AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Select the correct option:
Read the given statements.
I. Fructose is the sweetest sugar.
ii. Glycine is the simplest amino acid.
iii. Lactose is a disaccharide composed
of one molecule each of glucose and
galactose.
iv. Cellulose is an unbranched chain of
glucose molecules linked by \( \beta 1,4 \) glycosidic bond. Which of the given statements are
correct?
A \( \cdot \) (i) and (ii)
B. (iii) and (iv)
c. (i), (ii) and (iii)
D. (i), (ii), (iii) and (iv)
Subject: Chemistry
The number of \( \boldsymbol{P}-\boldsymbol{H} \) bond(s) in
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
respectively, is:
\( \mathbf{A} \cdot 2,0,1 \)
B. 1,1,1
c. 2,0,0
D. 2,1,0
Subject: Chemistry
In acidic medium the rate of reaction
between \( \left(B r O_{3}\right)^{-} \) and \( B r^{-} \) ion is given by the expression.
\( -\left[\boldsymbol{d}\left(\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}\right) / \boldsymbol{d} \boldsymbol{t}\right]= \)
\( \boldsymbol{K}\left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}\right]\left[\boldsymbol{B r}^{-}\right]\left[\boldsymbol{H}^{+}\right]^{2} . \) It means:
A. Rate constant of overall reaction is 4 sec\( ^{-1} \)
B. Rate of reaction is independent of the concentration of acid
C. The change in pH of the solution will not affect the rate
D. Doubling the concentration of \( H^{+} \) ions will increase the reaction rate by 4 times.
Subject: Maths
Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is an even prime
number less than 16 .
A \( \cdot \frac{5}{28} \)
B. \( \frac{3}{50} \)
\( c \cdot \frac{3}{25} \)
D. \( \frac{1}{100} \)
Subject: Chemistry
A balloon is filled with hydrogen at room temperature. It will burst if pressure
exceeds 0.2 bar

If at 1 bar pressure the gas occupies \( 22.7 \mathrm{L} \) volume up to what volume can the balloon be expanded?
A . 11.35 L
B. 22.7 L
c. \( 44.8 \mathrm{L} \)
D. 67.3 L
Subject: Physics
Select the correct orders for gases
represented with their characteristics:
This question has multiple correct options
A. Critical temperature < Boyle's temperature
B. van der Waal's constant 'a' : \( H_{2} O>N H_{3}>N_{2}>N e \)
C. Heat capacity: \( N H_{3}>C O_{2}>O_{2}=N_{2}>A r \)
D. Mean free path: \( H e>H_{2}>O_{2}>N_{2}>C O_{2} \)
Subject: Chemistry
Given the following bond dissociation enthalpies (kJ mol-1) :
\begin{tabular}{c|c}
\( \boldsymbol{P} \equiv \boldsymbol{P} \) & \( \mathbf{4 9 0} \) \\
\( \boldsymbol{P}-\boldsymbol{P} \) & \( \mathbf{2 0 9} \) \\
\( \boldsymbol{N} \equiv \boldsymbol{N} \) & \( \mathbf{9 4 6} \) \\
\( \boldsymbol{N}-\boldsymbol{N} \) & \( \mathbf{1 6 0} \)
\end{tabular}
Compare the enthalpy changes for the process and comment if the reactions are possible
(i) \( 2 P_{2}(g) \longrightarrow P_{4}(g) \)
(ii) \( 2 N_{2}(g) \longrightarrow N_{4}(g) \)
A . (i) possible (II) not possible
B. (i) possible (II) possible
\( c \cdot \) (i) not possible (II) possible
D. (i) not possible (II)not possible
Subject: Maths
If \( \sin ^{x} \alpha+\cos ^{x} \alpha \geq 1,0<\alpha<\frac{\pi}{2}, \) then
A. \( x \in[2,+\infty) \)
в. \( x \in(-\infty, 2] \)
c. \( x \in[-1,1] \)
D. none of these
Subject: Physics
\( A \) and \( B \) are two concentric circular
conductors of centre \( \boldsymbol{O} \) and carrying
currents \( I_{1} \) and \( I_{2} \) as shown in the
adjacent figure. If ratio of their radii is
1 : 2 and ratio of the flux densities at \( O \)
due to \( A \) and \( B \) is \( 1: 3, \) then the value of
\( \boldsymbol{I}_{1} / \boldsymbol{I}_{2} \) is:
Subject: Maths
Say true or false:
A positive integer is of the form \( 3 q+1 \)
\( \boldsymbol{q} \) being a natural number, then you write its square in any form other than \( 3 m+1, \) i.e.,3m or \( 3 m+2 \) for some
integer \( \boldsymbol{m} \)
A. True
B. False
Subject: Maths
The ratio in which \( \bar{i}+2 \bar{j}+3 \bar{k} \) divides the join of \( -2 \bar{i}+3 \bar{j}+5 \bar{k} \) and \( 7 \bar{i}-\bar{k} \) is
\( \mathbf{A} \cdot-3: 2 \)
B. 1: 2
\( c \cdot 2: 3 \)
D. -4: 3
Subject: Physics
Consider the following statements A and B and identify the correct statements.
