AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \sin ^{2} m x+\cos ^{2} n y=a^{2} \) then \( \frac{d y}{d x}= \)
A. \( \frac{m \cdot \sin 2 m x}{n \cdot \sin 2 n y} \)
B. \( \frac{m \cdot \sin m x}{n \cdot \sin n x} \)
c. \( \frac{-m \cdot \cos 2 m x}{n \cdot \cos 2 n x} \)
D. \( \frac{n \cdot \sin 2 m x}{m \cdot \sin 2 n x} \)
Subject: Biology
Q Type your question
are true?
a. In phase 3 , some bacteria may be
dividing.
b. Phase 2 is called as the lag phase and phase 1 is called as the log phase.
c. Phase 4 could be caused by the buildup of metabolic toxins.
d. Growth in phase 2 follows an exponential progression.
e. The fastest rate of growth is seen at
the plateau, i.e., phase 3
\( A \cdot a, b \) and \( c \)
B. b and e
\( c . a, c \) and \( d \)
D. a and d
三
Subject: Maths
If \( \bar{E} \) and \( \bar{F} \) are the complementary
events of events \( \boldsymbol{E} \) and \( \boldsymbol{F} \) respectively
and if \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{F})<\mathbf{1}, \) then
\( ^{\mathbf{A}} \cdot_{P}\left(\frac{E}{F}\right)+P\left(\frac{\bar{E}}{F}\right)=1 \)
в. \( \quad P\left(\frac{E}{F}\right)+P\left(\frac{E}{\bar{F}}\right)=1 \)
\( ^{\mathbf{c}} \cdot_{P}\left(\frac{\bar{E}}{F}\right)+P\left(\frac{E}{\bar{F}}\right)=1 \)
\( P\left(\frac{E}{\bar{F}}\right)+P\left(\frac{\bar{E}}{\bar{F}}\right)=1 \)
Subject: Chemistry
A reaction carried out by 1 mol of \( N_{2} \)
and 3 mol of \( H_{2} \) at equilibrium. The
mole fraction of \( N H_{3} \) as 0.012 at \( 500 C \) and 10 atm pressure.What the pressure
at which mole \( \% \) of \( N H_{3} \) in equilibrium mixture is increased to \( 10.4 ? \). (in atm)
A . 57
в. 105
\( c \cdot 200 \)
D. None of these
Subject: Chemistry
A compound \( (80 \mathrm{g}) \) on analysis gave \( \boldsymbol{C}=\mathbf{2 4} \) g, \( \boldsymbol{H}=\mathbf{4} \) g, \( \boldsymbol{O}=\mathbf{3 2} \) g. Its
empirical formula is :
A \( \cdot C_{2} H_{2} O_{2} \)
в. \( C_{2} H_{2} O \)
c. \( C H_{2} O_{2} \)
D. \( C H_{2} O \)
Subject: Chemistry
From the following data, calculate the standard enthalpy of formation of Propane \( \Delta_{f} H^{\ominus} C H_{4}=-17 K c a l m o l^{-1} \)
\( \Delta_{f} \boldsymbol{H}^{\ominus} \boldsymbol{C}_{2} \boldsymbol{H}_{6}=-\mathbf{2} 4 \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o l}^{-1} \)
\( \boldsymbol{B} \boldsymbol{E}(\boldsymbol{C}-\boldsymbol{H})=\boldsymbol{9} \boldsymbol{9} \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o l}^{-1}(\boldsymbol{C}- \)
\( C)=84 K c a l m o l^{-1} \)
A \( \cdot \Delta_{f} H=-31 \) Kcalmol \( ^{-1} \)
B. \( \Delta_{f} H=+31 K \) calmol \( ^{-1} \)
\( \mathbf{c} \cdot \Delta_{f} H=0 K c a l m o l^{-1} \)
D. None of these
Subject: Chemistry
For the process,
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})(\mathbf{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})(\boldsymbol{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r} ; \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}) \)
The correct set of thermodynamics
parameters is:
A. \( \Delta G=0, \Delta S=+v e \)
в. \( \Delta G=0, \Delta S=-v e \)
c. \( \Delta G=+v e, \Delta S=0 \)
D. \( \Delta G=-v e, \Delta S=+v e \)
Subject: Physics
Four concentric spherical shell is \( A, B, C \) AND \( D \) has radius \( a, 2 a, 3 a \) and
\( 4 a \) shell \( B \) and \( D \) has charge \( +q \) and \( -q \)
The shell \( ^{\prime} C^{\prime} \) is earthed. Find \( V_{A}-V_{C} \)
A \( \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( c \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)
Subject: Chemistry
Calculate the ratio of degree of
dissociation \( (a) \) when \( 1 ~ M \) acetic acid solution is diluted to times.
