AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The displacement of the medium in a sound wave is given by the equation
\( \boldsymbol{y}_{1}=\boldsymbol{A} \cos (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{t}) \) where \( \boldsymbol{A}, \boldsymbol{a} \& \boldsymbol{b} \) are
positive constants. The wave is reflected by an obstacle situated at
\( \boldsymbol{x}=\mathbf{0} . \) The intensity of the reflected
wave is 0.64 times that if the incident
wave
(a) What are the wavelength and frequency of the incident wave?
(b) Write the equation for the reflected
wave.
(c) In the resultant wave formed after
reflection, find the minimum value of
the particle speed in the medium?
Subject: Chemistry
Vapour pressure of \( C C l_{4} \) at \( 25^{\circ} \mathrm{C} \) is 143
\( \mathrm{mm} \) of Hg. \( 0.5 \mathrm{g} \) of a non-volatile solute (mol. Mass \( =\mathbf{6 5} \) ) is dissolved in \( 100 \mathrm{mL} \)
\( \boldsymbol{C C l}_{4} . \) Find the vapour pressure of the
solution: (Density of \( \boldsymbol{C} \boldsymbol{C l}_{4}= \)
\( 1.58 g / c m^{3} \)
\( \mathbf{A} \cdot 141.93 \mathrm{mm} \)
B. \( 94.39 \mathrm{mm} \)
c. \( 199.34 \mathrm{mm} \)
D. \( 143.99 \mathrm{mm} \)
Subject: Biology
Which of the following is an event which
does not occur during anaphase- \( 1 ? \)
A. Spindle fibres pull homologous chromosomes towards the opposite poles of the spindle
B. The homologous chromosomes break their connection and separate out into two haploid sets or dyads
C. One such set is present at each end of the spindle
D. The process of separation of chromosomes which take place is called disengagement
Subject: Biology
Match the excretory organs listed under
column I with the animals given under
column II and select the correct option.
Column I (Excretory organs)
A. Nephridia \( \quad \) (i) \( \quad \) Hydra
Malpighian \( \quad \) (ii) \( \quad \) Leech
B. tubules
C. Protonephridia
(iii) Shark
D. Kidneys
(iv) \( \quad \) Roundworms
(v) Cockroach
A. A-(ii), B-(v), C-(iv), D-(iii)
B. A-(iv), B-(ii), C-(i), D-(v)
c. \( A-(v), B-(\text { ii) }, C-(i v), D-( \text { iii) } \)
D. A-(ii), B-(iv), C-(v), D-(i)
Subject: Maths
Let \( A=\{0,1\} \) and \( N \) the set of all
natural numbers. Then show the
mapping \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{A} \) defined by
\( \boldsymbol{f}(\boldsymbol{2 n}-\mathbf{1})=\mathbf{0}, \boldsymbol{f}(\boldsymbol{2 n})=\mathbf{1} \forall \boldsymbol{n} \in \boldsymbol{N} \) is
many-one onto.
Subject: Maths
Find a vector perpendicular to each of the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b}, \) where \( \vec{a}= \) \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
A \( \cdot \frac{\hat{i}}{i}-\hat{2} \hat{j}+\hat{2} k \)
B.
c. \( -\hat{i}-\hat{3} j+\hat{2 k} \)
D. None of these
Subject: Physics
The distance between electron and
proton in the H-atom is about 5.3
\( \times 10^{-11} \) metre. What is the magnitude
of electric force between these two
particles? \( \left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{N m^{2}}{C^{2}}\right) \)
Subject: Chemistry
The vapour pressure of a liquid
decreases by 10 tor \( r \) when a nonvolatile solute is dissolved. The mole
fraction of the solute in solution is 0.1
What would be the mole fraction of the
liquid if the decrease in vapour pressure is 20 tor \( r, \) the same solute
being dissolved?
A . 0.2
B. 0.9
\( c .0 .8 \)
D. 0.6
Subject: Biology
Consider the following statements regarding gymnosperms and choose the
correct option.
