AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In the circuit shown here, \( \boldsymbol{E}_{\mathbf{1}}=\boldsymbol{E}_{2}= \)
\( \boldsymbol{E}_{3}=2 \boldsymbol{V} \) and \( \boldsymbol{R}_{1}=\boldsymbol{R}_{2}=\boldsymbol{4} \) ohms. The
current flowing between points \( A \) and \( B \)
through battery \( \boldsymbol{E}_{2} \) is :-
A . zero
B. 2 amp from A to B
c. 2 amp from \( B \) to \( A \)
D. none of the above
Subject: Maths
For \( \mathbf{r}=\mathbf{0}, \mathbf{1}, \dots, 10, \) let \( \mathbf{A}_{\mathbf{r}}, \mathbf{B}_{\mathbf{r}} \) and \( \mathbf{C}_{\mathbf{r}} \)
denote, respectively, the coefficient of \( x^{r} \) in the expansions of \( (1+x)^{10},(1+ \)
\( \mathbf{x})^{20} \) and \( (\mathbf{1}+\mathbf{x})^{30} \) Then \( \sum_{r=1}^{10} \boldsymbol{A}_{r}\left(\boldsymbol{B}_{10} \boldsymbol{B}_{r}-\right. \)
\( \left.C_{10} A_{r}\right) \) is equal to
A. \( \mathrm{B}_{10}-\mathrm{C}_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c. 0
D. \( C_{10}-B_{10} \)
Subject: Physics
A rectangular solid box of length \( 0.3 m \) is held horizontally, with one of its sides on the edge of a platform of height \( 5 \mathrm{m} \) When released, it slips off the table in a very short time \( \tau=0.01 s, \) remaining
essentially horizontal. The angle by which it would rotate when it hits the
ground will be (in radians) close to :-
A. 0.02
2
в. 0.28
\( c .0 .5 \)
D. \( 0 . \)
Subject: Maths
Antoine bought a new electric guitar
that \( \operatorname{cost} \$ 588.60 \) after \( 9 \% \) sales tax
was added. What was the price of the guitar without tax?
\( A \cdot \$ 536 \)
B. \( \$ 540 \)
\( c . \$ 542 \)
D. \( \$ 545 \)
E. \( \$ 548 \)
Subject: Chemistry
Out of the given oxides, how many of these are the anhydrides of dibasic oxyacid?
(i) \( \boldsymbol{S O}_{2} \)
(ii) \( P_{4} O_{10} \)
(iii) \( N O_{2}(\text { iv }) C O_{2}(v) \)
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{O}\left(v_{i}\right) \boldsymbol{C O}\left(v_{i i}\right) \boldsymbol{C l O}_{2}\left(v_{i i i}\right) \boldsymbol{C l}_{2} \boldsymbol{O}(i \mathbf{x}) \)
\( \boldsymbol{I}_{2} \boldsymbol{O}_{5} \)
Subject: Chemistry
Consider the following reaction
sequence, \( \boldsymbol{C H}_{3} \boldsymbol{C} \equiv \boldsymbol{C H} \frac{2 \operatorname{mole}}{\boldsymbol{H C l}} \boldsymbol{A} \frac{\boldsymbol{H e a t}}{\boldsymbol{a q . K O H}} \boldsymbol{B} \)
The products \( (A) \) and \( (B) \) are, respectively:
\( \mathbf{A} \cdot(A): C H_{3} C H_{2} C H C l_{2} \) and \( (\mathbf{B}): C H_{3} C H_{2} C H O \)
B . (A): \( C H_{3} C(C l)_{2} C H_{3} \) and
(В): \( C H_{3} C O C H_{3} \)
c. \( (\mathrm{A}): C H_{3} C(C l)_{2} C H_{3} \) and
(В): \( C H_{3} C \equiv C H \)
D・(A): \( C H_{3} C H(C l) C H_{2} C l \) and
(В) \( : C H_{3} C H(O H) C H_{2} C l \)
Subject: Chemistry
A liquid mixture of benzene \( (B) \) and
toluene \( (T) \) contains 1 mole each of \( B \)
and \( T \)
\( \boldsymbol{P}_{\boldsymbol{T}}^{\boldsymbol{o}}=\mathbf{4 . 2 7 4} \boldsymbol{k} \boldsymbol{N} \boldsymbol{m}^{-2} \) and \( \boldsymbol{P}_{\boldsymbol{B}}^{\boldsymbol{o}}= \)