\( \left[\text { Given: } \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{3}}\right] \)
Subject: Maths
An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are 2: 1 and the odds in favor of the
price remaining the same are \( 1: 3 . \) The probability that the price of the stock will go down during the next week, is
A \( \cdot \frac{4}{12} \)
в. \( \frac{5}{12} \)
\( c \cdot \frac{7}{12} \)
D. none of these
Subject: Chemistry
Among the given compounds, the most susceptible to nucleophilic attack at the carbonyl group is:
A. \( C H_{3} C O O C H_{3} \)
в. \( C H_{3} C O N H_{2} \)
с. \( C H_{3} \) СООСОСН\( _{3} \)
D. \( C H_{3} C O C l \)
Subject: Maths
A unit vector which is coplanar to vector \( i+2 j+k \) and \( i+2 j+k \) and
perpendicular to \( i+j+k, \) is
A \( \frac{i-j}{\sqrt{2}} \)
\( ^{\mathrm{B}} \pm\left(\frac{j-k}{\sqrt{2}}\right) \)
c. \( \frac{k-i}{\sqrt{2}} \)
D. \( \frac{i+j+k}{\sqrt{3}} \)
Subject: Maths
Draw the graph of i) \( y=2 x+5, \) ii)
\( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{5}, \) iii) \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x} \) and find the
point of intersection on \( x \) -axis. Is the \( x \)
coordinates of these points also the zero of the polynomial?
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}+\mathbf{5} \)
for the given functions \( \left(g o f^{-1}\right)(10)= \)
A . 21
B . 29
\( c \cdot 7 \)
D.
Subject: Physics
We have \( 2.0 \mathrm{kg} \) of a block of a
substance at its melting point. The
substance has a latent heat of fusion of
\( 1500 J \) per kilogram and a specific heat
of \( 2500 J \) per kilogram degree Celsius. How much heat is needed to change the block entirely into a liquid?
\begin{tabular}{l} 
A. \( 5000 \mathrm{J} \) \\
\hline
\end{tabular}
B. \( 750 J \)
c. \( 1250 J \)
D. 3000 \( J \)
ह. \( 8000 J \)
Subject: Chemistry
One volume of nitrogen combines with one volume of oxygen to form two
volumes of nitric oxide. Calculate the
amount of each reactant required to produce \( 250 \mathrm{ml} \) of nitric oxide.