Statement \( A: p-n ; p-p ; n-n \) forces
between nucleons are not equal and charge dependent statement B : In nuclear reactor the
fission reaction will be in accelerating state if the value of
neutron reproduction factor is \( k>1 \)
A. Both A and B are correct
B. Both A and B are wrong
c. A is wrong B is correct
D. A is correct B is wrong
Subject: Chemistry
Which of the followings are dissociation?
1. \( M g C l_{2} \rightarrow M g^{2+}+2 C l^{-} \)
2. \( P b B r_{2} \rightarrow P b^{2+}+2 B r^{-} \)
3. \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \rightarrow \boldsymbol{N} \boldsymbol{a}^{+}+\boldsymbol{C l}^{-} \)
A. Only 1 and 2
B. Only 1 and 3
c. only 2 and 3
D. All 1,2 and 3
Subject: Chemistry
The equilibrium constant for the reaction \( \boldsymbol{w}+\boldsymbol{x} \rightleftharpoons \boldsymbol{y}+\boldsymbol{z} \) is \( 9 . \) If one mole
of each of wand \( x \) are mixed and there is
no change in volume, the number of moles of y for formed is :
A . 0.10
B. 0.50
c. 0.75
D. 0.54
Subject: Chemistry
The rate of a reaction quadruples when
the temperature changes from 300 to
310K. What is the activation energy of
this reaction?
(Assume activation energy and preexponential factor are independent of temperature ; \( \ln 2=0.693 ; \mathrm{R}=8.314 \)
\( \left.\boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
Subject: Physics
Assertion
The time of flight 'T' is the sum of time
of ascent and time of descent.
Reason
The time of ascent is equal to the time
of descent.
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
What is the equation of the plane containing the parallel lines
\( \boldsymbol{r}=\boldsymbol{a}+\boldsymbol{t c}, \boldsymbol{r}=\boldsymbol{b}+\boldsymbol{p} \boldsymbol{c} \)
\( \mathbf{A} \cdot r \cdot(b-a) \times c=[a b c] \)
B \cdot \( r \cdot(a-b) \times c=[a b c] \)
C \( \cdot r \cdot(b-a) \times c=-[a b c] \)
D \( \cdot r c \times(b-a) \times c=[a b c] \)
Subject: Maths
Prove that polynomial \( \boldsymbol{x}^{\boldsymbol{4} \boldsymbol{p}}+\boldsymbol{x}^{\boldsymbol{4} \boldsymbol{q}+1}+ \)
\( x^{4 r+2}+x^{4 s+3} \) can be divided by \( x^{3}+ \)
\( \boldsymbol{x}^{2}+\boldsymbol{x}+1, \) where \( \boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}, \boldsymbol{s} \in \boldsymbol{N} \)
Subject: Maths
Find the least values of \( x \) and \( y \) which
satisfy the equations:
\( 77 y-30 x=295 \)
A . \( x=32, y=27 \)
в. \( x=21, y=34 \)
c. \( x=47, y=35 \)
D. \( x=46, y=32 \)
Subject: Physics
A metallic calorimeter of mass 100 g
contains 200 g of ice and the initial temperature of the calorimeter and the
ice is \( -10^{\circ} \mathrm{C} . \) Heat is supplied to the system containing calorimeter and ice
at a constant rate of 50 cals\( ^{-1} \). Find the
time required to raise the temperature
of the system to \( 50^{\circ} \mathrm{C} \). [Neglect the loss of heat to the surroundings]. Take specific heat capacity of calorimeter and ice as \( 0.2 c a l g^{-1 \circ} C^{-1} \) and \( \frac{1}{2} c a l g^{-1 \circ} C^{-1} \).Take latent heat of
fusion of ice as \( 80 \mathrm{calg}^{-1} \) and specific
heat capacity of water as 1 calg\( ^{-1 \circ} C^{-1} \)
Subject: Chemistry
Find out the incorrect reaction involved
in Contact process
A. \( H_{2} S_{2} O_{7}+H_{2} O \rightarrow 2 H_{2} S O_{4} \)