\( \mathbf{1 3 . 7 3 4} \mathbf{k} \mathbf{N m}^{-\mathbf{2}} \)
If the pressure is reduced further, pressure \( \left(\text { in } k N m^{-2}\right) \) (write only integer part) at which the last trace of liquid does disappear
is
Subject: Maths
The largest sphere is cut off from a cube of side \( 5 \mathrm{cm} . \) The volume of the sphere
will be
\( \mathbf{A} \cdot 27 \pi \mathrm{cm}^{3} \)
в. \( 30 \pi \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 108 \pi \mathrm{cm}^{3} \)
D. \( \frac{125 \pi}{6} \mathrm{cm}^{3} \)
Subject: Maths
Suppose \( A \) and \( B \) are two \( 3 \times 3 \) non
singular matrices such that \( (A B)^{k}= \)
\( \boldsymbol{A}^{k} \boldsymbol{B}^{k} \)
for \( k=2008,2009,2010, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A B^{-1} A^{-1}=B^{-1} \)
B. \( A^{-1} B^{-2} A=B^{2} \)
\( \mathbf{c} . A B=B A \)
D. \( A^{-2} B^{2} A^{2}=\left(A^{-1} B A\right)^{2} \)
Subject: Maths
Classify the following function \( \boldsymbol{f}(\boldsymbol{x}) \)
defined in \( R \rightarrow R \) as injective,
surjective, both or none
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{1} \mathbf{1} \boldsymbol{x}+\boldsymbol{6} \)
A. Surjective but not injective
B. Injective but not surjective
c. Neither injective nor surjective
D. Both injective and surjective
Subject: Physics
In H-atom, if 'x' is the radius of the first
Bohr orbit, de Broglie wavelength of an electron in 3rd orbit is :
\( \mathbf{A} \cdot 3 \pi x \)
в. \( 6 \pi x \)
c. \( \frac{9 x}{2} \)
D. \( \frac{x}{2} \)
Subject: Physics
Three blocks \( A, B \) and \( C \) are connected
together with the help of strings as shown in figure. The masses are respectively \( 10 \mathrm{kg}, 30 \mathrm{kg} \) and \( 50 \mathrm{kg} \)
They are pulled by a force of 18 N on a frictionless horizontal surface
Calculate the following:
(i) Tension \( T_{1} \) in the first string
(ii) Tension \( T_{2} \) in the second string and
(iii) Acceleration of the blocks.
Subject: Chemistry
Which of the following metals will react
with \( N a O H \) and \( K O H \) to liberate
hydrogen gas?
A. \( Z n, A l, F e \) and \( M g \)
в. \( A l, F e, M g \) and \( S n \)
c. \( Z n, \) Sn and \( A l \)
D. \( F e, M g \) and \( A l \)
Subject: Chemistry
Give the condensed formula
of Hexanedial:
A \( \cdot O H C\left(C H_{2}\right)_{4} C H O \)
в. \( O H C\left(C H_{2}\right)_{3} C H O \)
с. \( O H C\left(C H_{2}\right)_{4} \) СООН
D. \( \operatorname{COOH}\left(C H_{2}\right)_{3} \)COOH
Subject: Chemistry
Anhydrous calcium chloride is often used as a dessicant. In the presence of
excess of \( C a C l_{2}, \) the amount of the
water taken up is governed by \( \boldsymbol{K}_{\boldsymbol{p}}= \) \( 6.4 \times 10^{8} 5 \) for the following reaction at
room temperature, \( \boldsymbol{C a} \boldsymbol{C l}_{2}(\boldsymbol{s})+ \)
\( 6 H_{2} O(g) \rightleftharpoons C a C l_{2} .6 H_{2} O(s) . \) What is
the equilibrium vapour pressure of
water in a closed vessel that contains
\( \boldsymbol{C a} \boldsymbol{C l}_{2}(\boldsymbol{s}) ? \)
\( \mathbf{A} \cdot P_{H_{2} O}=5 \times 10^{-15} a t m \)
