AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An oil drop of 10 excess electrons is
held stationary under a constant electric field of \( 3.65 \times 10^{4} N C^{-1} \) in
Millikan's oil drop experiment. The density of oil is \( 1.26 g c m^{-3} . \) Radius of
the oil drop is
(Take \( \left.g=9.8 m s^{-2}, e=1.6 \times 10^{-19} C\right) \)
A \( \cdot 1.04 \times 10^{-6} \mathrm{m} \)
в. \( 4.8 \times 10^{-5} \mathrm{m} \)
\( \mathbf{c} \cdot 4.8 \times 10^{-18} m \)
D. \( 1.13 \times 10^{-18} \mathrm{m} \)
Subject: Biology
In the given food chain, suppose the amount of energy at fourth trophic level is \( 5 \mathrm{kJ} \), what will be the energy available at the producer level?Grass Grasshopper- - Frog - Snake - - Hawk
A . 5 kJ
B. 50 kJ
c. \( 500 \mathrm{kJ} \)
D. 5000 k J
Subject: Chemistry
\( \boldsymbol{H}_{2} \stackrel{14}{C}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \frac{\operatorname{low} \operatorname{conc.of} B r_{2}}{\operatorname{orhightemp}}(?) \)
Product of the above reaction is :
A \( \cdot H_{2}^{14}=C H-C H_{2}-B r \)
в. \( _{H_{2}} C=C H-_{C H_{2}}^{14}-B r \)
D. both (a) and (b)
Subject: Physics
A unit vector in the direction of vector \( \overrightarrow{P Q}, \) where \( P \) and \( Q \) are the points
(1,2,3) and (4,5,6) respectively is
A \( \cdot \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}} \bar{k} \)
B. \( \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}} \hat{k} \)
c. \( 2 \hat{i}-\hat{j}+\bar{k} \)
D. None
Subject: Maths
If \( z=x+i y \) and \( x^{2}+y^{2}=16, \) then the
range of \( \|\boldsymbol{x}|-| \boldsymbol{y}\| \) is
A . [0,4]
B. [0,2]
c. [2, \( 4] \)
D. none of these
Subject: Physics
n figure, \( \boldsymbol{k}=\mathbf{1 0 0} \boldsymbol{N} / \boldsymbol{m}, \boldsymbol{M}= \)
1 kgand \( F=10 N . \) Write the potential
energy of the spring when the block is at the right extreme during simple harmonic motion
If your answer is \( x \) write the value of \( 4 x \)
Subject: Chemistry
The rate of certain hypothetical reaction \( A \) \( +\mathrm{B}+\mathrm{C} \rightarrow \) Products, is given by \( r= \) \( -\frac{d A}{d t}=k[A]^{1 / 2}[B]^{1 / 3}[C]^{1 / 4} \) The order of a
reaction is given by:
A . 1
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. \( \frac{13}{12} \)
Subject: Chemistry
A drug becomes ineffective after \( 30 \% \) decomposition. The original concentration of a sample was \( 5 \mathrm{mg} / \mathrm{ml} \) which becomes \( 4.2 \mathrm{mg} / \mathrm{ml} \) in 20 months. The expiry time of the drug in months assuming the first order decomposition is:
A. 41 months
B. 79 months
c. 20 months
D. 60 months
Subject: Chemistry
Consider the given reaction, the product
\( A^{\prime} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} O H \)
в. \( C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C l \)
D. \( C_{6} H_{5} C H O \)
Subject: Chemistry
What is pH formula?
A. \( -\log _{e}\left[H^{+}\right] \)
B. \( -\log _{10}\left[H^{-}\right] \)
c. \( -\log _{10}\left[O H^{-}\right] \)
D. \( -\log _{10}\left[H^{+}\right] \)
Subject: Maths
An insurance company issued 3000 scooters, 4000 cars and 5000 trucks.