B. \( H_{2} S O_{4}+2 N a O H \rightarrow 2 H_{2} O+N a_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{SO}_{3} \rightarrow \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D \( \cdot 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)
Subject: Chemistry
Consider the reaction of chloromethane
with \( O H^{-} \) in aqueous solution
\( \boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{a q})+ \)
\( O H(a q) \stackrel{K_{f}}{\underbrace{K_{r}}} C H_{3} O H(a q)+C l(a q) \)
At \( 25^{\circ} C, \) the rate constant for the
forward reaction is \( 6 \times 10^{6} M^{1} s^{-1}, \) and
the equilibrium constant \( K_{c} \) is \( 1 \times 10^{16} \)
Calculate the rate constant for the
reverse reaction at \( 25^{\circ} C \)
A \( .3 \times 10^{22} \)
B . \( 6 \times 10^{22} \)
C \( \cdot 12 \times 10^{22} \)
D. \( 12 \times 10^{23} \)
Subject: Biology
Match the following items in column I with column II and choose the correct
answer.

Column I
A. Arsenic
1. Minamata
disease
B. Nitrate
2. Itai-itai
C. Mercury
3. Blue-baby syndrome
D. Cadmium
4. Skeletal
fluorosis
E. Fluoride
5. Black-foot
disease
A \( \cdot A-2, B-3, C-5, D-1, E-4 \)
B. A- 5, B- - 3, С-1, D- 2, E- 4
c. \( A-3, B-4, C-5, D-1, B-2 \)
D. A- 5, B- 4, C- 3, D-2, B-1
E. A- 2, B- 5, C- 4, D- 3, E-1
Subject: Maths
The area of the triangle formed by the points (2,6),(10,0) and \( (0, k) \) is zero square units. Find the value of \( k \)
A \( \cdot \frac{15}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{7}{2} \)
D. \( \frac{13}{2} \)
Subject: Maths
\( \lim _{x \rightarrow \pi / 4} \frac{1-\cot ^{3} x}{2-\cot x-\cot ^{3} x} \) is
A \( \cdot \frac{11}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)
Subject: Physics
Steam at \( 100^{\circ} \mathrm{C} \) is passed into 20 g of
water acquires a temperature of \( 80^{\circ} \mathrm{C} \) the mass of water presents will be [Take
specific heat of water 1 cal \( g^{-1} c^{-1} \) latent heat of steam \( \left.=\$ \$ 540 \text { lcal } \mid g^{\wedge}\{-1\} \$ \$\right] \)
A. \( 31.5 g \)
в. \( 42.5 g \)
c. \( 22.5 g \)
D. \( 24 g \)
Subject: Physics
\( \ln \) an \( A C \) circuit \( V \) and \( I \) are given by
\( \boldsymbol{V}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) \) volt, \( \boldsymbol{I}= \)
\( 100 \sin \left(100 t+\frac{\pi}{3}\right) \) amp the power
dissipated in the circuit is
A . \( 5.0 k W \)
в. \( 2.5 k W \)
c. \( 1.25 k W \)
D. zero
Subject: Chemistry
The blue compound is formed in the
positive test for nitrogen with Lassaigne's solution of an organic compound is:
\( \mathbf{A} \cdot \operatorname{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5}(\mathrm{NOS})\right. \)
в. \( N a_{3}\left[F e(C N)_{6}\right. \)
\( \mathbf{c} \cdot\left[F e(C N)_{3}\right. \)
D. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)
Subject: Physics
A vessel is filled with an ideal gas at a
pressure of 10 atmospheres and temp \( 27^{\circ} \)
C. Half of the mass of the gas is removed from the vessel \& the temp. of the remaining gas is increased to \( 87^{0} \mathrm{C} \). Then
the pressure of the gas in the vessel will be
\( A \cdot 5 \) atm
B. 6 atm
c. 7 atm
\( D \cdot 8 \operatorname{atm} \)
Subject: Maths
f \( |z|=1, z \neq i, \) then \( z \) can be written in
the form