A \( \cdot N_{2}=100 \mathrm{ml}, \mathrm{O}_{2}=100 \mathrm{ml} \)
в. \( N_{2}=120 \mathrm{ml}, \mathrm{O}_{2}=120 \mathrm{ml} \)
c. \( N_{2}=125 \mathrm{ml}, \mathrm{O}_{2}=125 \mathrm{ml} \)
D. \( N_{2}=100 \mathrm{ml}, \mathrm{O}_{2}=125 \mathrm{ml} \)
Subject: Chemistry
Primary and secondary valency of
\( \boldsymbol{P t} \) in \( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 4,4 \)
B. 4,6
\( c \cdot 6,6 \)
D. 4,2
Subject: Maths
The solution of the equations \( \frac{\boldsymbol{m}}{\boldsymbol{x}}+ \) \( \frac{n}{y}=a \) and \( \frac{n}{x}+\frac{m}{y}=b \) is given by
A \( x=\frac{n^{2}+m^{2}}{a m-b n}, y=\frac{m^{2}-n^{2}}{b m-a n} \)
B. \( _{x}=\frac{m^{2}-n^{2}}{a m-b n}, y=\frac{n^{2}-m^{2}}{b m-a n} \)
c. \( _{x}=\frac{m^{2}-n^{2}}{a m-b n}, y=\frac{m^{2}-n^{2}}{b m-a n} \)
D. \( x=\frac{n^{2}-m^{2}}{a m-b n}, y=\frac{n^{2}-m^{2}}{b m-a n} \)
Subject: Maths
Assertion
\( \int_{0}^{\pi / 2} x \cot x d x=\frac{\pi}{2} \log 2 \)
Reason
\( \int_{0}^{\pi / 2} \log \sin x d x=-\frac{\pi}{2} \log 2 \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Biology
Efforts to repeat the cloning of Dolly (the sheep) have been unsuccessful. The scientists who claim to have cloned
Dolly have been challenged to produce additional evidence that Dolly is really derived from an adult cell (an originally claimed), rather than a foetal cell which
might have contaminated the experiment (as the sceplor suggest). Which of the following could provide evidence that Dolly was created from an
adult cell, rather than a foetal cell?
A. Dolly's DNA fingerprints
B. The heterozygosity of random pieces of Dolly's DNA
c. The melting point of Dolly's DNA
D. The length of Dolly's telomeres
Subject: Physics
In the nuclear fusion reaction \( :_{1}^{2} \boldsymbol{H}+_{1}^{3} \) \( \boldsymbol{H} \rightarrow_{2}^{4} \boldsymbol{H} e+\boldsymbol{n}, \) given that the
repulsive potential energy between the two nuclei is \( \sim 7.7 \times 10^{-14} \mathrm{J} \), the
temperature to which the gases must be heated to initiate the reaction is
nearly (Boltzmann's constant \( \left.k=1.38 \times 10^{-23} \mathrm{J}\right) \)
\( \mathbf{A} \cdot 10^{7} K \)
B . \( 10^{5} K \)
\( \mathbf{c} \cdot 10^{3} K \)
D. \( 10^{9} K \)
Subject: Maths
In \( \triangle A B C, A B=A C . \) Points \( D \) and \( E \)
are on the sides \( B C \) and \( A C \)
respectively such that \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{A} \boldsymbol{E} \). If
\( \angle B A D=30^{\circ}, \) then the measure of
\( \angle E D C \) is:
A \( .10^{\circ} \)
B . 15
\( c \cdot 20 \)
D. 25
Subject: Chemistry
Which of the following statements are
true regarding oxides of nitrogen?
This question has multiple correct options
\( \mathbf{A} \cdot N O_{2} \) is a mixed anhydride of \( H N O_{2} \) and \( H N O_{3} \)
B. \( N_{2} O_{3} \) is not soluble in water.
C \( \cdot N_{2} O \) and \( N O \) are anhydrides of \( H N O_{2} \)
D. \( N_{2} O_{5} \) is anhydride of \( H N O_{3} \)
Subject: Physics
A body of mass m falls freely through a height h from the top of a tower. The velocityjust before touching the ground is \( \sqrt{\frac{3}{2} g h} . \) The air drag is:
A \( . m g \)
в. \( \frac{m g}{2} \)
\( c \cdot \frac{m g}{3} \)
D. \( \frac{m g}{4} \)
Subject: Maths
n fig. \( \mathbf{7 . 8}, \boldsymbol{O A}=\boldsymbol{O B} \) and \( \boldsymbol{O D}=\boldsymbol{O C} \)
Show that (i) \( \Delta A O D \cong \Delta B O C \) and (ii)
\( \boldsymbol{A} \boldsymbol{D} \| \boldsymbol{B} \boldsymbol{C} \)
Subject: Chemistry
\( \left[\begin{array}{ccc}-\boldsymbol{C H}_{2}- & \boldsymbol{C H}-\boldsymbol{C H}_{2}- & \boldsymbol{C H}-\boldsymbol{C I} \\ & \boldsymbol{O H} & \boldsymbol{O H}\end{array}\right. \)
Polyvinyl alcohol (as shown above) is a unique polymer having high affinity for water. Which of the following procedures would be most suitable for
its preparation?