(A) In gymnosperms, the male and female gametophytes have an independent existence.
(B) The multicellular female
gametophyte is retained within the
megasporangium.
(C) The gymnosperms are heterosporous.
\( A \cdot(A) \) and
(B) are true but (C) is false.
B. (A) and
(C) are true but (B) is false.
c. (B) and
(C) are false but (A) is true
D. (A) and
(C) are false but (B) is true.
E. (B) and
(C) are true but (A) is false.
Subject: Chemistry
The correct order of decreasing metallic
character is:
\( \mathbf{A} \cdot C l>S i>A l>M g>N a \)
В \( . N a>M g>A l>S i>C l \)
\( \mathbf{c} . N a>A l>M g>C l>S i \)
D. \( A l>N a>S i>C l>M g \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( \ln x \)
What is \( [f o(f o f)](2) \) equal to?
A .2
B. 8
c. 16
D. 256
Subject: Chemistry
If the bond dissociation energies of \( \boldsymbol{X} \boldsymbol{Y} \)
\( X_{2} \) and \( Y_{2} \) (all diatomic molecules) are
in the ratio of 1: 1: 0.5 and \( \Delta H_{f} \) for the formation of \( \boldsymbol{X} \boldsymbol{Y} \) is \( -\mathbf{2 0 0} \) kJ/mol. The
bond dissociation energy of \( X_{2} \) will be :
\( \mathbf{A} \cdot 100 \mathrm{kJ} / \mathrm{mol} \)
B. 800 kJ/mol
c. 300 kJ/mol
D. 400 kJ/mol
Subject: Chemistry
How many moles of electrons are
needed in the balanced equation for the oxidation of ethanol (1 mol) to acetic
\( \operatorname{acid} ?\left(C_{2} H_{5} O H \rightarrow C H_{3} C O O H\right) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
Subject: Physics
If \( x_{0}=10 \mathrm{cm} \) and the object is given
velocity \( 18 \mathrm{m} / \mathrm{s} \) towards left, then the
speed of the image at that instant is
A. \( 2 \mathrm{m} / \mathrm{s} \)
B. \( 6 \mathrm{m} / \mathrm{s} \)
\( c .9 \mathrm{m} / \mathrm{s} \)
D. 162 \( \mathrm{m} / \mathrm{s} \)
Subject: Physics
If \( C \) and \( L \) denote the capacitance and
inductance, the dimensions of \( L C \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{-1}\right] \)
B . \( \left[M^{0} L^{-1} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-1} T^{0}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{0} T^{2}\right] \)
Subject: Biology
Read the following statements and select the option having both incorrect statements.
(i) Condoms decrease sperm motility.
(ii) Diaphragms, cervical caps and vaults are for both males and females.
(iii) IUDs are inserted by-expert nurses.
(iv) Sterilisation is a terminal method
to prevent further pregnancy.
A. (i) and (iii)
B. (i) and (ii)
c. (iii) and (iv)
D. (ii) and (iv)
Subject: Physics
A Pitot tube (Shown in figure above) is mounted along the axis of a gas
pipeline whose cross-sectional area is
equal to \( S \). Assuming the viscosity to be negligible, the volume of gas flowing across the section of the pipe per unit time, if the difference in the liquid columns is equal to \( \Delta h, \) and the densities of the liquid and the gas are
\( \rho_{0} \) and \( \rho \) respectively is \( Q= \) \( \boldsymbol{S} \sqrt{\frac{\boldsymbol{x} \boldsymbol{\Delta} \boldsymbol{h} \boldsymbol{\rho}_{0} \boldsymbol{g}}{\boldsymbol{\rho}}} . \) Find the value of \( \boldsymbol{x} \)
Subject: Physics
A transistor is used in the common
emitter mode as an amplifier. Then
This question has multiple correct options
A. the base-emitter junction is forward-biased.
B. the base-emitter junction is reverse-biased.
C. the input signal is connected in series with the voltage applied to bias the base-emitter junction.
D. the input signal is connected in series with the voltage applied to bias the base-collector junction In p-type semiconductor \( n_{h}>n_{e} \)
Subject: Maths
If the function \( \boldsymbol{f}:[\mathbf{0}, \mathbf{8}] \rightarrow \boldsymbol{R} \) is
differentiable and \( 0<\alpha<1<\beta<2 \)
then \( \int_{0}^{8} f(t) d t \) is equal to?