B. \( P_{H_{2} O}=6 \times 10^{-15} a t m \)
C \( \cdot P_{H_{2} O}=7 \times 10^{-15} a t m \)
D. \( P_{H_{2} O}=9 \times 10^{-15} a t m \)
Subject: Chemistry
The reaction for \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \) at
\( 27^{\circ} \mathrm{C} \) is \( -91.94 k J . \) What will be its
value at \( 50^{\circ} \mathrm{C} \) ? (The molar heat
capacities at constant \( \boldsymbol{P} \) and \( 27^{\circ} \mathrm{C} \) for
\( N_{2}, H_{2} \) and \( N H_{3} \) are 28.45,28.32 and
\( 37.07 k J \) respectively
\( \mathbf{A} \cdot-92.843 k J \)
в. \( -47.7723 k J \)
c. \( -132.5 k J \)
D. \( -176,11 k J \)
Subject: Maths
The least value of the product xyz for which the determinant \( \left|\begin{array}{lll}\boldsymbol{x} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{y} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{z}\end{array}\right| \) is
non-negative, is :
\begin{tabular}{l} 
A \( -16 \sqrt{2} \) \\
\hline
\end{tabular}
В. \( -2 \sqrt{2} \)
\( c \cdot-1 \)
D. - -
Subject: Chemistry
In photosynthesis, 6 molecules of
carbon dioxide combine with an
equal number of water molecules through a complex series of reactions to give a molecule of glucose having a
molecular formula \( C_{6} H_{12} O_{6} . \) How many
grams of water would be required to
produce \( 18 ~ g \) of glucose? Compute the volume of water so consumed
assuming the density of water to be
\( 1 g c m^{-3} \)
Subject: Chemistry
Composition of Ziegler-Natta catalyst
is:
A \( \cdot\left(E t_{3}\right)_{3} \) Al.TiCla
В \( \cdot(M e)_{3} \) Аl.TiCl
\( \mathbf{c} \cdot(E t)_{3} A l \cdot T i C l_{4} \)
D・ \( (E t)_{3} \) Al.Pt \( C l_{4} \)
Subject: Chemistry
Energy levels \( A, B \) and \( C \) of a certain
atoms correspond to increasing values
of every level i.e., \( \boldsymbol{E}_{\boldsymbol{A}}<\boldsymbol{E}_{\boldsymbol{B}}<\boldsymbol{E}_{\boldsymbol{C}} \). If
\( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} \) are the wavelengths of radiations corresponding to the transitions \( C \) to \( B, B \) to \( A \) and \( C \) to
A respectively, then which of the following statements is correct?
B. \( \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D. \( \lambda_{3}^{2}=\lambda_{1}^{2}+\lambda_{2}^{2} \)
Subject: Physics
A motor ship covers the distance of
\( 300 k m \) between two localities on a river
in 10 hours downstream and in 12
hours upstream. Find the flow velocity of the river assuming that these velocities are constant.
A. \( 2.0 \mathrm{km} / \mathrm{h} \)
B. 2.5 km/h
\( c .3 \mathrm{km} / \mathrm{h} \)
D. 3.5 km/h
Subject: Maths
Solve: \( \int \frac{1}{x\left(x^{4}-1\right)} d x \)
A. \( -\frac{1}{4} \ln \left|\frac{x^{4}-1}{x^{4}}\right|+c \)
B \( \cdot \frac{1}{4} \ln \left|\frac{x^{4}-1}{x^{4}}\right|+c \)
c. \( -\frac{1}{4} \ln \left|\frac{x^{2}-1}{x^{2}}\right|+c \)
D. \( \frac{1}{4} \ln \left|\frac{x^{2}-1}{x^{2}}\right|+c \)
Subject: Physics
A ball is released from the top of a tower
of height \( h \) meters. It takes \( T \) second to
reach the ground. What is the position
of the ball in \( T / 3 \) second?
