AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Relation \( R \) in the set \( A \) of human beings
in a town at a particular time given by
\[
\boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \text { is } \boldsymbol{w} \boldsymbol{i} f e \boldsymbol{o} \boldsymbol{f} \boldsymbol{y}\}
\]
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only 4-Equivalence 5-Neither reflexive, nor symmetric, nor transitive
Subject: Maths
If \( p, q, r, s \) are in \( A . P \) ad if \( (x)= \)
\[
\begin{array}{rl}
\boldsymbol{p}+\sin \boldsymbol{x} & \boldsymbol{q}+\sin \boldsymbol{x}-\boldsymbol{r}+\sin \boldsymbol{x} \\
\| \boldsymbol{q}+\sin \boldsymbol{x} & \boldsymbol{r}+\sin \boldsymbol{x} \quad-\mathbf{1}+\sin \boldsymbol{x} \\
\boldsymbol{r}+\sin \boldsymbol{x} & \boldsymbol{s}+\sin \boldsymbol{x} \quad \boldsymbol{s}-\boldsymbol{q}+\boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{x}
\end{array}
\]
such that \( \int_{0}^{2} f(x) d x=-4 \) then the common difference of the \( A . P . \) cn
A. -1
B.
c. 1
D. none
Subject: Maths
The points (2,5) and (5,1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line \( y=2 x+k, \) then the value
of k is
\( A \cdot 4 \)
B. 3
\( c \cdot-4 \)
\( D \cdot-3 \)
\( E \)
Subject: Maths
Evaluate \( \int \frac{\log (x / e)}{(\log x)^{2}} d x \)
A \( \cdot \frac{\log x}{x}+c \)
B. \( \frac{x}{\log x}+c \)
c. \( \frac{x}{\log (x)^{2}}+c \)
D. \( \frac{(\log x)^{2}}{x}+c \)
Subject: Maths
If \( a_{1}, a_{2}, \dots, a_{n} \) are positive real numbers
whose product is a fixed number \( c \), the
minimum value of \( \boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}+\ldots+ \)
\( \boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{2} \boldsymbol{a}_{\boldsymbol{n}} \) is
A \( \cdot n(2 c)^{1 / n} \)
B \cdot \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D・ \( (n+1)(2 c)^{1 / n} \)
Subject: Chemistry
Statements that are true of d-and \( f- \)
block elements are:
1. The colour of \( K_{2} C r_{2} O_{7} \) is due to d-d
transition.
2. Actinides have larger number of oxidation states than lanthanides.
3. Tripositive ions of \( \operatorname{Pr}(\text { At. } N o .=59) \)
and \( T m(A t . N o .=69) \) have the same
(green) colour.
4. Actinides have paramagnetic moments less than theoretically predicted values.
A. 2,3,4
B. 1,2,3
\( c \cdot 2,4 \)
D. 1,2,4
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0} \) then what is the value
of \( \frac{x^{2}}{y z}+\frac{y^{2}}{z x}+\frac{z^{2}}{x y} ? \)
A \( \cdot(x y z)^{2} \)
B. \( x^{2}+y^{2}+z^{2} \)
c. 9
D. 3
Subject: Maths
Assertion
\( \mid \mathfrak{f}^{6} \boldsymbol{C}_{\boldsymbol{n}}+\boldsymbol{2} \cdot^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+1}+^{\boldsymbol{6}} \boldsymbol{C}_{\boldsymbol{n}+\boldsymbol{2}}>^{\boldsymbol{8}} \boldsymbol{C}_{\boldsymbol{3}} \) then
the quadratic equations whose roots \( \operatorname{are} \alpha, \beta \) and \( \alpha^{n-1}, \beta^{n-1} \) (for least value
of
n) have two common roots.