A \( \cdot 3\left[a^{3} f\left(a^{2}\right)+\beta^{2} f\left(\beta^{2}\right)\right] \)
B・3 \( \left[a^{3} f(a)+\beta^{3} f(\beta)\right. \)
c \( \cdot 3\left[a^{2} f\left(a^{2}\right)+\beta^{2} f\left(\beta^{3}\right)\right] \)
D \( \cdot 3\left[a^{2} f\left(a^{3}\right)+\beta^{2} f\left(\beta^{3}\right)\right] \)
Subject: Chemistry
The hydride ion \( H^{-} \) is stronger base
than hydroxide ion \( O H^{-} . \) Which of the following reaction will occur if sodium hydride \( (N a H) \) is dissolved in water?
A \( \cdot H^{-}(a q .)+H_{2} O \rightarrow H_{3} O^{-} \)
B . \( H^{-}(a q .)+H_{2} O(l) \rightarrow O H^{-}+H_{2} \)
c. \( H^{-}+H_{2} O \rightarrow \) No reaction
D. None of the above
Subject: Physics
A non-uniform thin rod of length \( L \) is placed along \( x- \) axis as such its one of
ends at the origin. The linear mass
density of rod is \( \lambda=\lambda_{0} x . \) The distance
of centre of mass of rod from the origin
is:
A \( . L / 2 \)
B. \( 2 L / 3 \)
c. \( L / 4 \)
D. L/5
Subject: Chemistry
Match the List-I with List-II.
List-I List-II
\( A) \)
Liquid \( \rightarrow \) vapour
1) 32.8
В) \( H_{2}+C l_{2} \rightarrow 2 H C l-\Delta H=-44 \)
kcal
2) -22 Then, heat of formation \( H C l \) in kcal):
C) Heat of combustion of graphite
\[
\text { is }-393.5 \mathrm{kJ}
\]
3
Then its calorific value (kJ)
D) 4.184 Joules is equal to (in 4) calories): \( \quad \) endothermic
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-4, B-3, C-2, D-1
\( C \cdot A-4, B-2, C-1, D-3 \)
D. \( A-2, B-1, C-4, D-3 \)
Subject: Physics
From a uniform circular disc of mass
\( M \) and radius \( R \) a small disc of radius
\( R / 2 \) is removed is such away that both have a common tangent. Find the distance of center of mass of remaining
part from the center of original disc.
\( \mathbf{A} \cdot R / 20 \)
в. \( R / 16 \)
c. \( R / 6 \)
D. \( \frac{3}{4} R \)
Subject: Physics
In the figure shown, a block A moving with velocity \( 10 \mathrm{m} / \mathrm{s} \) on a horizontal
surface collides with another block \( \mathrm{B} \) at
rest initially. The coefficient of restitution is \( \frac{1}{2} . \) Neglect fricition every
where. The distance between the blocks
5s after the collision takes place is \( 5 \times \)
\( (i n \quad m), \) then \( c \) is :
Subject: Maths
Let \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{B}=\{1,2\} \)
Consider a relation \( \boldsymbol{R} \) defined from set
\( A \) to set \( B . \) Then \( R \) is equal to set
A. \( A \)
в. \( B \)
c. \( A \times B \)
D. \( B \times A \)
Subject: Physics
A microscope has an objective of focal
length \( 1.5 \mathrm{cm} \) and eye piece of focal
length \( 2.5 \mathrm{cm} . \) If the distance between
objective and eye-piece is \( 25 \mathrm{cm} \). What is the approximate value of magnification produced for relaxed
eye?