A . radical chain polymerisation of \( C H_{2}=C H-C H_{2} \)
\( O H \)
B. radical chain polymerisation of \( C H_{2}=C H-O H \)
c. radical chain polymerisation of \( C H_{2}=C H- \) \( C O_{2} C H_{3}, \) following by base catalysed hydrolysis
D. radical chain polymerisation of \( C H_{2}=C H- \) \( O C O C H_{3}, \) followed by acid catalysed hydrolysis
E. radical chain polymerisation of \( C H_{2}=C H- \) \( O C O C H_{3}, \) followed by base catalysed hydrolysis
Subject: Maths
A vector \( C \) when added to vectors \( A= \) \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{5} \hat{\mathbf{j}}+\widehat{\boldsymbol{k}} \) and \( \boldsymbol{B}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \widehat{\boldsymbol{j}}-\mathbf{4} \widehat{\boldsymbol{k}} \)
gives a unit vector along the y-axis.
Then, \( C \) is
\( \mathbf{A} \cdot-5 \hat{i}+3 \hat{j}+3 \widehat{k} \)
B. \( 5 \hat{i}-3 \hat{j}-3 \widehat{k} \)
\( \mathbf{c} .-5 \hat{i}+2 \hat{j}-3 \widehat{k} \)
D. \( 5 \hat{i}-2 \hat{j}-3 \hat{k} \)
Subject: Chemistry
One litre of a buffer solution is prepared
by dissolving 0.6 mole of \( N H_{3} \) and 0.4
mole of \( N H_{4} C l . \) What is the pH of the
solution? for \( \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8 5} \times \mathbf{1 0}^{-\mathbf{5}} \)
(i) What is the pH of the buffer after addition of 0.1 mole of \( H C l \)
(ii) What is the pH of the buffer after
addition of 0.1 mole of \( N a O H \)
Subject: Chemistry
Which of the following statements is
correct?
This question has multiple correct options
A. \( S O_{2} \) is anhydride of sulphurous acid
B. \( S O_{2} \) acts as only oxidising agent
c. The coloured matter lost colour on exposure to \( S O_{2} \) can regain colour on exposure to atmosphere
D. \( S O_{2} \) can get oxidised to sulphur
Subject: Physics
The moment of inertia of a metre stick
of mass \( 300 g \), about an axis at right
angles to the stick and located at \( 30 \mathrm{cm} \)
mark, is
\( \mathbf{A} \cdot 8.3 \times 10^{5} g \mathrm{cm}^{2} \)
в. \( 5.8 g \mathrm{cm}^{2} \)
C. \( 3.7 \times 10^{5} \mathrm{g} \mathrm{cm}^{2} \)
D. None of these
Subject: Physics
Three rods of identical cross-sectional
area are made from the same metal and form the sides of an isosceles triangle
\( A B C, \) right-angled at \( B . \) The points \( A \)
and \( B \) are maintained at temperatures \( T \) and \( (\sqrt{2}) T, \) respectively. In the steady
state, the temperature of the point is \( T_{c} \) Assuming that only heat conduction
takes place, \( \boldsymbol{T}_{c} / \boldsymbol{T} \) is
\( ^{A} \cdot \frac{1}{2(\sqrt{2}-1)} \)
в. \( \frac{3}{\sqrt{2}+1} \)
c. \( \frac{1}{\sqrt{3}(\sqrt{2}-1)} \)
D. \( \frac{1}{\sqrt{2}+1} \)
Subject: Maths
\( A B C D \) is a trapezium in which \( A B \| \)
\( D C, B D \) is a diagonal and \( E \) is the
mid-point of \( A D . A \) line is drawn
through \( E \) parallel to \( A B \) intersecting \( B C \) at \( F \) (see Fig). Show that \( F \) is the
mid-point of \( \boldsymbol{B C} \)
Subject: Chemistry
Number of \( \pi \) bonds in \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
Solve the following Linear Programming Problems graphically:
Minimise \( Z=-3 x+4 y \)