Reason
Equation \( a x^{2}+b c+c=0 \) and \( a^{1} x^{2}+ \)
\( b^{1} x+c^{1}=0 \) have two roots common
\( \operatorname{then}\left(b c^{1}-b^{1} c\right)\left(a b^{1}-a^{1} b\right)=\left(c a^{1}-\right. \)
\( \left.\boldsymbol{c}^{1} \boldsymbol{a}\right)^{2} \)
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
The differential equation satisfied by all
the straight lines \( x y \) - plane (not parallel to \( y \) -axis ) is:
A \( \cdot \frac{d y}{d x}=a \) constant
в. \( \frac{d^{2} y}{d x^{2}}=0 \)
c. \( _{y+\frac{d y}{d x}}=0 \)
D. \( \frac{d^{2} y}{d x^{2}}+y=0 \)
Subject: Chemistry
Calculate the amount of ammonium
chloride required to dissolve in \( 500 m L \)
water to have \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4 . 5}\left(\boldsymbol{K}_{\boldsymbol{b}} \) for \right.
\( \left.N H_{4} O H \text { is } 1.8 \times 10^{-5}\right) \)
Subject: Chemistry
Which of the following represents the
given mode of hybridisation \( s p^{2}- \)
\( s p^{2}-s p \) from left to right?
A. \( C H_{2}=C H-C \equiv N \)
в. \( C H \equiv C-C \equiv C H \)
c. \( C H_{2}=C=C=C H_{2} \)
D. \( C H_{2}=C H-C H=C H_{2} \)
Subject: Physics
A slit of width \( a \) is illuminated by a
monochromatic light of wavelength \( \mathbf{6 5 0} \) nm. The value of \( a \) when the first
minima falls at an angle of diffraction
of \( 30^{0} \) is
A. \( 1.3 \times 10^{-6} m \)
B . \( 2.6 \times 10^{-6} m \)
c. \( 3.9 \times 10^{-6} \mathrm{m} \)
D. \( 5.2 \times 10^{-6} m \)
Subject: Maths
The differential equation of all circles passing through the origin and having their centers on the x-axis is:
A \( \cdot y^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( y^{2}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( x^{2}=y^{2}+2 x y \frac{d y}{d x} \)
D. None of these
Subject: Physics
In two beakers \( (A \text { and } B) 50 m l \) water of
about \( 70^{\circ} \mathrm{C} \) each is taken. Then in
beaker \( A, 50 m l \) of water of about \( 30^{\circ} C \)
is added and after 5 minutes, in beaker
\( B, 50 m l \) of water of about \( 30^{\circ} C \) is
added. What would observe if the
temperatures of both beakers recorded immediately? Why?
Subject: Biology
In
T.S. Pheretima, the correct sequence of body wall layers from outer to inner side
(a) Circular muscles
(b) Parietal peritoneum
(c) Epidermis
(d) Cuticle
(e) Longitudinal muscles
A. \( c \) be a d
B. \( d c \) e a b
\( c \cdot d c a e b \)
D. d b a ec
Subject: Chemistry
An excess of liquid Hg was added to
\( 10^{-3} \mathrm{M} \) acidified solution of \( F e^{3+} \) ions.
was found that only \( 4.6 \% \) of the ions
remained as \( F e^{3+} \) at equilibrium at \( 25^{\circ} \)
C. Calculate \( \boldsymbol{E}^{o} \) for \( \mathbf{2} \boldsymbol{H} \boldsymbol{g} / \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \) at \( \boldsymbol{2} \mathbf{5}^{\boldsymbol{o}} \mathbf{C} \)
for,
\( 2 H g+2 F e^{3+} \rightleftharpoons H g_{2}^{2+}+2 F e^{2+} \) and
\( \boldsymbol{E}_{\boldsymbol{F e}^{2+} / \boldsymbol{F e}^{3+}}^{o}=-\mathbf{0 . 7 7 1 2} \boldsymbol{V} \)
A. - -0.7912 V
в. - 0.7721 V
c. \( -0.9922 \mathrm{v} \)
D. None of these
Subject: Physics
Two small boats are \( 10 m \) apart on a
lake. Each pops up and down with a period of 4.0 seconds due to wave motion on the surface of the water.
When one boat is at its highest point. the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
B. \( 5.0 \mathrm{m} / \mathrm{s} \)
c. \( 14 \mathrm{m} / \mathrm{s} \)
D. \( 40 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A car travels on a straight road from point \( A \) to point \( B \) in four hours, and then from point \( B \) back to point \( A \) in six
hours. The distance between the two
points is \( 240 k m \)

Find out the car's average velocity?