[Disclaimer: Option A is changed from
\( \mathbf{7 5} \) to \( \mathbf{1 8 3 . 3 3} \) as the correct answer is
183.33 which is not present in the given options.]
A . 183.33
B. 110
c. 140
D. 25
Subject: Chemistry
Find the oxidation number of elements
in each case:
\( C r \) in
\( \boldsymbol{C r} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}, \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r}_{3} \boldsymbol{O}_{10}, \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \) and
\( \left[\boldsymbol{C r} \boldsymbol{O}_{8}\right]^{3-} \)
A. +6,+6,+3,+5
В. +5,+6,+3,+4
\( \mathbf{c} \cdot+4,+6,+2,+5 \)
D. None of the above
Subject: Maths
If \( A \) and \( B \) are two points having coordinates (3,4) and (5,-2)
respectively and \( P \) is a point such that \( P A=P B \) and area of \( P A B=10 \) sq. units, then coordinates of \( \mathrm{P} \) are
в. (7,2)\( \&(1,0) \)
c. (2,7)\( \&(4,13) \)
D. (7,4)\( \&(13,4) \)
Subject: Maths
Mark the correct alternative of the
following. n figure, \( A B|| C D \) and \( E F \) is a transversal intersecting \( A B \) and \( C D \) at \( P \) and \( Q \)
respectively. The measure of \( \angle D Q P \) is?
\( A \cdot 65 \)
В. 25
\( c .115 \)
0.105
Subject: Chemistry
toppr
Q Type your question-
as the only product. The unbalanced equation for the reaction is
\( N_{2} O(g)+O_{2}(g) \rightarrow N_{2} O_{4}(g) \)
The \( N_{2} O / O_{2} \) mixture is shown in the
figure. Which of the following represents the composition of the system after reaction has gone to completion?
Legend
\( \bigcirc=\mathrm{o} \)
\( \mathrm{O}=\mathrm{N} \)
\( A \)
\begin{tabular}{|ccc|}
\hline 00 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
& 0 & 0 \\
\hline
\end{tabular}
в. \( \begin{array}{lll}00 & 8 & 8 & 80 \\ 00 & 0 & 00 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array} \)
\( c \)
D.
Subject: Maths
\( \mathbf{1} \)
\( \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]= \)
\( \left[\begin{array}{ll}1 & 78 \\ 0 & 1\end{array}\right], \) then the inverse of \( \left[\begin{array}{ll}1 & n \\ 0 & 1\end{array}\right] \) is?
A. \( \left[\begin{array}{cc}1 & -13 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 0 \\ 12 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & -12 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}1 & 0 \\ 13 & 1\end{array}\right] \)
Subject: Maths
\( \begin{array}{lll}\text { Weight (Kg) } & \text { Frequency } \\ \text { 60 up to 70 } & 13 \\ \text { 70up to 75 } & 2 \\ \text { 75 up to 95 } & 45 \\ \text { 95 up to 100 } & \text { 7 }\end{array} \)
Given the table above, find the modal
class.
\( A \cdot 70 \) up to 75
\( B .75 \) up to 95
\( \mathbf{C} \cdot 60 \) up to 70
D. 95 up to 100
Subject: Maths
The value of \( \cos ^{2} 45^{\circ}-\sin ^{2} 15^{\circ} \) is
\( A \cdot \frac{3}{4} \)
B. \( \frac{\sqrt{5}}{4} \)
\( c \cdot \frac{\sqrt{3}}{4} \)
D. \( \frac{\sqrt{5}+1}{4} \)
Subject: Chemistry
Mark the incorrect statement
(I) Fractionating column is a long tube.
(II) Fractionating column is provided
with obstructions to the passage of vapours upwards and to the liquids
downward.
(III) Column itself is fitted with a
thermometer.
A . ।, ॥।, ॥।
B. ।,।
\( c \cdot \) ।, ॥
D. None of the above
Subject: Chemistry
Which pair of molecules will have a permanent dipole moment for both
members?