A. \( 2 h / 9 \) meter from the ground
B. \( 7 h / 9 \) meter from the ground
c. \( 8 h / 9 \) meter from the ground
D. \( 17 h / 18 \) meter from the ground
Subject: Maths
How many arrangements of the word \( A R R A N G E \) can be made
\( (i) \) If the two \( R^{\prime} s \) are not allowed to
come together, let it be \( k ? \)
\( (i i) \) If neither the two \( R^{\prime} s \) nor the two
\( A^{\prime} s \) are allowed to come together, let it
be \( \mathrm{m} \)
Find the sum of digits of \( \mathrm{m}+\mathrm{k} \) ?
Subject: Physics
Three identical spheres each of mass 1
kg are placed touching one another with their centres in a straight line. Their
centres are marked as \( A, B, C \) respectively. The distance of centre of
mass of the system from A is.
A \( \cdot \frac{A B+A C}{2} \)
в. \( \frac{A B+B C}{2} \)
c. \( \frac{A C-A B}{3} \)
D. \( \frac{A B+A C}{3} \)
Subject: Physics
The radius of two metallic sphere \( A \) and
\( B \) are \( r_{1} \) and \( r_{2} \) respectively \( \left(r_{1}>r_{2}\right) \)
They are connected by a thin wire and the system is given a certain charge. The charge will be greater
A. Equal to both
B. Zero on both
c. on the surface of sphere \( A \)
D. On the surface of sphere \( B \)
Subject: Physics
In a uniform circular motion
(horizontal) of a ball tied with a string,
velocity at any time is at an angle, \( \boldsymbol{\theta} \)
with acceleration. Then \( \boldsymbol{\theta} \) is:
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c .90^{\circ} \)
D. none of the above
Subject: Maths
In a series of \( 2 n \) observations, half of
them equal \( a \) and remaining half
equation \( -a . \) If the standard deviation of the observations is \( 2, \) then \( |a| \) equals:
A \( \cdot \frac{1}{n} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \frac{\sqrt{2}}{n} \)
Subject: Chemistry
8 mol of a gas \( A B_{3} \) are introduced into a \( 1.0 d m^{3} \) vessel. It dissociates as
\( \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{B}_{2}(\boldsymbol{g}) \)
At equilibrium, 2 mol of \( A_{2} \) is found to be present. The equilibrium constant for the reaction is :
A \( \cdot 2 m o l^{2} L^{-2} \)
B. \( 3 m o l^{2} L^{-2} \)
c. \( 27 m o l^{2} L^{-2} \)
D. \( 36 m o l^{2} L^{-2} \)
Subject: Chemistry
Assertion
Newland's law of octaves of elements is
a function of their state that the
property of every eighth element is the repetition of the first.
Reason
In order to fit new elements into his
table Newland adjusted two elements in the same colum.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Subject: Maths
On comparing the ratios \( \frac{\boldsymbol{a}_{1}}{\boldsymbol{a}_{2}}, \frac{\boldsymbol{b}_{1}}{\boldsymbol{b}_{2}} \) and \( \frac{\boldsymbol{c}_{1}}{\boldsymbol{c}_{2}} \)
find out whether the following pairs of linear equations are consistent, or inconsistent.
\( \mathbf{5} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}=\mathbf{1 1} ;-\mathbf{1 0} \boldsymbol{x}+\mathbf{6} \boldsymbol{y}=\mathbf{2 2} \)
A. Consistent
B. Inconsistent
c. Ambiguous
D. Data insufficient
Subject: Chemistry
The reaction \( A \stackrel{K}{\longrightarrow} \) Product is zeroorder while the reaction \( B \stackrel{K}{\longrightarrow} \) Product
is first-order reaction. For what initial
concentration of \( A \) is the half lives of the
two reactions equal?
A. 2\operatorname{ln } 2 \text { M }
B. 2 M
\( c \cdot \ln 2 M \)
D. In 4 M
Subject: Chemistry
Which complex among the following gives a white precipitate on treatment with an aqueous solution of barium
chloride?
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \)
B \( \cdot\left[C o\left(N H_{3}\right)_{5} S O_{4}\right] N O_{2} \)
c. \( \left[C o\left(N H_{3}\right)_{5} N O_{2}\right] S O_{4} \)
D. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \)
Subject: Chemistry
Write the basicity order of the following.