\( \mathbf{A} \cdot 0 k m / h \)
в. \( 48 k m / h \)
c. \( 50 k m / h \)
D. \( 60 k m / h \)
E . \( 100 k m / h \)
Subject: Maths
Solve the following differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}-\mathbf{1} \)
A \( \cdot y=x^{2}+x \)
B . \( y=x^{2} \)
c. \( y=x^{2}-x \)
D. None of the above
Subject: Maths
\( \boldsymbol{A}=\{1,2,3,5\} \) and \( \boldsymbol{B}=\{\mathbf{4}, \mathbf{6}, \mathbf{9}\} \)
Define a relation \( \mathrm{R} \) from \( A \) to \( \mathrm{B} \) by \( \boldsymbol{R}= \)
\( \{(x, y): \text { the difference between } x \text { and } y \)
is odd, \( x \in A, y \in B\} . \) Write \( R \) in Roster
form
Subject: Maths
\( \int \frac{e^{x}}{\sqrt{5-4 e^{x}+e^{2 x}}} d x \)
\( \mathbf{A} \cdot \cos ^{-1}\left(\frac{e^{x}+2}{3}\right)+c \)
\( \mathbf{B} \cdot \cos ^{-1}\left(\frac{e^{x}-3}{2}\right)+c \)
\( \mathbf{C} \cdot \sin ^{-1}\left(\frac{e^{x}+2}{3}\right)+c \)
\( \mathbf{D} \cdot \sin ^{-1}\left(\frac{e^{x}-3}{2}\right)+c \)
Subject: Maths
The \( (n+1)^{t h} \) term from the end in
\( \left(x-\frac{1}{x}\right)^{3 n} \) is
A. \( 3 n_{n} . . x^{-n} \)
B . \( (-1)^{n} .^{3 n} C_{n} . x^{-n} \)
\( \mathrm{c} \cdot^{3 n} C_{n} \cdot x^{n} \)
D. \( (-1)^{n} .^{3 n} C_{n} . x^{n} \)
Subject: Chemistry
Coordination compounds have great
importance in biological systems. In
this context which of the following
statements is incorrect?
A. Carboxypeptidase-A is an enzyme and contains zinc.
B. Haemoglobin is the red pigment of blood and contains iron
C. Cyanocobalamin is \( B^{12} \) and contains cobalt.
D. Chlorophylls are green pigments in plants and contain calcium.
Subject: Maths
If the binary operation \( * \) is on set of
integers \( Z \) is defined as
\( a * b=a+2 b^{2}, \) then the value of \( (8 * \)
\( \mathbf{3}) * \mathbf{2} \)
A . 26
B. 22
\( c .32 \)
D. 34
Subject: Physics
Assertion
Sound waves do not travels through
vacuum.
Reason
The speed of sound is too small when
compared to speed of light.
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: Chemistry
Which of the following two substances react to produce blister copper?
\( \mathbf{A} \cdot C u_{2} S_{(s)} \) and \( C u_{2} O_{(s)} \)
B. \( C u_{2} O_{(s)} \) and \( F e S_{S_{s}} \)
c. \( C u_{2} S_{(s)} \) and \( O_{2(g)} \)
D. \( C u_{2} S_{(s)} \) and \( F e S_{2(s)} \)
Subject: Maths
Given \( : A B=12 \mathrm{cm}, A C=13 \mathrm{cm}, \mathrm{ED}=\mathrm{FG}= \)
\( 5 \mathrm{cm}, \mathrm{EF}=10 \mathrm{cm} \) and \( \mathrm{GD}=4 \mathrm{cm} \)
Find the area and the perimeter of the
adjoining figure
\( A \cdot 88 \) sq. \( \mathrm{cm} \) and \( 50 \mathrm{cm} \)
B. 88 sq. \( m \) and 50 cm
\( c .88 \) sq. \( \mathrm{cm} \) and \( 50 \mathrm{m} \)
D. 8.8 sq. \( \mathrm{cm} \) and \( 50 \mathrm{cm} \)
Subject: Chemistry
In the synthesis of sodium carbonate, the recovery of ammonia is done by
treating \( N H_{4} C l \) with \( C a(O H)_{2} \)
The by-product obtained in this process is:
A. \( C a C l_{2} \)
в. \( N a C l \)
c. \( N a O H \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)
Subject: Chemistry
Match the column (I) and (II) and select
the correct answer using the codes given below.