A. \( N O_{2} \) and \( O_{3} \)
B. \( \operatorname{SiF}_{4} \) and \( C O_{2} \)
c. \( \operatorname{SiF}_{4} \) and \( N O_{2} \)
D. \( N O_{2} \) and \( C O_{2} \)
Subject: Maths
Assertion
STATEMENT-1: A straight line passing
through the origin intersects the branches of the hyperbola \( x y=9 \) at \( Q \) in the first and \( \mathrm{R} \) in the third quadrant. The
point P divides the segment QR internally in the ratio \( 1: 2, \) then the locus of \( P \) is ellipse
Reason
STATEMENT- 2 : \( \boldsymbol{A} \equiv\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{B} \equiv \)
\( \left(x_{2}, y_{2}\right) \)
If \( P \) divides line joining Aand \( B \) in the ratio \( m: n, \) then \( c o \) -ordinates of \( P \) are \( \left[\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right] \)
A. Statement-1 is True, Statement -2 is True ; Statement
-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Chemistry
In an experiment, addition of \( 5.0 \mathrm{mL} \) of
\( 0.006 \mathrm{M} \mathrm{BaCl}_{2} \) to \( 10.0 \mathrm{mL} \) of arsenic
sulphite sol just causes the complete coagulation in 34 hours. The flocculating value of the effective ion is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
\( 58.5 g m \) of \( N a C l \) and \( 180 g m \) of
glucose were separately dissolved in
1000 \( m l \) of water. Identify the correct
statement regarding the elevation of boiling point (b.p.) of the resulting solutions.
A. \( N a C l \) solution will show higher elevation of b.p.
B. Glucose solution will show higher elevation of b.p.
C. Both the solutions will show equal elevation of b.p.
D. The b.p. elevation will be shown by neither of the solutions
Subject: Chemistry
\( p H \) of \( 0.1 \mathrm{M} N a_{2} H P O_{4} \) and \( 0.2 \mathrm{M} \)
\( N a H_{2} p O_{4} \) are respectively:
\( \left(p K_{a} \text { for } H P O_{4} \text { are } 2.2,7.2 \text { and } 12.0\right) \)
A . 4.7,9.6
B. 9.6, 4.7
c. 4.7,5.6
D. 5.6, 4.7
Subject: Chemistry
Which among the following sets of compounds is used as raw material for the preparation of sodium carbonate by
solvay process?
A. \( N a O H, H C l, C O_{2} \)
в. \( N H_{4} C l, H_{2} O, N a C l \)
c. \( N a C l, N H_{3}, C a(O H)_{2} \)
D. \( N a C l, C a C O_{3}, H_{2} S O_{4} \)
Subject: Physics
Three identical solid spheres each of
mass \( M \) and radius \( R \) are fixed at three
corners of light equilateral triangular
frame of side length \( 3 R \) such that centre of spheres coincide with corners
of the frame. Find the moment of inertia
of these 3 spheres about an axis passing through any side of frame.
\( ^{\mathbf{A}} \cdot \frac{121 M R^{2}}{5} \)
B. \( \frac{159 M R^{2}}{5} \)
c. \( \frac{121 M R^{2}}{20} \)
D. \( \frac{159 M R^{2}}{20} \)
Subject: Chemistry
Boron and nitrogen form bonds analogous to carbon-carbon bonds. For example, compound ammonia borane,
\( N H_{3}-B H_{3}, \) contains \( B-N \) bond
analogous to the \( C-C \) bond in ethane.