subject to \( x+2 y \leq 8,3 x+2 y \leq \)
\( \mathbf{1 2}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Physics
Two resistances of \( 400 \Omega \) and \( 800 \Omega \) are
connected in series with a 6 volt battery of negligible internal resistance. A
voltmeter of resistance \( 10,000 \Omega \) is used to measure the potential difference across \( 400 \Omega \). The error in the
measurement of the potential difference in volts approximately is :
A . 0.01
B. 0.02
\( c .0 .03 \)
D. 0.05
Subject: Physics
\( \mathbf{5 0} \boldsymbol{V} \) battery is supplying current of \( \mathbf{1 0} \) amp when connected to a resistor. If the
efficiency of battery at this current is 25
\%. Then internal resistance of battery
is:-
A . \( 2.5 \Omega \)
B. \( 3.75 \Omega \)
c. \( 1.25 \Omega \)
D. \( 5 \Omega \)
Subject: Maths
If the middle term of \( (1+x)^{2 n} \) is the
greatest term then \( x \) lies between
A. \( n-1<x<n \)
в. \( \frac{n}{n+1}<x<\frac{n+1}{n} \)
c. \( n<x<n+1 \)
D. \( \frac{n+1}{n}<x<\frac{n}{n+1} \)
Subject: Maths
A trust fund has Rs. 30,000 that must
be invested in two different type of bounds the fist bond pays \( 5 \% \) interest
per year and the second bond pays \( 7 \% \) interest per yer using matrix multiplication determine how to divide Rs.30,000 among the two type of bound if the trust fund must obtain an annual
total interest of
a)Rs.1800
Subject: Maths
The value of \( 1+\cot ^{2} A \) is
\( \mathbf{A} \cdot \cos ^{2} A \)
B. \( \sec ^{2} A \)
\( \mathbf{c} \cdot \tan ^{2} A \)
D. \( \operatorname{cosec}^{2} A \)
Subject: Chemistry
Arrange the following in the decreasing order of solubility in water:
¡) \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
ii) \( \left(C_{2} H_{5}\right)_{2} N H \)
iii) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. i > ii > ii
\( \mathbf{c} . \) iii \( >\mathbf{i}>\mathrm{i} \mathrm{i} \)
D. iii >ii >
Subject: Physics
Assertion(A): An inductor in a D.C.
circuit opposes both a steady current and a changing current. Reason(R): Induced emf is generated
only when the flux linked with the inductor remains unchanged.
A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of \( A \)
c. A is true but R is false
D. Both A and R are false
Subject: Biology
Which is the wrong statement from the
following?
A. When tripalmitin is used as a substrate in respiration, the R.Q. is 0.7
B. The intermediate compound which links glycolysis with Kreb's cycle is malic acid.
C. One glucose molecule yields a net gain of 36 ATP molecules during aerobic respiration.
D. One glucose molecule yields a net gain of 2 ATP molecules during fermentation.
E. The scheme of glycolysis was given by Embden, Meyerhof and Parnas.
Subject: Chemistry
How many moles of \( N i(C O)_{4} \) could be
obtained from the CO produced by the
reaction of \( 75.0 \mathrm{g} \) of carbon? [Assume \( 100 \% \) reaction and \( 100 \% \)
recovery in both steps and molar mass of \( \mathrm{Ni}=59 \mathrm{g} / \mathrm{mol}] \)
A . 6.25
B. 1.5625
c. 3.125
D. 25.0
Subject: Physics
A particle moves on the \( X \) -axis
according to the equation \( \boldsymbol{x}= \)
\( x_{0} \sin ^{2} \omega t . \) The motion is simple
harmonic.