The probabilities of the accident involving a scooter, a car and a truck are 0.02,0.03 and 0.04 respectively. One of the insured vehicles meet with an
accident. Find the probability that it is a
(i) scooter
(ii) car (iii) truck.
Subject: Physics
A long, straight wire of radius a carries a current distributed uniformlt over its
cross-section. The ratio of the magnetic fields due to the wire at distance \( \frac{a}{3} \) and
\( 2 a, \) respectively from the axis of the
wire is?
A \( \cdot 2 / 3 \)
B. \( 3 / 2 \)
c. \( 1 / 2 \)
D. 2
Subject: Chemistry
A very dilute saturated solution of a
sparingly soluble salt \( A_{3} B_{4} \) has a vapour pressure of \( 20 \mathrm{mm} \) of Hg at temperature \( T, \) while pure water exerts a pressure of \( 20.0126 \mathrm{mm} \) Hg at the same temperature. Calculate the
solubility product constant of \( \boldsymbol{A}_{3} \boldsymbol{B}_{4} \) at the same temperature.
A. \( 2.7 \times 10^{-13} \)
В. \( 4.45 \times 10^{-7} \)
c. \( 6.8 \times 10^{-12} \)
D. \( 13.6 \times 10^{-7} \)
Subject: Chemistry
Which of the following is secondary amine?
A. \( C H_{3}-N H_{2} \)
в.
\[
C-N_{L}^{C}^{\ominus}-C
\]
c. \( C H_{3}-N H C H_{3} \)
D. \( C H_{3}-N\left(C H_{3}\right)_{2} \)
Subject: Chemistry
Statement \( I: H_{2} S O_{4} \) is not used during
the reaction of alcohols with \( K I \)
Statement II : \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) oxidises \( \boldsymbol{K} \boldsymbol{I} \) to \( \boldsymbol{I}_{2} \)
and will prevent reaction of alcohol with
\( \boldsymbol{K} \boldsymbol{I} \)
A. Statement I \& Statement II are correct and statement I is correct explanation of statement
B. Statement I \& Statement II are correct and statement
Il is not correct explanation of statement
c. Statement lis correct and Statement II is wrong
D. Statement I is wrong and Statement II is correct
Subject: Biology
If the skeletal muscle fibres are soaked
and treated with high concentration of salts, large quantities of proteins are removed. The fibres can no longer contract and the A-bands disappear This shows that
A. Myosin is essential for contraction of the fibres
B. Actin is essential for contraction
c. Both myosin and actin are essential for contraction
D. Proteins do not play any role in the contraction of fibres
Subject: Physics
The force exerted by a weird, stretch
cord at given displacements is shown in
the above table. Experimentally the force is found to vary proportionally to
the square of the displacement, i.e.
\( \boldsymbol{F}(\boldsymbol{x})=-\boldsymbol{h} \boldsymbol{x}^{2} \) where \( h \) is some
constant.
If the potential energy at \( x=0 m \) is
\( U_{0}=0 J \) as shown above, determine
the potential energy at \( x=1.5 m \)
\begin{tabular}{|c|c|}
\hline Displacement \( x \) & Force \( F \) \\
\hline \( 0 \mathrm{m} \) & \( 0 \mathrm{N} \) \\
\hline \( 1 \mathrm{m} \) & \( -2 \mathrm{N} \) \\
\hline \( 2 \mathrm{m} \) & \( -8 \mathrm{N} \) \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 1.13 J \)
B. \( 2.25 J \)
c. \( 4.50 J \)
D. \( 6.75 J \)
E \( .7 .50 J \)
Subject: Physics
The moon's radius is \( 1 / 4 \) times that of the earth and its mass \( 1 / 80 \) times that
of the earth. If \( g \) represents the acceleration due to gravity on the surface of the earth, then on the surface
of the moon its value is :
\( \mathbf{A} \cdot g / 4 \)
в. \( g / 5 \)
c. \( g / 6 \)
D. \( g / 8 \)
Subject: Maths
\( \boldsymbol{x} * \boldsymbol{y}=\sqrt{\frac{(\boldsymbol{x}+\boldsymbol{y})\left(\boldsymbol{y}^{2}-\mathbf{1 2} \boldsymbol{x}\right)}{(\boldsymbol{x}-\mathbf{2})(\boldsymbol{y}-\mathbf{7})}} \) then what
will be the value of \( 5 * 9 ? \)
\( A \cdot 7 \)
B. 8
c. 10
D.