Borazine \( \left(B_{3} N_{3} H_{6}\right) \) is analogous to benzene and is prepared by reacting
\( N H_{4} C l \) with \( B C l_{4} \) followed by
reduction using \( L i B H_{4} . \) The correct statement(s) is/are:
This question has multiple correct options
A. boron nitride \( (B N) \) has a structure similar to graphite and is a good conductor of electricity
B. the \( B \) -center in borazine is susceptible to nucleophilic attack
c. ethane is a gas at room temperature, while ammonia borane is not so
D. the reaction of \( H C l \) with borazine gives hexachloro derivative of borazine
Subject: Maths
The model class for the following
frequency distribution is
\begin{tabular}{lllll} 
Marks & \( 0- \) 10 & \( 10- \) 20 & \( 20- \) 40 & \( 40- \) 50 \\
Number of students & 4 & 6 & 14 & 16 \\
\hline
\end{tabular}
A. \( 20-40 \)
B . \( 40-50 \)
\( \mathbf{c} .50-60 \)
D. \( 70-90 \)
Subject: Physics
The average translational energy and the rms speed of molecules in a sample
of oxygen gas at \( 300 \mathrm{K} \) are \( 6.21 \times 10^{-21} \mathrm{J} \)
and \( 484 \mathrm{m} / \mathrm{s} \) respectively. The corresponding values at \( 600 \mathrm{K} \) are nearly (assume ideal gas behaviours)
A \( .12 .42 \times 10^{-21} \mathrm{J}, 968 \mathrm{m} / \mathrm{s} \)
B. \( 8.78 \times 10^{-21} \) J, \( 684 \mathrm{m} / \mathrm{s} \)
c. \( 6.21 \times 10^{-21} \) J, \( 968 \mathrm{m} / \mathrm{s} \)
D. \( 12.42 \times 10^{-21} \) 」, \( 684 \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( A B C D \) a parallelogram, \( A_{1} \) and \( B_{1} \) are the midpoints of sides \( B C \) and \( C D \) respectively. If \( \boldsymbol{A} \boldsymbol{A}_{1}+\boldsymbol{A} \boldsymbol{B}_{1}=\boldsymbol{\lambda} \boldsymbol{A} \boldsymbol{C} \)
then \( \lambda \) is equal to
A \( \cdot \frac{1}{2} \)
B. 1
\( c \cdot \frac{3}{2} \)
D. 2
Subject: Physics
A thin rod placed long \( x \) -axis from \( x=-a \) to \( x=+a, \) the rod carries a change uniformly distributed along its length with linear charge density \( \lambda \). The
potential at the point \( P(2 a, 0,0) \) will be
A \( \cdot \frac{\lambda}{\pi \epsilon_{0}} \operatorname{In} 3 \)
в. \( \frac{\lambda}{4 \pi \epsilon_{0}} \) In 2
c. \( \frac{\lambda}{4 \pi \epsilon_{0}} \) In 3
D. \( \frac{\lambda}{\pi \epsilon_{0}} \) In 2
Subject: Physics
Two blocks of masses \( 2 \mathrm{kg} \) and \( 1 \mathrm{kg} \) are
placed on a smooth horizontal table i contact with each other.A horizontal
force of 3 newton is applied on the first
so that the block moves with a constant
acceleration. The force between the
blocks would be:-
\( A \cdot 3 N \)
B. 2 N
c. \( 1 \mathrm{N} \)
D. ZERO
Subject: Maths
Show that the function is continuous at
\[
\begin{array}{l}
x=0, \text { if } f(x)=\frac{\sin 3 x}{\tan 2 x}, x<0 \\
=\frac{\log (1+3 x)}{e^{2 x}-1}, x>0 \\
=\frac{3}{2}, x=0
\end{array}
\]
Subject: Chemistry
The solubility of silver acetate in pure water at \( 25^{\circ} \mathrm{C} \) 8.35g.litre \( ^{-1} \) and
\( 61.8 g . l i t r e^{-1} \) in an acid solution of
\( \boldsymbol{p} \boldsymbol{H}=\mathbf{3} . \) Calculate:
(i) \( K_{s p} \) of silver acetate and
(ii) dissociation constant of acetic acid.