A \( \cdot \frac{1+x}{1-x}(x \in R) \)
B. \( \frac{1+i x}{1-i x}(x \in R) \)
c. \( \frac{i+x}{1-x}(x \in R) \)
D. None of these
Subject: Chemistry
In dimer of phosphorus pentaoxide, in what order number of PP, P=0 \& POP
bonds are there?
A \( . P O P>P=O>P P \)
в. \( P=O>P O P>P P \)
c. \( P O P>P P>P=O \)
\( D, P=O>P P>P O P \)
Subject: Chemistry
Which one is more basic,
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{o r} \boldsymbol{C F}_{3} \boldsymbol{N H}_{2} \)
\( \mathbf{A} \cdot C H_{3} N H_{2} \)
В \( \cdot C F_{3} N H_{2} \)
c. Both have similar basicity
D. None of the above
Subject: Maths
\( A \) and \( B \) have 460 coins altogether. If \( \frac{3}{4} \) of \( A^{\prime} \) s number of coins is equal to \( \frac{2}{5} \) of
B's number of coins, find how many
coins must \( B \) give to \( A, \) so that they
both have equal number of coins.
A . 50
B. 70
c. 20
D. 90
Subject: Physics
A block of mass \( 2.0 \mathrm{kg} \) is pushed down
an inclined plane of inclination \( 37^{\circ} \) with
a force of \( 20 N \) acting parallel to the incline. It is found that the block moves
on the incline with an acceleration of
\( 10 m / s^{2} . \) If the block started from rest, find the work done
(a) by the applied force in the first second
A . 100
B. 105
c. 150
D. 200
Subject: Physics
From one corner A of a rectangular
billiard table ABCD placed on a
horizontal surface, a ball of mass and
negligible dimension is projected in the
direction making \( \theta \) with side \( A B \) it strikes in other sides \( \mathrm{BC}, \mathrm{AD}, \mathrm{DC} \) and \( \mathrm{BC} \)
and then return to same point A. Then
the value of coefficient of restitution is:
\( A \)
в. \( \sqrt{\frac{a \sin \theta}{b \cos \theta+a \sin \theta}} \)
c. \( \sqrt{\frac{a \sin \theta}{b \sin \theta-a \cos \theta}} \)
D. \( \sqrt{\frac{a \sin \theta}{b \sin \theta+a \cos \theta}} \)
Subject: Chemistry
Heat of \( 30 k c a l \) is supplied to a system
and \( 4200 J \) of external work is done on
the system so that its volume
decreases at constant pressure. What
is the change in its internal energy. \( = \) \( (J=4200 J / k c a l) \)
A \( \cdot 1.302 \times 10^{5} \mathrm{J} \)
J. \( 1.302 \times 10^{2} \)
в. \( 2.302 \times 10^{5} \mathrm{J} \)
c. \( 3.302 \times 10^{5} J \)
D. \( 4.302 \times 10^{5} \mathrm{J} \)
Subject: Chemistry
The end product \( ^{\prime} C^{\prime} \) in the following sequence of chemical reactions is:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{C a C O}_{3}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H e a t}}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{N H_{2} O H}{\longrightarrow} \boldsymbol{C} \)
A. Acetaldehyde oxime
B. Formaldehyde oxime
c. Methyl nitrate
D. Acetoxime
Subject: Maths
Integrate: \( \int \frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} d x \)
\( \mathbf{A} \cdot I=2 \tan \sqrt{x}+c \)
B. \( I=2 \cot \sqrt{x}+c \)
\( \mathbf{c} \cdot I=3 \tan \sqrt{x}+c \)
D \( \cdot I=2^{2} \tan \sqrt{x}+c \)
Subject: Maths
Measure of \( \angle B \) and \( \angle C \) are
\( \mathbf{A} \cdot 75^{\circ}, 85 \)
B \( \cdot 75^{\circ}, 75 \)
\( \mathbf{c} \cdot 55^{\circ}, 55^{\circ} \)
D. \( 65^{\circ}, 65^{\circ} \)
Subject: Chemistry
What is the acidity order of the
following compounds?