ColumnColumn-II
(a)
(1) Halide ore of magnesium Argentite
(b) Cuprite
(2) Carbonate ore of iron
(c) Siderite
(3) Oxide ore of copper
(d) Carnallite
(4) Sulphide ore of silver
A. a-4, b-3, c-2
B. a-1, b-2, c-3, d-4
c. \( a-2, b-3, c-3, d-1 \)
D. a-3, b-4, c-1 \( d-2 \)
Subject: Maths
\( \int_{0}^{1} \frac{e^{x}}{1+e^{2 x}} d x \)
\( \mathbf{A} \cdot \tan ^{-1} e-\frac{\pi}{4} \)
B \( \cdot \tan ^{-1} e+\frac{\pi}{4} \)
\( \mathrm{C} \cdot \tan e-\frac{\pi}{4} \)
D. None of these
Subject: Chemistry
A full bottle of concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) left
uncorked for several days was observed to overflow. This was probably due to
A. dissolution of oxygen from the air
B. temperature changes size of the bottle
c. hygroscopic property of sulphuric acid
D. reaction between the acid and the bottle
Subject: Physics
Two positive charges \( \boldsymbol{q}_{1}=\boldsymbol{4} \times \mathbf{1 0}^{-\mathbf{6}} \boldsymbol{C} \)
and \( q_{2}=9 \times 10^{-6} C \) are placed \( 10 \mathrm{cm} \)
a part in air. The position of a third charge to be placed between them, such that there will be no resultant force on it
is:
A \( .6 \mathrm{cm} \) from \( q_{1} \)
B. \( 3 \mathrm{cm} \) from \( q_{1} \)
c. \( 4 \mathrm{cm} \) from \( q_{1} \)
D. \( 7 \mathrm{cm} \) from \( q_{1} \)
Subject: Physics
A vertical steel post of diameter \( 25 \mathrm{cm} \)
and length \( 2.5 m \) supports a weight of
\( 8000 k g . \) Find the change in length
produced. (Given \( \left.\boldsymbol{Y}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{P a}\right) \)
\( A \cdot 2.1 \mathrm{cm} \)
B. 0.21 \( \mathrm{cm} \)
c. \( 0.21 \mathrm{mm} \)
D. 0.021 mm
Subject: Physics
Two fishes are \( 1 m \) apart underwater
The gravitational force between them is
\( F_{1}, \) Theyjump above the surface of water keeping the same distance (i.e 1 m)
between them. The new gravitational
force between them is \( F_{2} \). The
relationship between \( \boldsymbol{F}_{1} \) and \( \boldsymbol{F}_{2} \) is
A \( \cdot F_{1}>F_{2} \)
B. \( F_{1}<F_{2} \)
c. \( F_{1}=F_{2} \)
D. \( F_{1}: F_{2}=1: 2 \)
Subject: Biology
Select the correct option: \( \ln (\mathrm{i}) \)
protoxylem lies towards periphery and metaxylem lies towards centre. Such an
arrangement of primary xylem is called \( \operatorname{as}(i i) \)
(i) 1 (ii)
stems ems endrach
exarch stems \( \mathrm{h} \)
roots endrach \( \mathrm{ch} \)
roots exarch A
A. A-stems,B-endrach
B. A-stems, B-exarch
C. A-roots, B-endrach
D. A-roots, B-exarch
Subject: Physics
A uniform length of wire \( 1.2 \mathrm{m} \) has a resistance of \( 16 \Omega . \) It is stretched such
that its resistance is \( 36 \Omega \). The new
length is
A. \( 1.8 m \)
в. \( 2.4 m \)
\( c .2 .7 m \)
D. \( 3 m \)
Subject: Maths
The sum of the intercepts of the tangent to the curve \( \sqrt{x}+\sqrt{y}=3 \) on the coordinate axes where it meets the curve
\( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \)
\( A \cdot S \)
B. 10
\( c \cdot 11 \)
D. 12
Subject: Biology
Choose the correct sequence of tissues
containing \( C O_{2} \) from highest
concentration level to the lowest.