Subject: Maths
The differential equation of family of coaxial circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{\lambda} \boldsymbol{x}+\boldsymbol{c}=\boldsymbol{0} \) is
A \( \cdot \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}+1=0 \)
B. \( y \cdot \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
\( ^{\mathbf{c}}\left(\frac{d^{2} y}{d x^{2}}\right)+\left(\frac{d y}{d x}\right)^{2}+1=0 \)
D \( \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
Subject: Chemistry
In a hydrocarbon, \( C \) is \( 3 g \) per \( g \) of
hydrogen. Hence, the hydrocarbon is :
A \( \cdot C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{10} \)
Subject: Chemistry
Assertion
Colloidal solutions are purified by
dialysis.
Reason
In the process of dialysis, colloidal
particles pass through parchment
paper.
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
A wire has a non-uniform cross-section
as shown in figure. A steady current
flows through it. The drift speed of
electrons at points \( \mathrm{P} \) and \( \mathrm{Q} \) is \( v_{P} \) and \( v_{Q} \)
then?
\( \mathbf{A} \cdot v_{P}=v_{Q} \)
в. \( v_{P}<v_{Q} \)
\( \mathbf{c} \cdot v_{P}>v_{Q} \)
D. Data is insufficient
Subject: Chemistry
The value of \( \Delta_{\circ} \) for complexes given below follow the order
(i) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \)
(ii) \( \left[\boldsymbol{R h}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \)
(iii) \( \left[\operatorname{Ir}\left(N H_{3}\right)_{6}\right]^{+3} \)
A. \( I<I I I<I I \)
В. \( I>I I>I I I \)
c. \( I<I I<I I I \)
Subject: Chemistry
The equilibrium constant for the reaction \( 3 A+2 B \rightleftharpoons C \) will be:
A \( \cdot \frac{[3 A][2 B]}{[C]} \)
\( ^{\mathbf{B}} \cdot \frac{[A]^{3}[B]}{[C]} \)
c. \( \frac{[C]}{[A]^{3}[B]^{2}} \)
D. \( \frac{[C]}{[3 A][2 B]} \)
Subject: Physics
Two long conductors, separated by a
distance \( d \) carry currents \( I_{1} \) and \( I_{2} \) in
the same direction. They exert a force \( \boldsymbol{F} \)
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:
\( \mathbf{A} \cdot-2 F \)
В. \( \frac{F}{3} \)
c. \( \frac{-2 F}{3} \)
D. \( \frac{-F}{3} \)
Subject: Chemistry
At what temperature would the volume of a given mass of a gas at constant
pressure be twice its volume at \( 0^{\circ} \mathrm{C} \) ?
\( \mathbf{A} \cdot 546^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 273^{\circ} \mathrm{C} \)
D. \( 373^{\circ} \mathrm{C} \)
Subject: Maths
The shaded region in the figure is the
solution set of the inequations.
\( \mathbf{A} \cdot 5 x+4 y \geq 20, x \leq 6, y \geq 3, x \geq 0, y \geq 2 \)
B. \( 5 x+4 y \geq 20, x \geq 6, y \leq 3, x \geq 0, y \geq 2 \)
c. \( 5 x+4 y \geq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 0 \)
D. \( 5 x+4 y \leq 20, x \leq 6, y \leq 3, x \geq 0, y \geq 2 \)
Subject: Physics
Two pieces, one of mass \( \mathrm{M} \) and the other of mass \( 4 \mathrm{M} \). After the explosion, the mass \( \mathrm{M} \) ends up traveling in the same circular orbit, but in opposite direction.
After the explosion the mass \( 4 \mathrm{M} \) is :
\( A \). In a circle orbit
B. unbound
c. elliptical orbit
D. data is insufficient to determent the nature of the orbit
Subject: Chemistry
Select the correct statement (s) about
the compound \( N O\left[B F_{4}\right] \)
This question has multiple correct options
A. It has \( 5 \sigma \) and \( 2 \pi \) bond
B. Nitrogen - oxygen bond length is higher than nitric oxide \( (N O) \)
C. It is a diamagnetic species
D. \( B F \) bond length in this compound is lower than in \( B F_{3} \)