Subject: Physics
A rod of mass \( \mathrm{m} \) and length lis bent into
shape of L. Its moment of inertia about
the axis shown in figure:
A \( \cdot \frac{m^{2}}{6} \)
B. \( \frac{m^{2}}{3} \)
\( c \cdot \frac{m l^{2}}{12} \)
D. None
Subject: Chemistry
Nucleophilic addition reaction will be
most favoured in:
A \( \cdot C H_{3}-C H_{2}-C H_{2} C-C H_{3} \)
В \( \cdot\left(C H_{3}\right)_{2} C=O \)
c. \( C H_{3} C H_{2} C H O \)
D. \( C H_{3} C H O \)
Subject: Chemistry
Which statement is wrong?
This question has multiple correct options
A. In polar aprotic solvents such as DMSO, DMF, and DMA, the fugacity order is \( I^{\ominus}>B r^{\ominus}>C l^{\ominus}>F^{\ominus} \)
B. Strong bases are good leaving groups
C - The leaving group order of the following is : \( \stackrel{\ominus}{O H}> \) \( R O^{\ominus}>C H \equiv C^{\ominus}>\stackrel{\ominus}{N} H_{2} \)
D. Charged species are good leaving groups than neutral species
Subject: Physics
Explain, with the help of a circuit diagram, the working to a photo-diode. Write briefly how it is used to detect the
optical signals. OR
Mention the important considerations required while fabricating a \( \boldsymbol{p}-\boldsymbol{n} \)
junction diode to be used as a Light Emitting Diode (LED). What should be
the order of band gap of an LED if it is required to emit light in the visible
range?
Subject: Physics
Find how long the cylinder will move with sliding.
A \( \cdot t=\frac{\omega_{0} R}{3 k g} \)
В. \( t=\frac{\omega_{0} R}{6 k g} \)
c. \( _{t=2} \frac{\omega_{0} R}{3 k g} \)
D. \( t=2 \frac{\omega_{0} R}{6 k g} \)
Subject: Chemistry
Zinc sulphate contains \( 22.65 \% Z n \) and
\( 43.9 \% H_{2} O . \) If the law of constant
proportions is true, then the mass of
zinc required to give \( 40 g \) crystal will be:
A. \( 9.06 g \)
в. \( 90.6 g \)
c. \( 0.906 g \)
D. \( 906 g \)
Subject: Chemistry
Pick the wrong statement from the
following.
A. Consumption of citrus fruits and green leafy vegetables in food prevents scurvy.
B. Deficiency of Vitamin \( B_{6} \) (pyridoxime) results in convulsions.
C. Deficiency of vitamin D causes xerophthalmia.
D. Sources of Vitamin \( B_{1} \) are yeast, milk, green vegetables and cereals.
Subject: Maths
If \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{x}+\frac{\boldsymbol{x}^{2}}{\mathbf{2 !}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{3 !}}+\ldots+\frac{\boldsymbol{x}^{\boldsymbol{n}}}{\boldsymbol{n} !} \)
then \( \frac{d y}{d x} \) is equal to
\( \mathbf{A} \cdot \underline{y} \)
B. \( y+\frac{x^{n}}{n !} \)
c. \( y-\frac{x^{n}}{n !} \)
D. \( y-1-\frac{x^{n}}{n !} \)
Subject: Chemistry
Quicklime is made by heating
limestone. Which equation represents this reaction?