A. with amplitude \( x_{0} \)
B. with amplitude \( 2 x_{0} \)
c. with time period \( \frac{2 \pi}{\omega} \)
D. with time period \( \frac{\pi}{\omega} \)
Subject: Physics
In the circuit shown in the figure, the
heat produced in the \( 5 \Omega \) resistor due to
a current flowing in it, is 10 calories per
second. The heat produced in the \( 4 \Omega \)
resistor is?
A \( \cdot 1 \) cal \( s^{-} \)
B . 2 cal \( s^{-1} \)
\( c \cdot 3 \) cal \( s^{-1} \)
D. 4 cal \( s^{-} \)
Subject: Maths
Equation of a tangent to the curve \( y= \) \( \cos (x+y), 0 \leq x \leq 2 \pi \) that is parallel
to the line \( x+2 y=0 \) is
A \( \cdot x+2 y=\frac{\pi}{2} \)
в・ \( x+2 y=\frac{\pi}{4} \)
c. \( x+2 y=\pi \)
D. \( x+y=\pi \)
Subject: Physics
Estimate the mean free path and
collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17
\( ^{o} C . \) take the radius of a nitrogen
molecule to be roughly 1.0 A. Compare the collision time with the time the
molecule moves freely between two successive collisions (Molecular mass
of \( \mathrm{N}_{2}=28.0 \mathrm{u} \)
Subject: Chemistry
Assertion
Alkaline earth metal oxides are quite
stable to heat.
Reason
Enthalpies of formation of alkaline
earth metal oxides are quite high.
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
With reference to a right handed system of mutually perpendicular unit vectors \( i, j, k, \alpha=3 i-j \) and \( \beta=2 i+j-3 k . \)
\( \beta=\beta_{1}+\beta_{2}, \) where \( \beta_{1} \) is parallel to \( \alpha \)
and \( \beta_{2} \) is perpendicular to \( \alpha, \) then This question has multiple correct options
A \( , \beta_{1}=\frac{3}{2} i+\frac{1}{2} j \)
в. \( \beta_{1}=\frac{3}{2} i-\frac{1}{2} j \)
c. \( _{\beta_{2}}=\frac{1}{2} i+\frac{3}{2} j-3 k \)
D. \( _{\beta_{2}}=\frac{1}{2} i-\frac{3}{2} j-3 k \)
Subject: Physics
Two vessels \( A \) and \( B \) of different shapes
have the same base area and are filled
with water up to the same height h (see figure). The force exerted by water on
the base is \( F_{A} \) for vessel \( A \) and \( F_{B} \) for
vessel B. The respective weights of the
water filled in vessels are \( W_{A} \) and \( W_{B} \)
Then
\( \mathbf{A} \cdot F_{A}>F_{B} ; W_{A}>W_{B} \)
B . \( F_{A}=F_{B} ; W_{A}>W_{B} \)
C \( \cdot F_{A}=F_{B} ; W_{A}<W_{B} \)
D. \( F_{A}>F_{B} ; W_{A}=W_{B} \)
Subject: Physics
Three blocks are initially placed as shown in the figure. block \( A \) has mass
\( m \) and initial velocity \( v \) to the right.
Block \( B \) with mass \( m \) and block \( C \) with
mass \( 4 m \) are both initially at rest.
Neglect friction. All collisions are
elastic. The final velocity of block \( \boldsymbol{A} \) is :
A. \( 0.6 v \) to the left
B. \( 1.4 v \) to the left
\( c . v \) to the left
D. \( 0.4 v \) to the right
Subject: Chemistry
The active constituent of bleaching
powder is:
\( \mathbf{A} \cdot C a(O C l)_{2} \)
в. \( C a(O C l) C l \)
c. \( C a\left(C l O_{2}\right)_{2} \)
D. \( \operatorname{Ca}\left(\text {ClO}_{2} \text { ) } \)Cl\right.
Subject: Physics
At a certain location in Africa, a
compass points \( 12^{\circ} \) west of the
geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian
points \( 60^{\circ} \) above the horizontal. The
horizontal component of the earth's field is measured to be 0.16 G. Specify the direction and magnitude of the earth's field at the location.