\( \begin{array}{ll}\text { сн }_{3}-c \overbrace{C}^{\mathscr{Y}}^{\mathrm{NH}} & \mathrm{cH}_{3}-\mathrm{cH}_{2}-\mathrm{NH}_{2} \quad\left(\mathrm{cH}_{3}\right)_{2} \mathrm{NH} \\ & \mathrm{NH}_{3}\end{array} \)
(I)
\( A \cdot(\|)>(1)>(\| 1)>(1 V) \)
B. (I) > (III) > (II) > (IV)
\( c \cdot(\| I)>(I)>(\|)>(I V) \)
D. (I) > (II) > (III) > (IV)
Subject: Physics
A wire is stretched \( 1 \mathrm{mm} \) by a force of 1
kN. How far would a wire of the same
material and length but of four times that diameter he stretched by the same force?
\( ^{\mathbf{A}} \cdot \frac{1}{2} \mathrm{mm} \)
в. \( \frac{1}{4} \mathrm{mm} \)
c. \( \frac{1}{8} \mathrm{mm} \)
D. \( \frac{1}{16} \mathrm{mm} \)
Subject: Maths
The angles of some triangles are given below. Classify each triangle acuteangled,obtuse-angled or right-angled on the basis of its angles. \( \boldsymbol{a} \cdot \boldsymbol{9} \boldsymbol{0}^{o}, \boldsymbol{4} \boldsymbol{5}^{o}, \boldsymbol{4} \boldsymbol{5}^{\boldsymbol{o}} \)
\( b .60^{\circ}, 60^{\circ}, 60^{\circ} \)
\( c .80^{\circ}, 60^{\circ}, 40^{\circ} \)
\( \boldsymbol{d} . \boldsymbol{9} \boldsymbol{2}^{o}, \mathbf{5} \boldsymbol{0}^{o}, \boldsymbol{3} \boldsymbol{8}^{\boldsymbol{o}} \)
\( e .120^{\circ}, 50^{\circ}, 10^{\circ} \)
\( \boldsymbol{f} \cdot \boldsymbol{9} \boldsymbol{0}^{o}, \boldsymbol{3} \boldsymbol{5}^{o}, \boldsymbol{5} \boldsymbol{5}^{\boldsymbol{o}} \)
Subject: Maths
Factorise and then divide the given
algebraic expressions.
1. \( \left(12 r^{2}+8 r^{2}-4 r^{2}\right) b y\left(-4 r^{2}\right) \)
2. \( \left(\frac{4}{9} x^{2}-49 z^{2}\right) b y(2 x+21 z) \)
\( 3 \cdot\left(5 a^{2} b^{2}+15 a^{2} b^{2}-20 a^{4} b\right) b y 25 a b^{2} \)
4. \( \left(49 a^{2}-56 a\right) b y(21 a-24) \)
Subject: Chemistry
Which is(are) correct statements about
the role of a catalyst in a reaction?
A. It is reactant in a rate-determining step and then a product of some subsequent step.
B. It provides an alternate mechanism with a lower energy of activation.
C. It increases the rate of chemical reaction but does not
itself undergo a permanent change during the course of the reaction.
D. Enzyme catalysts are protein molecules.
E. All of the above.
Subject: Maths
If \( \sin \alpha+\sin \beta=a \) and \( \cos \alpha-\cos \beta= \)
\( b, \) then \( \tan \frac{\alpha-\beta}{2} \) is equal to
A. \( -\frac{a}{b} \)
в. \( -\frac{b}{a} \)
c. \( \sqrt{a^{2}-b^{2}} \)
D. None of these
Subject: Maths
n Fig. \( P Q R \) is an equilateral
triangle. Arcs have been drawn with
radii \( 14 \mathrm{cm} \) each and with centres \( \boldsymbol{P}, \boldsymbol{Q} \)
and \( R \). The area of the shaded region is
A \( \cdot 102.6 \mathrm{cm}^{2} \)
B \( .206 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 308 \mathrm{cm}^{2} \)
D. \( 345 \mathrm{cm}^{2} \)
Subject: Physics
A bus is moving with a speed of \( 10 \mathrm{ms}^{-1} \)
on a straight road. A scooterist wishes
to overtake the bus in 100 s. If the bus is
at a distance of \( 1 \mathrm{km} \) from the scooterist, with what speed should the scooterist chase the bus?