A. Pulmonary veins-left atrium- tissues-right ventricle
- pulmonary arteries
B. Left atrium- tissues - right ventricle-pulmonary veins-pulmonary arteries
C. Pulmonary arteries- right ventricle- tissues-left atrium- pulmonary veins
D. Right ventricle- pulmonary arteries- pulmonary veins-left atrium- tissues
E. Tissues-pulmonary veins-pulmonary arteries-left atrium-right ventricle
Subject: Chemistry
The correct statement(s) about the
following reaction sequence is(are):
Cumene \( \left(C_{9} H_{12}\right) \frac{i) O_{2}}{i i) H_{3} O^{+}} \)
\( P \frac{C H C l_{3} / N a O H}{ } Q(\text { major })+ \)
\( \boldsymbol{R}(\boldsymbol{m} \boldsymbol{i n} \boldsymbol{o r}) \boldsymbol{Q} \frac{\boldsymbol{N a O H}}{\boldsymbol{P h C H}_{2} \boldsymbol{B r}} \boldsymbol{S} \)
This question has multiple correct options
A. \( R \) is steam volatile
B. Q gives dark violet coloration with \( 1 \% \) aqueous \( F e C l_{3} \) solution
c. \( \operatorname{sgives} \) yellow precipitate with \( 2,4- \) dinitrophenylhydrazine
D. s gives dark violet coloration with \( 1 \% \) aqueous \( F e C l_{3} \) solution.
Subject: Physics
The potential energy of a particle varies
with height \( h \) from a fixed point as \( \boldsymbol{E}= \) \( \left(\frac{\boldsymbol{P} \sqrt{\boldsymbol{h}}}{\boldsymbol{h}+\boldsymbol{Q}}\right) \) where, \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are
constants. The dimensions of \( P Q \) are
A \( \cdot\left[M L^{2} T^{-2}\right] \)
B. \( \left[M^{3 / 2} L^{3 / 2} T^{-2}\right. \)
C . \( \left[M L^{7 / 2} T^{-2}\right] \)
D \cdot \( \left[M L^{3 / 2} T^{-2}\right. \)
Subject: Chemistry
If the half-life period of a first-order
reaction is 138.6 min, then the value of
decay constant for the reaction will be:
A \( .5 \mathrm{min}^{-1} \)
B. 0.5 min \( ^{-1} \)
c. 0.05 min \( ^{-1} \)
D. \( 0.005 \min ^{-1} \)
Subject: Chemistry
An organic compound was used with sodium metal and extracted with
distilled water. On adding freshly
prepared \( F e S O_{4} \) solution followed by
the addition of \( F e C l_{3} \) and dil. \( H C l \)
produced a greenish blue solution. \( 0.30 \mathrm{g} \) of the organic compound after Kjeldahlisation evolved a gas \( (\boldsymbol{X}) \)
which was passed on \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \)
\( H_{2} S O_{4} . \) The excess of acid required 20
\( \mathrm{ml} \) of \( 0.5 \mathrm{M} \) NaOH for neutralization.
The organic compound which suitably fits into the above data is:
\( A \)
\( C H_{3}-C-N H_{2} \)
в. \( C_{6} H_{5}-\stackrel{\|}{C}-N H_{2} \)
c. \( H_{2} N-C-N H_{2} \)
D. \( H_{2} N-\stackrel{\|}{C}-N H_{2} \)
Subject: Physics
If a disc starting from rest acquires an
angular velocity of 240 revolution/ min in \( 10 s, \) then its angular acceleration
will be
A . 1.52 rads\( ^{-1} \)
B. 3.11 rads \( ^{-1} \)
c. 2.51 rads \( ^{-1} \)
D. 1.13 rads\( ^{-1} \)
Subject: Physics
The surface of a black body is at a
temperature \( 727^{\circ} C \) and its cross
section in \( 1 m^{2} . \) Heat radiated from this
surface in one minute in Joules is
(Stefan's constant \( =\mathbf{5 . 7} \times \)
\( \left.\mathbf{1 0}^{-8} \boldsymbol{W} / \boldsymbol{m}^{2} \boldsymbol{k}^{4}\right) \)
A \( \cdot 34.2 \times 10^{5} \)
B . \( 2.5 \times 10^{5} \)
c. \( 3.42 \times 10^{5} \)
D. \( 2.5 \times 10^{6} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}], \) then
which of the following is false?