A \( \cdot C a C O_{3} \rightarrow C a+O_{2}+C O \)
в. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CaO}+\mathrm{H}_{2} \mathrm{CO}_{3} \)
D. \( C a C O_{3}+H_{2} O \rightarrow C a(O H)_{2}+C O_{2} \)
Subject: Physics
Assertion
An electric motor will have maximum
efficiency when back emf becomes equal to half of applied emf.
Reason
Efficiency of electric motor depends only on magnitude of back emf.
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 value of \( c \) of mean value theorem
when \( f(x)=x^{3}-3 x-2 \) in [-2,3] is
A \( \cdot \sqrt{\frac{7}{3}} \)
B. \( \sqrt{\frac{3}{7}} \)
c. \( \frac{\sqrt{7}}{3} \)
D. \( \frac{\sqrt{3}}{7} \)
Subject: Physics
If one of the two electrons of a \( \boldsymbol{H}_{2} \)
molecule is removed, we get a hydrogen
molecular ion \( \boldsymbol{H}_{2}^{+} . \) In the ground state
of an \( H_{2}^{+}, \) the two protons are separated by roughly \( 1.5 A \), and the electron is roughly \( 1 A \) from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.
Subject: Physics
A cannon of mass \( 10 \times 10^{3} k g \) is
rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a \( 2.1 \times 10^{3} k g \) shell
horizontally with an initial velocity of \( 550 m / s . \) Suppose the cannon is then
unbolted from the earth and no external force hinder its recoil. What would be the velocity (in \( \boldsymbol{m} / \boldsymbol{s} \) ) of a shell fired horizontally by the loose cannon? (Hint:
In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)
Subject: Maths
The point on the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}+\mathbf{3}}{-\mathbf{2}}= \)
\( \frac{z+5}{-2} \) at a distance of 6 from the point
(1,-3,-5) is
в. (3,-7,-9)
D. (-3,5,3)
Subject: Physics
are examples of isobars.
\( \mathbf{A} \cdot_{14} S i^{31},_{15} P^{32} \)
\( \mathbf{B} \cdot_{6} C^{13},_{7} N^{13} \)
\( \mathbf{C} \cdot_{7} N^{14},_{7} N^{15} \)
D. None of the above
Subject: Chemistry
Arrange the following compounds in
increasing order of their boiling points:
\( \mathbf{C H}_{3} \mathbf{C H}_{2} \mathbf{C H}_{2} \mathbf{C H O}, \mathbf{C H}_{3} \mathbf{C H}_{2} \mathbf{C H}_{2} \mathbf{C H}_{2} \)
Subject: Physics
A steel wire of length \( 1 \mathrm{m} \) has cross sectional area \( 1 \mathrm{cm}^{2} \). If young's modulus
of steel is \( 10^{11} N / m^{2}, \) then force required to increase the length of wire by \( 1 \mathrm{mm} \) will be :
\( \mathbf{A} \cdot 10^{11} N \)
В. \( 10^{7} N \)
\( \mathbf{c} \cdot 10^{4} N \)
D. \( 10^{2} N \)
Subject: Chemistry
An element \( A \) (atomic mass \( =75 \) ) and
\( B \) (atomic mass \( =25 \) ) combine to form
a compound. The compound contains
\( 75 \% A \) by mass.The formula of the compound will be :
A \( . A_{2} B \)
в. \( A_{3} B \)
\( \mathrm{c} \cdot A B_{3} \)
D. \( A B \)
Subject: Maths
If \( \alpha, \beta, \gamma, \delta \) are in arithmetic
progression. Then which is of the following is correct
A. \( \tan (\alpha+\delta)=\tan (\beta+\gamma) \)
B. \( \tan (\alpha+\gamma)=\tan (\beta+\delta) \)
c. \( \tan (\alpha+\beta)=\tan (\gamma+\delta) \)
D. none of these
Subject: Maths
If \( A \) is a \( 3 x 3 \) non singular matrix and
\( |\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}|=|\boldsymbol{A}|^{x},|\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})|= \)
\( |\boldsymbol{A}|^{y},\left|\boldsymbol{A}^{-1}\right|=|\boldsymbol{A}|^{z} \) then the values of
\( \mathbf{x}, \mathbf{y}, \mathbf{z}, \) in descending order
A. \( \mathrm{x}, \mathrm{Y}, \mathrm{z} \)
в. Z, Y, х
c. \( \mathrm{z}, \mathrm{x}, \mathrm{y} \)
D. Y, x, z
Subject: Chemistry
Which of the following solutions will be acidic?
