
B. 3:4
\( c \cdot 2: 3 \)
D. 3:2
Subject: Maths
If the price of potatoes is reduced by \( 25 \%, \) one can buy \( 6.25 \mathrm{kg} \) more for Rs.
100. The reduced price of potatoes is
A. Rs. 3 per kg
B. Rs. 3.50 per kg
c. Rs. 4 per \( \mathrm{kg} \)
D. Rs. 4.50 per kg
Subject: Physics
If velocity of light \( c, \) Planck's constant \( h \) and gravitational constant G are taken as fundamental quantities then the dimensions of length will be:
A \( \cdot \sqrt{\frac{c h}{G}} \)
в. \( \sqrt{\frac{h G}{c^{5}}} \)
c. \( \sqrt{\frac{h G}{c^{3}}} \)
D. \( \sqrt{\frac{h c^{3}}{G}} \)
Subject: Chemistry
\( 3.4 \mathrm{g} \) of \( H_{2} O_{2} \) decomposes, the weight of oxygen liberated from it is:
A \( .1 .6 g \)
B . 2.24 g
c. \( 1.16 \mathrm{g} \)
D. \( 3.2 \mathrm{g} \)
Subject: Physics
A small electric dipole is placed at origin with its axis being directed along the positive x-axis. The direction of
electric field due to the dipole at a point \( (1 \mathrm{m}, \sqrt{2} \mathrm{m}, 0) \) is along the:
A . z-axis
B. y-axis
c. x-axis
D. line \( y=x \)
Subject: Chemistry
The following are some statements about diagonal relationship.
i) It is due to nearly same size, electronegativity and same polarising power
ii) \( L i \) has similar properties with \( H_{2} \)
iii) \( B e O, A l_{2} O \) are amphoteric in
nature
iv) All \( d \) -block elements are stable
A. Only (i) correct
B. Only (ii) correct
c. only (iii) correct
D. Only (iv) is correct
Subject: Chemistry
In a homogeneous reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+ \)
\( C+D \) the initial pressure was \( P_{0} \) and
after time \( t \) it was \( P . \) Expression for rate
constant \( k \) in terms of \( P_{0}, P \) and \( t \) will
be:
A \( \quad k=\frac{2.303}{t} \log \frac{2 P_{0}}{3 P_{0}-P} \)
В. \( _{k=} \frac{2.303}{t} \log \frac{2 P_{0}}{P_{0}-P} \)
c. \( _{k=} \frac{2.303}{t} \log \frac{3 P_{0}-P}{2 P_{0}} \)
D. \( _{k}=\frac{2.303}{t} \log \frac{2 P_{0}}{3 P_{0}-2 P} \)
Subject: Chemistry
Assertion
Bond order of \( \boldsymbol{O}_{2} \) and \( \boldsymbol{B} \boldsymbol{N} \) is same.
Reason
\( O_{2} \) and \( B N \) are isoelectronic.
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 modal class of the following frequency distribution is
class \( \begin{array}{cc}0- & 10- \\ 10 & 20\end{array} \) 30 40
Frequency
15
17
A . \( 20-30 \)
в. \( 10-20 \)
c. \( 30-40 \)
D. \( 40-50 \)
Subject: Physics
In a series LCR circuit connected to an
ac source of variable frequency and voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t}, \) draw a plot
showing the variation of current (I) with angular frequency ( \( \omega \) ) for two different values of resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{1}>\right. \)
\( \left.R_{2}\right), \) Write the condition under which
the phenomenon of resonance occurs. For which value of the resistance out of
the two curves a sharper resonance is produced? Define \( Q \) -factor of the circuit and give its significance
Subject: Physics
How many electrons make up a charge of \( 20 \mu C ? \)
A \( \cdot 1.25 \times 10^{14} \)
B. \( 2.23 \times 10^{14} \)
c. \( 3.25 \times 10^{14} \)
D. \( 5.25 \times 10^{14} \)
Subject: Maths
If \( \hat{i}, \hat{j} \) and \( \hat{k} \) represents unit vectors
along the \( x, y \) and \( z- \) axes respectively
then find the value of angle \( \theta \) between the vectors \( \hat{i}+\hat{j}+\hat{k} \) and \( \hat{i}+\hat{j} \)
Subject: Physics
An alternating voltage \( \boldsymbol{V}=\boldsymbol{V}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
is applied across a circuit. As a result, a
current \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{\pi} / 2) \) flows in it
The power consumed per cycle is
A . zero
в. \( 0.5 V_{0} I_{0} \)
c. \( 0.707 V_{0} I_{0} \)
D. \( 1.414 \mathrm{V}_{0} \mathrm{I}_{0} \)
Subject: Maths
If \( a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+ \)
\( c=0 \) then \( \frac{d y}{d x}= \)
A. \( -\left(\frac{a x+h y+g}{h x+b y+f}\right) \)
в. \( -\left(\frac{a x+h y+g}{b x+h y+f}\right) \)
c. \( -\left(\frac{h x+b y+f}{a x+h y+g}\right) \)
D. \( -\left(\frac{h x+b y+f}{h x+a y+g}\right) \)
Subject: Maths
If \( a, b, c \) are in A.P., then \( \frac{1}{\sqrt{b}+\sqrt{c}} \) \( \frac{1}{\sqrt{\boldsymbol{c}}+\sqrt{\boldsymbol{a}}}, \frac{1}{\sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}}} \) are in
A . G.P.