A. \( 40 \mathrm{ms}^{-1} \)
B. 25 \( m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 20 \mathrm{ms}^{-1} \)
Subject: Chemistry
List I
A. Van Arkel's \( \quad \) 1. Refining of silver method
B. Solvay process
2. Purification of titanium
3. Manufacture of
C. Cupellation
\[
N a_{2} C O_{3}
\]
4. Purification of copper
D. Poling
Match List I with List II select the
correct answer using the codes gives
below the lists:
A . A-2, B-1, C-3, D-4
B. \( A-4, B-3, C-2, D-5 \)
c. \( A-2, B-3, C-1, D-4 \)
D. A-5, B-1, C-3, D-4
Subject: Physics
Two drops of the same radius are falling through air with a steady velocity of \( 5 \mathrm{cm} \) per sec. If the two drops coalesce, the terminal velocity would be
A. \( 10 \mathrm{cm} \) per sec
B. 2.5 \( \mathrm{cm} \) per sec
c. \( 5 \times(4)^{1 / 3} \) cm per sec
D. \( 5 \sqrt{3} \mathrm{cm} \) per sec
Subject: Maths
What is the angle between the lines
\( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{1}}=\frac{\boldsymbol{y}+\mathbf{1}}{-\mathbf{2}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{1}} \) and \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}= \)
\( \frac{2 y+3}{3}=\frac{z+5}{2}=? \)
\( ^{A} \cdot \frac{\pi}{2} \)
в.
c. \( \frac{\pi}{6} \)
D. None of the above
Subject: Chemistry
The decreasing order of basicity of the
following amines is :
A. \( (I I)>(I I I)>(I V)>(I) \)
в. \( (I)>(I I I)>(I V)>(I I) \)
c. \( (I I I)>(I I)>(I)>(I V) \)
D. \( (I I I)>(I)>(I I)>(I V) \)
Subject: Physics
In the arrangement shown, by what
acceleration the boy must go up so that \( 100 \mathrm{kg} \) block remains stationary on the wedge. The wedge is fixed and friction is
absent everywhere. (takeg \( =\mathbf{1 0 m} / \mathbf{s 2}) \)
\( A \cdot 2 m / s^{2} \)
B \( \cdot 4 m / s^{2} \)
\( \mathrm{c} \cdot 6 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{D} \cdot 8 m / s^{2} \)
Subject: Physics
A fixed volume of iron is drawn into a wire of length \( l \). The extension produced
in this wire by a constant force \( \boldsymbol{F} \) is
proportional to :
A \( \cdot \frac{1}{l^{2}} \)
B. \( \frac{1}{l} \)
\( c \cdot l^{2} \)
D. \( l \)
Subject: Physics
The de-Broglie wavelength of electron in
\( 3^{r d} \) orbit of \( H e^{+1} \) ion is approximately
\( \mathbf{A} \cdot 2 A^{0} \)
B. \( 3 A^{\circ} \)
c. \( 4 A^{\circ} \)
D. \( 5 A^{\circ} \)
Subject: Chemistry
Among the following molecules in
increasing order of \( \sigma \) to \( \pi \) bond ratio.
(1)
(2)
(3)
(4)
\( \mathbf{A} \cdot 2<3<4<1 \)
B . \( 2<4<3<1 \)
c. \( 3<2<1<4 \)
D. \( 2<3<1<4 \)
Subject: Physics
Which of the following statements is/are correct about work?
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} \) a certain reference frame, \( W_{\text {pseudo force}}+ \)
\( W_{\text {conservattive force}}+W_{\text {non-conservattive force}}+ \)
\( W_{\text {other forces}}=\Delta K \)
B. Work done by friction is always negative.
C. Work done by a force is defined as the dot product of the force and the displacement of the point of application of force.
D. Work done by conservative force in moving a body from \( A \) to \( B= \) potential energy of the body at \( A \) potential energy of the body at B
Subject: Chemistry
If \( \mathrm{N}_{2} \) gas is hubbled through water at
\( 293 \mathrm{K}, \) how many millimoles of \( \mathrm{N}_{2} \) gas would dissolve in 1 litre of water?