\( \mathbf{A} \cdot I>I I>I I I>I V>V \)
\( \mathbf{B} \cdot I I>I I I>I V>V>I \)
\( \mathbf{c} \cdot V>I I I>I>I I>I V \)
D. \( V>I I I>I I>I>I V \)
Subject: Physics
A charged oil drop is suspended in uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be (take the mass of the charge \( =\mathbf{9 . 9} \times \mathbf{1 0}^{-\mathbf{1 5}} \) and \( \boldsymbol{g}=\mathbf{1 0} \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
B . \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)
Subject: Maths
The the focal distance of an end of the
minor axis of any ellipse (reffered to its axes of \( x \) and \( y \) respectively) is \( k \) and
the distance between the foci is \( 2 h \)
then its equation is:
A \( \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}+h^{2}}=1 \)
B. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}-k^{2}}=1 \)
\( ^{\mathrm{C}} \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}-h^{2}}=1 \)
D. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}}=1 \)
Subject: Physics
The dimensional formula for electric
flux density is given by
A \( \cdot\left[M L T^{-3} A-1\right] \)
B . \( \left[M L T^{3} A-1\right] \)
c. \( \left[M L T^{-3} A 1\right] \)
D. \( \left[M L T^{3} A 1\right] \)
Subject: Physics
A progressive wave of frequency
\( \mathbf{5 0 0} \boldsymbol{H z} \) is travelling at a speed of
\( 360 m s^{-1} . \) How far are the two points on
it having a phase difference of \( 60^{\circ} \)
A . \( 0.12 \mathrm{m} \)
B. \( 0.36 m \)
c. 0.24 m
D. \( 0.18 m \)
Subject: Maths
State whether the following statement is True or False?

The differential equation of a circuit
with inductance \( L \) and resistance \( R \) is
\( \operatorname{givenby} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\frac{\boldsymbol{R}}{\boldsymbol{L}} \boldsymbol{i}=\frac{\boldsymbol{E}}{\boldsymbol{L}} \boldsymbol{e}^{-\boldsymbol{a t}}(\boldsymbol{i}= \)
0 at \( t=0 \). The current at time \( t \) is given
by \( i=\frac{E}{R-a L}\left(e^{-a t}\right) \)
A . True
B. False
Subject: Physics
What is the dimensional formula of
resistance?
\( \mathbf{A} \cdot\left[M^{-1} L^{-2} T^{4} A^{-2}\right] \)
В \( \cdot\left[M L^{2} T^{-5} A^{-3}\right] \)
C \( \cdot\left[M^{-1} L^{-2} T^{4} A^{2}\right] \)
D. None of these
Subject: Chemistry
Which one of the following reactions is
incorrect?