B. H.P.
c. A.P.
D. None of these
Subject: Physics
A neutral metal rod \( A B \) of length \( l \)
rotates with a constant angular velocity
\( \omega \) about an axis passing through 0 and normal to its length as shown in the figure.The potential difference between
\( A \& B \) will be:
(e is the charge of an electron)
A \( \cdot V_{A}-V_{B}=\frac{1}{3} \frac{m \omega^{2} l^{2}}{e} \)
в. \( \quad V_{A}-V_{B}=\frac{m l^{2} \omega^{2}}{e} \)
c. \( _{V_{B}-V_{A}}=\frac{1}{2} \frac{m \omega^{2} l^{2}}{e} \)
D. \( _{V_{B}-V_{A}}=\frac{1}{4} \frac{m \omega^{2} l^{2}}{e} \)
Subject: Physics
For transistor action, state which statements are true:
(1) Base, emitter and collector regions should have similar size and doping concentrations.
(2) The base region must be very thin and lightly doped.
(3) The emitter-base junction is forward
biased and base-collector junction is reverse biased
(4) Both the emitter-base junction as well as the base-collectorjunction are
forward biased
\( A \cdot(4) \) and (1)
B. (1) and (2)
c. (2) and (3)
\( D \cdot(3) \) and (4)
Subject: Physics
In a metre bridge experiment, null point is obtaining at \( 20 \mathrm{cm} \) from one end of
the wire when
resistance \( X \) is balanced against
another resistance Y. If \( X<Y \), then where
will be the new position of the null point from the same end, if one decides to balance a resistance of
4X against Y?
\( A .50 \mathrm{cm} \)
B. 80 cm
c. \( 40 \mathrm{cm} \)
D. 70 cm
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\mathbf{1}, \boldsymbol{a}=\mathbf{1}, \boldsymbol{l}=\mathbf{3} \) and \( \boldsymbol{\epsilon}= \)
\( 0.001, \) then \( \delta>0 \) satisfying \( 0<\mid x- \)
\( \boldsymbol{a} \mid<\boldsymbol{\delta} \) such that \( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{l}|<\boldsymbol{\epsilon}, \) is
A . 0.0005
B. 0.005
c. 0.001
D. 0.0001
Subject: Biology
Which of the following sequences is correct regarding regulation of kidney
function?