Assume that \( \mathrm{N}_{2} \) exerts a partial
pressure of 0.987 bar. Given that Henry's
law constant for \( \mathrm{N}_{2} \) at \( 293 \mathrm{K} \) is 76.48
kbar
A . \( 0.561 \mathrm{mmol} \)
B. 0.222 mmol
c. \( 0.716 \mathrm{mmol} \)
D. \( 0.828 \mathrm{mmol} \)
Subject: Physics
A body is projected up along the rough inclined plane from the bottom with some velocity. It travels up the incline
and then returns back. If the time of
ascent is \( t_{a} \) and time of descent is \( t_{d} \)
then
\( \mathbf{A} \cdot t_{a}=t_{d} \)
в. \( t_{a}>t_{d} \)
c. \( t_{a}<t_{d} \)
D. Data in-sufficient
Subject: Physics
Assuming the water resistance to be negligible, find the horizontal
component of the force with which the man acted on the raft during the
motion.
\( ^{\mathrm{A}} \cdot_{F}=-\frac{2 m M}{M+m} \frac{d v^{\prime}}{d t} \)
\( ^{\mathrm{B}} \cdot_{F}=\frac{2 m M}{M+m} \frac{d v^{\prime}}{d t} \)
c. \( _{F}=\frac{m M}{M+m} \frac{d v^{\prime}}{d t} \)
D. \( F=-\frac{m M}{M+m} \frac{d v^{\prime}}{d t} \)
Subject: Chemistry
Consider the following four statements
(1) Benzene does not favour the attack
of \( N u^{-} \) on itself.
(2) On benzene ring \( \boldsymbol{E}^{+} \) can attacks
easily because benzene ring is electron
rich
(3) Benzene ring does not undergo addition reaction readily because after addition reaction benzene ring loses its aromatically.
(4) When electron withdrawing groups are present on benzene ring, attack of
\( N u- \) on benzene nucleolus becomes
easy.
Out of these statements, correct
statements are-
\( A \cdot 1,3 \) and 4
B. 1,2 and 4
c. 2 and 4
D. All are correct
Subject: Physics
A uniform rod weighs \( 10 k g \) and with a
load \( 5 k g \) attached to one end, it
balances on a knife edge at \( 2 m \) from
that end. The length of rod is :
A. 10.34 m
B. \( 8.56 m \)
c. \( 6.21 m \)
D. 4.35 m
Subject: Physics
Two bodies have their moments of
inertia I and 21 respectively about their axis of rotation.lf their kinetic energies
of rotation are equal, their angular
momenta will be in the ratio-
A \( \cdot \sqrt{\frac{3}{1}} \)
в. \( \sqrt{\frac{6}{1}} \)
c. \( \sqrt{\frac{2}{1}} \)
D. \( \sqrt{\frac{5}{1}} \)
Subject: Chemistry
What is the electron configuration for
manganese?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B . \( [A r] 4 s^{1} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{1} \)
Subject: Physics
Journey in a train is adventurous
particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically
down and touched the ground in \( 0.2 s \)
After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. If a projectile has velocity greater than escape velocity which trajectory it
will follow
A. elliptic
B. hyperbola
c. vertical straight
D. parabolic
Subject: Maths
The lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect if \( \boldsymbol{K} \)
equals
\( A \cdot \frac{3}{2} \)
в. \( \frac{9}{2} \)
c. \( \frac{-2}{9} \)
D. \( \frac{-3}{2} \)
Subject: Maths
\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots \ldots \ldots . .+(\mathbf{2 n}- \)
1) \( (2 n+1)=\frac{n\left(4 n^{2}+6 n-1\right)}{3} \) is true
for
A. Only natural number \( n \geq 4 \)
B. Only natural numbers 3 \( \leq n \leq 10 \)
c. All natural numbers n
D. None
Subject: Physics
The acceleration-time graph of a
particle moving in a straight line is
shown in fig. The velocity of the
particle at time \( t=0 \) is \( 2 \mathrm{m} / \mathrm{s} \). The
velocity after 2 s will be:
\( A \cdot 6 \mathrm{m} / \mathrm{s} \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2 m / s \)
D. \( 8 \mathrm{m} / \mathrm{s} \)