(1) \( 0.1 M F e S O_{4} \)
(2) \( 0.1 M\left(N H_{4}\right)_{2} S O_{4} \)
(3) \( 0.1 M C H_{3} C O O N a \)
(4) \( 0.1 M N H_{4} O H \)
A \( \cdot 1,2 \) and 3 are correct
B. 1 and 2 are correct
\( c \cdot 2 \) and 4 are correct
D. 1 and 3 are correct
Subject: Physics
Assertion
In a two-body collision, the momenta of
the particles are equal and opposite to one another, before as well as after the
collision when measured in the centre
of mass frame.
Reason
The momentum of the system is zero from the centre of mass frame.
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
An ellipse passing through the point \( (2 \sqrt{13}, 4) \) has its foci at (-4,1) and \( (4,1), \) then its eccentricity is
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Chemistry
A 2.50 gram sample of which of the following would have the greatest mass of sulfur?
A. \( S r S ; \) molar mass \( =119.69 g / \mathrm{mol} \)
B. \( B e S \); molar mass \( =41.08 g / \mathrm{mol} \)
C . \( K_{2} S \); molar mass \( =110.26 g / \) mol
D. \( N a_{2} S ; \) molar mass \( =78.07 g / m o l \)
Subject: Maths
The median of the following data is :
\begin{tabular}{|c|c|c|c|c|c|}
\hline\( x: \) & 10 & 20 & 30 & 40 & 50 \\
\hline\( f: \) & 2 & 3 & 2 & 3 & 1 \\
\hline
\end{tabular}
A . 30
B. 40
\( c .35 \)
\( D \cdot 3 \)
Subject: Physics
Find the electric field in the copper wire
of area of cross section \( 2 m m^{2} \) carrying
a current of 1 A. The resistivity of
copper is \( 1.7 \times 10^{-8} \Omega m \)
A . \( 4.25 \times 10^{-3} \mathrm{V} / \mathrm{m} \)
B . \( 8.5 \times 10^{-3} \mathrm{V} / \mathrm{m} \)
c. \( 8.5 V / m \)
D. \( 9.5 \times 10^{-3} \mathrm{V} / \mathrm{m} \)
Subject: Physics
The necessary condition in making of a junction transistor (E-emitter, B-base
and C-collector)
A. \( E \) is heavily doped, \( B \) is thin and lightly doped and \( C \) is moderately doped
B. E and C are lightly doped and B is thick and heavily doped
C. \( \mathrm{E} \) and \( \mathrm{B} \) are heavily doped and \( \mathrm{C} \) is lightly doped
D. \( \mathrm{E} \) and \( \mathrm{B} \) are lightly doped an \( \mathrm{C} \) is heavily doped
Subject: Maths
The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the cylinder, then the ratio of the rates of increase of the
volume of the sphere and the volume of the cylinder is
A .4: 3
в. 3: 4
\( \mathbf{c} \cdot 4: 3 \pi \)
\( \mathbf{D} \cdot 3: 4 \pi \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{1} \\ \mathbf{0} & \mathbf{2} & -\mathbf{3} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left(\boldsymbol{a d} \boldsymbol{j}_{\boldsymbol{j}}\right. \)
and \( C=5 A, \) then \( \frac{|a d j \quad B|}{|C|} \) is equal to
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
\( c \)
\( D \)
Subject: Maths
If \( q \) is a real number, then which of the
following is incorrect?