A. An excess loss of water from body \( \rightarrow \) Hypothalamus \( \rightarrow \) Ormoreceptors \( \rightarrow \) Neurohypophysis \( \rightarrow \) ADH \( \rightarrow \) Increases water permeability of DCT and CT \( \rightarrow \) Prevention of diuresis
B. An excess loss of fluid from body \( \rightarrow \) Ormoreceptors \( \rightarrow \) Hypothalamus \( \rightarrow \) Neurohypophysis \( \rightarrow A D H \rightarrow \) Increases wter permeability of DCT and \( \mathrm{CT} \rightarrow \) PRevention of diuresis
C. An excess loss of fluid from body \( \rightarrow \) Ormoreceptors \( \rightarrow \) Hypothalamus \( \rightarrow \) Neurohypophysis \( \rightarrow \) Aldosterone \( \rightarrow \) Water permeability of DCT and CT increases \( \rightarrow \) Prevention of diuresis
D. An excess loss of fluid from body \( \rightarrow \) Ormoreceptor \( \rightarrow \) Hypothalamus \( \rightarrow \) Adenohypophysis \( \rightarrow \) ADH \( \rightarrow \) Increases water permeability of DCT and CT \( \rightarrow \) Prevention of diuresis
Subject: Chemistry
Which one has the electronic
configuration given below? \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} \)
A . \( N a^{+} \)
в. \( A l \)
\( c . F \)
D. \( T i \)
E . \( B r \)
Subject: Chemistry
\( A g N O_{3}(a q) \) was added to an aqueous
\( K C l \) solution gradually and the
conductivity of the solution was
measured. The plot of conductance \( (\boldsymbol{\Lambda}) \)
versus the volume of \( A g N O_{3} \) is :
\( A \cdot(P) \)
B . (Q)
c. (R)
\( D \cdot(S) \)
Subject: Chemistry
Select the correct statements for thiazy|
trifluoride \( \left(N S F_{3}\right) \)
This question has multiple correct options
\( \mathbf{A} \cdot S-N \) bond length is \( 141.5 \mathrm{pm}, \) probably the shortest
one between \( S \) and \( N \)
B. The three highly electronegative fluorine substituents contract the 3d-orbitals of sulphur sufficiently to effect the strong \( \pi \) -bonding with the half-filled \( p \) orbitals of nitrogen.
C. The bond angle \( F-\hat{S}-F=94^{\circ} \) indicates the
involvement of almost pure p-orbitals of \( S \) in binding the fluorine atoms.
D. The very strong bonding (due to multiple bond formation) between \( N \) and \( S \) demands the
participation of s-character enriched orbitals of sulphur.
Subject: Maths
\( \frac{\boldsymbol{d}^{20}(2 \cos \boldsymbol{x} \cos \mathbf{3} \boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}^{20}}= \)
A \( \cdot 2^{20}\left(\cos 2 x-2^{20} \cos 4 x\right) \)
B . \( -2^{20}\left(\cos 2 x+2^{20} \cos 4 x\right) \)
C \( \cdot 2^{20}\left(\sin 2 x+2^{20} \sin 4 x\right) \)
D. \( 2^{20}\left(\sin 2 x-2^{20} \sin 4 x\right) \)
Subject: Physics
Three discs \( A, B \) and \( C \) having radii
\( 2 m, 4 m \) and \( 6 m \) respectively are coated with carbon black on their outer
surface. The wavelengths corresponding to the maximum intensity are
\( 300 m m, 500 m m \) and \( 800 m m \)
respectively. The power radiated by
them are \( Q_{A}, Q_{B} \) and \( Q_{C} \) respectively.
Then
A. \( Q_{A} \) is maximum
B. \( Q_{B} \) is maximum
c. \( Q_{c} \) is maximum
Subject: Physics
A beam of white light traveling in medium \( A \) strikes the interface to
another transparent medium, medium
B. If the speed of white light is less in
medium \( B \) than in medium \( A \), the
beam will
A. refract toward the normal
B. refract away from the normal
c. undergo total internal reflection
D. have an angle of reflection smaller than the angle of incidence
E. have an angle of reflection greater than the angle of incidence
Subject: Maths
The value of \( \sin ^{-1}\left(\sin 2010^{0}\right)+ \)
\( \cos ^{-1}\left(\cos 2010^{0}\right)+\tan ^{-1}\left(\tan 2010^{0}\right) \) is
\( A \cdot \frac{\pi}{6} \)
B .
\( \mathbf{c} \cdot \frac{2 \pi}{3} \)
D. \( \frac{5 \pi}{6} \)
Subject: Physics
An empty freight car of mass \( \boldsymbol{m}_{1}= \)
\( \mathbf{1 0}, \mathbf{0 0 0 k g} \) rolls at speed \( u_{1}=2 m / s \) on
a level road and collide with a loaded
car of mass \( \boldsymbol{m}_{2}=\mathbf{2 0}, \mathbf{0 0 0 k g} \) standing
at rest. If the cars couple together, find
their speed \( V \) after the collision and
also the loss in kinetic energy. What should be speed of the loaded car towards the empty car, in order that both be brought to rest by the collision?