A \( . \) Maltose \( +H_{2} O \stackrel{\text { Maltase }}{\rightarrow} \) Glucose \( + \) Fructose
B . Sucrose \( +H_{2} O \stackrel{\text { Invertase }}{\rightarrow} \) Glucose \( + \) Fructose
c. Glucose \( +H_{2} O \stackrel{Z y m a s e}{\rightarrow} \) Ethyl alcohol \( +C O_{2} \)
D. \( S t a r c h+H_{2} O \stackrel{\text { Diastase }}{\rightarrow} \) Glucose only
Subject: Maths
The differential equation by eliminating the arbitary constants from the equation \( \boldsymbol{y}=\boldsymbol{a} \cos \boldsymbol{x}+\boldsymbol{b} \sin \boldsymbol{x}+\boldsymbol{x} \sin \boldsymbol{x} \)
is
\( \mathbf{A} \cdot y_{2}+y=3 \cos x \)
В. \( y_{2}+2 y=2 \cos x \)
C \( \cdot y_{2}+y=2 \cos x \)
D. \( y_{2}+y=4 \cos x \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}1 & 2 \\ 3 & 4 \\ 5 & 6\end{array}\right] \) and \( B=\left[\begin{array}{cc}-3 & -2 \\ 1 & -5 \\ 4 & 3\end{array}\right] \)
then find \( D=\left[\begin{array}{ll}\boldsymbol{p} & \boldsymbol{q} \\ \boldsymbol{r} & \boldsymbol{s} \\ \boldsymbol{t} & \boldsymbol{u}\end{array}\right] \) such that \( \boldsymbol{A}+ \)
\( \boldsymbol{B}-\boldsymbol{D}=\boldsymbol{O} \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}-1 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}-3 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-2 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
D. \( \left[\begin{array}{cc}-2 & 0 \\ 4 & -5 \\ 9 & 9\end{array}\right] \)
Subject: Maths
Find the inverse of \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{1} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{A}^{-1}=\left[\begin{array}{ccc}1 / 2 & -1 / 2 & 1 / 2 \\ a & 3 & b \\ c & -3 / 2 & 1 / 2\end{array}\right] \)
Find \( |\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}| ? \)
Subject: Chemistry
Which of the statements about
Denaturation' given below are correct? Statements:
(i) Denaturation of proteins causes loss of secondary and tertiary structures of the protein.
(ii) Denaturation leads to the conversion of double strand of DNA into
single strand.
(iii) Denaturation affects primary
structure which gets destroyed.
A. (ii) and (iii)
B. (i) and (iii)
c. (i) and (ii)
D. (i), (ii) and (iii)
Subject: Physics
A current \( i_{0} \) is flowing through an \( L-R \)
circuit of time constant \( t_{0} . \) The source
of the current is switched off at time
\( \boldsymbol{t}=\mathbf{0} . \) Let \( \boldsymbol{r} \) be the value of \( (-\boldsymbol{d i} / \boldsymbol{d} \boldsymbol{t}) \) at
time \( t=0 . \) Assuming this rate to be
constant, the current will reduce to zero
in a time interval of:
A \( \cdot t_{0} \)
B . \( e t_{0} \)
\( c \cdot t_{0} / e \)
D. \( \left(1-\frac{1}{e}\right) t_{0} \)
Subject: Physics
A parallel plate capacitor is given a
definite potential difference. Keeping the potential difference same, a slab of
thickness \( 3 \mathrm{mm} \) is placed between the plates. To do this, the distance between the plates is increased by \( 2.4 \mathrm{mm} \)
Calculate the dielectric constant of the
slab.
\( (\mathbf{a}) \)
(b)
\( A \cdot 10 \)
В. 15
\( c .5 \)
\( D \)
Subject: Maths
\( P, Q \) and \( R \) are partners in a business.
\( P \) whose money has been used for 4 months, claims \( \frac{1}{8} \) of the profit \( , Q \)
whose money has been used for 6 months, claims at \( \frac{1}{3} \) of the profit. \( \boldsymbol{R} \)
had invested Rs. 1560 for 8 months. How
much did \( P \) and \( Q \) contribute?