\( ^{A} \cdot \sin q=-\frac{1}{5} \)
B. \( \cos q=1 \)
\( \mathbf{c} \cdot \sec q=\frac{1}{7} \)
D. \( \tan q=-20 \)
Subject: Maths
Let \( R \) be the set of all real numbers and
\( \boldsymbol{f}:[-\mathbf{1}, \mathbf{1}] \rightarrow \boldsymbol{R} \) be defined by \( \quad \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{c}x \sin \frac{1}{x}, x \neq 0 \\ 0, x=0\end{array} . \) Then \right.
A. \( f \) satisfies the conditions of Rolle's theorem on [-1,1]
B. \( f \) satisfies conditions of Lagrange's Mean Value Theorem on [-1,1]
c. \( f \) satisfies the conditions of Rolle's theorem on [0,1]
D. \( f \) satisfies the conditions of Lagrange's Mean Value Theorem on [0,1
Subject: Physics
The \( H \) calories of heat is required to
increase the temperature of one mole of
monoatomic gas from \( 20^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) at
constant volume. The quantity of heat required to increase the temperature
of 2 moles of a diatomic gas from \( 20^{\circ} \mathrm{C} \)
to \( 25^{\circ} C \) is at constant volume is :
A \( \cdot \frac{4 H}{3} \)
в. \( \frac{5 H}{3} \)
c. \( 2 H \)
D. \( \frac{7 H}{3} \)
Subject: Physics
Assertion
The vectors \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}= \)
\( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) are mutually perpendicular.
Reason
\( \overrightarrow{\boldsymbol{A}} \bullet \overrightarrow{\boldsymbol{B}}=0 \)
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 container having a hole at the bottom
is free to move on a horizontal
surface. As the liquid comes out, the container moves in a backward
direction
with an acceleration \( \alpha \) and finally
acquires a velocity v (when all the liquid has drained out). Neglect the mass of the container. The correct option out of the following is :
A. Only v vepends on \( h \)
B. Only \( \alpha \) depends on h
c. Both v and \( \alpha \) depend on \( n \)
D. Neither v nor \( \alpha \) depends on \( h \)
Subject: Physics
wavefront and \( A O \) and \( B P \) the
corresponding extreme rays of
monochromatic light of wavelength ' \( \lambda \).
The value of angle \( \theta \) for which the ray \( \mathrm{BP} \)
and the reflected ray OP interfere
constructively is given by:
A \( \cdot \cos \theta=\frac{3 \lambda}{4 d} \)
B. \( \cos \theta=\frac{\lambda}{4 d} \)
\( \mathrm{c} \cdot \sec \theta=\frac{\lambda}{3 d} \)
D \( \sec \theta=\frac{2 \lambda}{3 d} \)
Subject: Chemistry
Assertion
The \( O^{2-} \) ion and the neon atom have
similar chemical properties because:
Reason
the \( O^{2-} \) ion and the neon atom have the
same number of electrons.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
Bag \( I \) contains 2 blacks and 8 red balls, bag IIcontains 7 black and 3 red balls
and bag \( I I I \) contains 5 black and \( 5 v \)
red balls. One bage is chosen at random and a ball is drawn from it which is
found to bered. Find the probability that the ball is drawn from bag \( I I \)
Subject: Physics
A dipole of dipole moment \( P \) is placed at
a distance r form a point change \( Q \) (as
shown in figure).Choose the incorrect
statement.