A \( \cdot(f+g)(x)=x \)
в. \( (f o g)(x)=0 \)
c. \( (g o f)(x)=0 \)
D. None of these
Subject: Physics
Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitudes \( A=3.00 \) and \( B=3.00 . \) Their vector product is \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}=-\mathbf{5 . 0 0 \hat { k }}+\mathbf{2 . 0 0 \hat { \mathbf { i } }} \)
What is the angle between \( \vec{A} \) and \( \vec{B} \) ?
\( ^{\mathrm{A}} \cdot \sin ^{-1}\left[\frac{\sqrt{29}}{9}\right] \)
\( ^{\mathrm{B}} \cdot_{\cos ^{-1}}\left[\frac{\sqrt{29}}{9}\right] \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left[\frac{\sqrt{29}}{10}\right] \)
D. \( \sin ^{-1}\left[\frac{\sqrt{29}}{19}\right] \)
Subject: Physics
How the linear velocity 'v' of an electron in the Bohr orbit is related to its
quantum number 'n'?
A \( \cdot v \propto \frac{1}{n} \)
в. \( v \propto \frac{1}{n^{2}} \)
c. \( _{v} \propto \frac{1}{\sqrt{n}} \)
D. \( v \propto n \)
Subject: Physics
A tangent galvanometer has 80 turns of wire. The internal and external
diameters of the coil are \( 19 \mathrm{cm} \) and
\( 21 \mathrm{cm} \) respectively. The reduction factor
of the galvanometer at a place where \( \boldsymbol{H}=\mathbf{0 . 3 2} \) oersted will be (1 oersted \( = \)
\( \mathbf{8 0} \boldsymbol{A} / \boldsymbol{m}) \)
A .0 .0064
B. 0.64
\( c \cdot 0.064 \)
D. None of these
Subject: Maths
\( \lim _{x \rightarrow \infty}(\sqrt{x^{2}+8 x+3}- \)
\( \sqrt{x^{2}+4 x+3})= \)
A . 0
B. \( \infty \)
\( c \cdot 2 \)
D. \( \frac{1}{2} \)
Subject: Chemistry
If EAN of a central metal ion \( X^{+2} \) in a
complex is 34 . and atomic number of \( \boldsymbol{X} \)
is \( 28 . \) The number of monodentate
ligands present in complex are:
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D.
Subject: Physics
n the arrangement shown in figure above the mass of body 1 is \( \eta=0.4 \) times as great as that of body 2 . The height \( h=20 \mathrm{cm} . \) The masses of the
pulleys and the threads, as well as the
friction are negligible. At a certain moment body 2 is released and the arrangement set in motion. Find the
maximum height that body 2 will go up
to in \( \mathrm{cm} \)
Subject: Physics
If you are traveling on a spaceship close to the speed of light (pick a number e.g.
0.95c), With or without constant acceleration whichever works for the
question. Time will slow down relative to earth
and you will be able to travel a greater distance than you would be able to without relativistic effects. You would
also be able to return to earth with
significant time passed relative to your experience. My question is, what would it feel like on the spaceship...I know the standard answer is you wouldn't feel anything, but logically, if you were traveling through galaxy after galaxy in a relativistic time of human life then
intuition says everything would look like it whizzing past. Basically, what is the human experience of being able to trave interstellar distances?
Subject: Chemistry
Dalton's law of partial pressure is not applicable to which of the following mixture of gases? This question has multiple correct options
\( A \cdot H_{2}+F_{2} \)
в. \( N H_{3}+H C l \)
\( \mathbf{c} \cdot S O_{2}+C l_{2} \)
D. \( H_{2}+O_{2} \)
Subject: Chemistry
If a compound has "n" asymmetric carbon atoms with different terminal groups, the number of stereoisomers is
given by the formula:
A \( \cdot\left(\frac{1}{2}\right)^{n} \)
B . \( 2^{n} \)
\( c \cdot 2 \sqrt{n} \)
D. \( \sqrt{2} n \)
Subject: Physics
A Cell of emf \( \mathrm{E} \) is connected across a
resistance R. The potential difference between the terminals of the cell
is found to be \( V \). The internal resistance
of the cell is given as:
A \( . R(E-V) \)
в. \( \frac{E-V}{R} \)
c. \( \frac{(E-V)}{R} E \)
D. \( \frac{(E-V)}{V} R \)
Subject: Physics
At the initial moment three points \( A, B \)
and \( C \) are on a horizontal straight line
at equal distances from one another.