Subject: Physics
In a photoelectric experiment, the collector plate is at \( 2.0 \mathrm{V} \) with respect to the emitter plate made of copper \( (\phi= \) 4.5 \( e V \) ). the emitter is illuminated by a
source of monochromatic light of
wavelength \( 200 \mathrm{nm} \)
A. The minimum kinetic energy of the photo electrons reaching the collector is 0
B. The maximum kinetic energy of the photo electrons reaching collector is 3.7 ev.
c. If the polarity of the battery is reversed then answer to part A will be o
D. If the polarity of the battery is reversed then answer to part B will be 1.7 eV
Subject: Maths
\( z_{1} \) and \( z_{2} \) are two non-zero complex
numbers such that \( \left|z_{1}\right|=\left|z_{2}\right| \) and
\( \arg z_{1}+\arg z_{2}=\pi, \) then \( z_{2} \) equals
\( A \cdot z_{1} \)
B. \( -\overline{z_{1}} \)
\( \mathbf{c} \cdot z_{1} \)
D. \( -z_{1} \)
Subject: Maths
Let the statement \( P(n): 2^{n} \geq 3 n \), the
truth of \( \boldsymbol{P}(\boldsymbol{k}), \forall \boldsymbol{k} \in \boldsymbol{N} \Rightarrow \) truth of
\( \mathbf{A} \cdot P(1) \)
B \( \cdot P(2) \)
\( \mathbf{c} \cdot P(3) \)
D \( \cdot P(k+1) \)
Subject: Chemistry
The difference between heat of reaction at
constant pressure and constant volume
for the reaction given below at \( 25^{0} \mathrm{C} \) in \( \mathrm{kJ} \)
is: \( 2 C_{6} H_{6(l)}+15 O_{2(g)} \rightarrow 12 C O_{2(g)}+6 H_{2} O_{(l)} \)
A \( .-7.43 \)
B. +3.72
c. - 3.72
D. +7.43
Subject: Maths
In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to
\( 30 . \) In order to maximize the area of the
trapezium, the smallest angle should be
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.
Subject: Maths
Find the max.value of the total surface
of a right circular cylinder which can be inscribed in a sphere of radius a.
A \( \cdot \pi a^{2}(1+1 / \sqrt{5}) \)
B \( \cdot \pi / 2 a^{2}(1+\sqrt{5}) \)
c. \( \pi a^{2}(1+\sqrt{5}) \)
D \cdot \( \pi a^{2}(2+\sqrt{5}) \)
Subject: Physics
An \( 8 k g \) cat is dragged along a hardwood
floor such that her final velocity is
\( 80 \mathrm{cm} / \mathrm{s} \) after being dragged through
\( 2 m \)
She is initially at rest. In this time interval, the work done on the cat by the normal force exerted by the floor is closest to:
A. zero
в. \( 1.88 J \)
c. \( 2.56 J \)
D . 78.48J
E . 156.965
Subject: Physics
toppr
Q Type your que
microscope is the product of the lateral
magnification \( m_{1} \) of the objective and
the angular magnification \( M_{2} \) of the eyepiece. The former is given by \( \boldsymbol{m}_{1}=\frac{\boldsymbol{S}_{1}^{\prime}}{\boldsymbol{S}_{1}} \)
Where \( S_{1} \) and \( S_{1}^{\prime} \) are the object and image distance for the objective lens. Ordinarily the object is very close to the focus, resulting in an image whose distance from the objective is much
larger than the focal length \( f_{1} \). Thus \( S_{1} \)
is approximately equal to \( f_{1} \) and \( m_{1}= \) \( -\frac{S_{1}^{\prime}}{\boldsymbol{f}_{1}}, \) approximately. The angular magnification of the eyepiece from \( M=-\frac{u^{\prime}}{u}=\frac{y / f}{y / 25}=\frac{25}{f} \)
centimeters) is \( M_{2}=25 \mathrm{cm} / \mathrm{f}_{2}, \) Where
\( f_{2} \) is the focal length of the eyepiece, considered as a simple lens. Hence the overall magnification M of the compound microscope is, apart from a negative sign, which is customarily ignored, \( M=m_{1} M_{2}=\frac{(25 c m) S_{1}^{\prime}}{f} \)
1. What is the resolving power of the instrument whose magnifying power is given in the passage?
A \( \cdot \frac{\mu \sin \theta}{0.61 \lambda} \)
в. \( \frac{\mu \sin \theta}{1.22 \lambda} \)
c. \( \frac{\mu \sin \theta}{\lambda} \)
D. \( \frac{\sin \theta}{1.22 \lambda} \)