A. Torque acting on the dipole is zero
B. Force acting on the dipole due to the electrie field produce by \( \mathrm{Q} \) is zero
C. potential energy of the dipole due to the point charge \( Q \) is \( \frac{Q p}{4 \frac{Q_{0}}{r^{2}}} \)
D. Force acting on the dipole due to the point charge \( \mathrm{Q} \) is \( \frac{Q p}{4 \pi \varepsilon_{0} r^{3}} \)
Subject: Maths
If \( \int \frac{(4 x+3)}{\sqrt{2 x^{2}+2 x-3}}= \)
\( 2 \sqrt{2 x^{2}+2 x-3}+ \)
\( \frac{1}{\sqrt{\boldsymbol{k}}} \log \left|\boldsymbol{x}+\frac{1}{2}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{x}-\frac{\boldsymbol{3}}{2}}\right|+\boldsymbol{C} \)
then value of \( k \) is
Subject: Maths
5 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that there are exactly 3 hearts is
A. \( \frac{13}{^{13} s_{3}+^{13} c_{4}+^{13} c_{5}} \)
в.
\( c \)
D. \( \frac{13}{^{13} s_{3} \times^{13} c_{4} \times^{13} c_{5}} \)
Subject: Physics
Protons are accelerated from rest by a potential difference \( 4 \mathrm{kV} \) and strike a
metal target. If a proton produces one photon on impact of minimum
wavelength \( \lambda_{1} \) and similarly an electron accelerated to \( 4 \mathrm{kV} \) strikes the target
and produces a minimum wavelength
\( \lambda_{2} \) then
A \( \cdot \lambda_{1}=\lambda_{2} \)
B. \( \lambda_{1}>\lambda_{2} \)
\( c \cdot \lambda_{1}<\lambda_{2} \)
D. no such relation can be established
Subject: Physics
The graph is shown in the figure is a
plot of the temperature of the body in
\( ^{o} C \) and \( ^{o} F . \) The value of \( \sin \theta \) is
4
\( \overline{\mathrm{q}} \)
B. \( \frac{5}{\sqrt{86}} \)
c. \( \frac{9}{\sqrt{86}} \)
D. \( \frac{5}{\sqrt{106}} \)
Subject: Maths
If \( A \& B \) are two events such that
\( P(B) \neq 1, B^{C} \) denotes the event
complementary to B, then This question has multiple correct options
\( ^{\mathbf{A}} \cdot P\left(A / B^{C}\right)=\frac{P(A)-P(A \cap B)}{1-P(B)} \)
B . \( P(A \cap B) \geq P(A)+P(B)-1 \)
C . \( P(A)><P(A / B) \) according as \( P\left(A / B^{C}\right)><P(A) \)
D \cdot \( P\left(A / B^{C}\right)+P\left(A^{C} / B^{C}\right)=1 \)
Subject: Physics
If \( M_{2}= \) magnetization of a
paramagnetic sample, \( \mathrm{B}= \) external magnetic field, \( T= \) absolute temperature, \( C= \) curie constant then according to Curie's law in magnetism, the correct relation is
A \( \cdot M_{z}=\frac{T}{C B} \)
В. \( \quad M_{z}=\frac{C B}{T} \)
\( ^{\mathrm{c}} \cdot_{C}=\frac{M_{z}}{T} \)
D. \( _{C}=\frac{T^{2}}{M_{z} B} \)
Subject: Chemistry
When \( K C l O_{3} \) is heated, it decomposes
into \( K C l \) and \( O_{2} . \) If some \( M n O_{2} \) is
added, the reaction goes much faster
because:
A. \( M n O_{2} \) decomposes to give \( O_{2} \)
B. \( M n O_{2} \) provides heat by reacting
C. better contact is provided by \( M n O_{2} \)
D. \( M n O_{2} \) acts as a catalyst
Subject: Chemistry
Name the functional groups present in the following compound:
(i) \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \)
(ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
(iv) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
Subject: Physics
An air filled balloon is at a depth of \( 2 \mathrm{km} \)
below the water level in an ocean.
Determine the normal stress on the
balloon [atmospheric pressure \( =10^{5} \) Pa \( ] \)
A \( .190 \times 10^{5} P a \)
В. \( 196 \times 10^{5} \mathrm{Pa} \)
c. \( 190 \times 10^{7} P a \)
D. \( 196 \times 10^{7} P a \)