Point \( A \) begins to move vertically
upward with constant velocity \( v \) and
point \( C \) vertically downward without
any initial velocity at constant acceleration \( a \). Assuming the point
begin to move simultaneously, then comment on the motion of the B such
that centre of mass of the
system doesn't move.
A \( \cdot \) acceleration \( \frac{1}{2} a \) downwards and initial velocity \( \frac{1}{2} v \) upwards
B. retardation \( \frac{1}{2} a \) and initial velocity \( \frac{1}{2} v \) both upwards
c. zero acceleration and initial velocity
D. acceleration \( \frac{1}{2} a \) and initial velocity \( \frac{1}{2} v \) both downwards
Subject: Physics
A coin is tossed with a velocity of \( 3 \mathrm{m} / \mathrm{s} \)
at
A.
a) What happens to the velocity along
AB, along DE and at C?
b) What happens to the acceleration of the coin along \( A C \) and \( C E ? \)
c) What is the distance and vertical
displacement covered by the coin between A and E.
Subject: Maths
If \( \frac{2 x^{2}+3 x+4}{(x-1)\left(x^{2}+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^{2}+2} \)
Then the value of \( B \) is equal to
A . 3
B. -
\( c \cdot-2 \)
D.
Subject: Maths
The value of \( \boldsymbol{I}= \)
\( \int_{\pi / 2}^{5 \pi / 2} \frac{e^{\tan ^{-1}(\sin x)}}{e^{\tan ^{-1}(\sin x)}+e^{\tan ^{-1}(\cos x)}} d x \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \)
D. \( \pi / 2 \)
Subject: Physics
A force of 5 N acts on a body of weight \( 9.8 \mathrm{N} . \) What is the acceleration
produced in \( \boldsymbol{m} / \boldsymbol{s e c}^{2} \)
A. \( 49.00 \mathrm{m} / \mathrm{s}^{\wedge 2} \)
B. \( 5.00 \mathrm{m} / \mathrm{s}^{2} 2 \)
c. \( 1.46 \mathrm{m} / \mathrm{s}^{2} \) ?
D. \( 0.5 \mathrm{m} / \mathrm{s}^{\wedge} 2 \)
Subject: Physics
The mutual inductance between two
coils when a current of 5 A changes to \( 10 \mathrm{A} \) in \( 1 \mathrm{s} \) and induces an emf of \( 100 \mathrm{m} \)
Vin the secondary is
A . \( 20 \mathrm{m} \) н
B. \( 10 \mathrm{mH} \)
c. \( 30 \mathrm{mH} \)
D. \( 15 \mathrm{mH} \)
Subject: Maths
Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{x}^{2}+ \)
\( 100 x+5 \sin x, \) then \( f(x) \) is bijective.
Reason
\( \mathbf{3} \boldsymbol{x}^{\mathbf{2}}+\mathbf{2} \boldsymbol{x}+\mathbf{9 5}>\mathbf{0} \boldsymbol{x} \in \boldsymbol{R} \)
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: Chemistry
(a) Account for the following:
(i) Acidic character increase from \( \boldsymbol{H} \boldsymbol{F} \)
to \( H I \)
(ii) There is large difference between melting and boiling points of oxygen and sulphur.
(iii) Nitrogen does not from pentahalide.
(b) Draw the structures of the following:
(i) \( C l F_{3} \)
\( (\text { ii }) X e F_{4} \)
Subject: Maths
The value of \( \sum_{k=0}^{n}\left(i^{k}+i^{k+1}\right), \) where
\( i^{2}=-1, \) is equal to :
\( \mathbf{A} \cdot i-i^{n} \)
B. \( -i+i^{n+1} \)
c. \( i-i^{n+1} \)
D. \( i-i^{n+2} \)
E \( .-i-i^{n} \)