Subject: Physics
A monochromatic source of light
operating at \( 200 \mathrm{W} \) emits \( 4 \times 10^{20} \)
photons per second. Find the wavelength of light.
A . 400 nm
B. 200nm
C \( .4 \times 10^{-10} \dot{A} \)
D. None of these
Subject: Physics
In vacuum, to travel distance 'd', light takes time 't' and in a medium to travel
distances '5 \( d \), it takes time 'T'. The
critical angle of the medium is
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
B. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
c. \( \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)
Subject: Chemistry
Consider the equilibrium
\( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+H C l(g) . A n \)
inert gas is added to the system at constant volume and temperature. The correct statement(s) is/ are:
This question has multiple correct options
A. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will increase
B. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will remain the same
c. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will decrease
D. the entropy of the system will increase
Subject: Physics
A body of mass \( 5 k g \) is acted upon by
two perpendicular force \( 8 N \) and \( 6 N \) find the magnitude and direction the
acceleration:
A \( \cdot 3 m s^{-2}, \theta=\cos ^{-1}(0.8) \) from \( 8 N \)
B . \( 2 m s^{-2}, \theta=\cos ^{-1}(0.6) \) from \( 6 N \)
c. \( 3 m s^{-2}, \theta=\cos ^{-1}(0.9) \) from \( 6 N \)
D. \( 5 m s^{-2}, \theta=\cos ^{-1}(0.81) \) from \( 8 N \)
Subject: Maths
If \( a, b, c \) are real and \( b^{2}-4 a c \) is perfect
square then the roots of the equation
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0}, \) will be:
A. Rational \& distinct
B. Real \& equal
C. Irrational \& distanct
D. Imaginary \& distinct
Subject: Physics
Consider the following statements (A) and (B) and identify the correct answer given below:
Statement A: Positive values of packing fraction implies a large value of binding energy Statement B: The difference between
the mass of the nucleus and the mass
number of the nucleus is called the
packing fraction
A. A and B are correct
B. A and B are false
c. A is true, B is false
D. A is false, B is true
Subject: Maths
The probability mass function (p.m.f) of
\( X \) is given below:
\[
\begin{array}{lllll}
X=x & 1 & 2 & 3 \\
P(X=x) & \frac{1}{5} & \frac{2}{5} & \frac{2}{5}
\end{array}
\]
Subject: Maths
\( \boldsymbol{T}_{\boldsymbol{r}}\left(\boldsymbol{A}+\boldsymbol{B}^{\boldsymbol{T}}+\boldsymbol{3} \boldsymbol{C}\right) \) equals-
(where \( T_{r}(A) \) denotes trace of matrix of
\( A) \)
A . 17
B . 18
c. 20
D. 21
Subject: Chemistry
Lanthanoids are
A. 14 elements in the sixth period(atomic number \( =90 \) to
103) that are filling 4f-sublevel
B. 14 elements in the seventh period(atomic number \( =90 \) to 103 ) that are filling \( 5 f \) -sublevel
C. 14 elements in the sixth period(atomic number \( =58 \) to
71) that are filling \( 4 f \) -sublevel
D. 14 elements in the seventh period(atomic number \( =58 \) to 71 ) that are filling \( 4 f \) -sublevel
Subject: Physics
In a vessel, as shown in fig, point \( P \) is
just visible when no liquid is filled in
vessel through a telescope in the air.
When liquid is filled in the vessel
completely, point \( Q \) is visible without
moving the vessel or telescope. Find the
refractive index of the liquid.
A \( \cdot \frac{\sqrt{14}}{3} \)
B. \( \frac{\sqrt{85}}{5} \)
\( c \cdot \sqrt{2} \)
\( D \)