AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \frac{x}{2}\right)(1-\sin x)}{\left(1+\tan \frac{x}{2}\right)(\pi-2 x)^{3}} \) is
A . 0
B. \( \frac{1}{32} \)
\( c \cdot \alpha \)
\( D \)
Subject: Maths
In the figure given below, \( A B C D \) is a
trapezium in which \( A B \| D C . E \) and \( F \)
are the midpoint of \( A D \) and \( B C \)
respectively. \( D F \) and \( A B \) are produced
to meet at \( G . \) Also \( A C \) and \( E F \) intersect
at point \( O . \) Show that :
\( (i) E O \| A B \)
\( (i) A O=C O \)
Subject: Chemistry
Account for the following:
(i) \( P C l_{5} \) is more covalent than \( P C l_{3} \)
(ii) Iron on reaction with \( H C l \) forms
\( F e C l_{2} \) and not \( F e C l_{3} \)
(iii) The two \( O-O \) bond lengths in the
ozone molecule are equal.
Subject: Physics
biased has a drop of \( 0.5 \% \) which is
assumed to be independent of current.
The current in excess of \( 10 m A \)
through the diode produces large joule
heating which damages the diode. If we
want to use a \( 1.5 ~ V \) battery to forward
bias the diode, the resistor used in
series with the diode so that the
maximum current does not exceed
\( 5 m A \) is
A \( .2 \times 10^{2} \Omega \)
B . \( 2 \times 10^{5} \Omega \)
C \( \cdot 2 \times 10^{3} \Omega \)
D . \( 2 \times 10^{4} \Omega \)
Subject: Physics
Two equal drops of water are falling through air with a steady velocity of \( 10 \mathrm{cm} / \mathrm{s} \). If the drops recombine to form a single drop then the terminal velocity is:
A \( \cdot 2^{\frac{2}{5}} \times 5 \) cm / \( s \)
B . \( 2^{\frac{2}{5}} \times 10 \mathrm{cm} / \mathrm{s} \)
c. \( 2^{\frac{2}{5}} \times 15 \mathrm{cm} / \mathrm{s} \)
D. \( 2^{\frac{2}{5}} \times 4 \) cm \( / s \)
Subject: Maths
If \( a, b, c, d \epsilon R \) are such that \( a^{2}+b^{2}=4 \)
and \( c^{2}+d^{2}=2 \) and if \( |a+i b|^{2}=\mid c+ \)
\( \left.i d\right|^{2}|x+i y| \operatorname{then} x^{2}+y^{2}= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
What is the relationship between the
two terminal \( \boldsymbol{H}_{2} \boldsymbol{C}= \) groups in a cumulene containing three consecutive double bonds? \( \left(\boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2}\right) \)
A. They are in the perpendicular plane
B. They are in same plane
c. They are in two planes at \( 120^{\circ} \)
D. They are in two planes at \( 109^{\circ} \)
Subject: Physics
Linear \( \& \) Angular acceleration of a particle is \( 10 \mathrm{m} / \mathrm{sec}^{2} \) and \( 5 \mathrm{rad} / \mathrm{sec}^{2} \)
respectively. What is its from rotational axis :
A . \( 50 m \)
B. \( 1 / 2 m \)
\( c .1 m \)
D. \( 2 m \)
Subject: Chemistry
Catenation i.e. linking of similar atoms depends on size and electronic
configuration of atoms. The tendency of catenation in Group 14 elements follows
the order:
A. \( C>S i>G e>S n \)
в. \( C>>S i>G e \approx S n \)
c. \( S i>C>S n>G e \)
D. \( G e>S n>S i>C \)
Subject: Chemistry
Assertion
The ground state electron configuration
orbitals of elemental \( \boldsymbol{C u} \) is \( [\boldsymbol{A} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{s}^{1} \boldsymbol{3} \boldsymbol{d}^{1} \)
Reason
Completely half-filled and filled dorbital best show special electronic
stabilization
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
Two blocks \( A \) and \( B \) of masses \( 5 \mathrm{kg} \) and
\( 3 \mathrm{kg} \) respectively rest on a smooth horizontal surface with \( B \) over \( A \). The
coefficient of friction between \( A \) and \( B \)
is \( 0.5 . \) The maximum horizontal force
(in kg wt.) that can be applied to \( A, \) so that there will be motion of \( A \) and \( B \)
without relative slipping, is?
A . 1.5
B . 2.
\( c \cdot 4 \)
D.
Subject: Maths
Find the sum of first \( n \) term of an \( A . P \) is
\( c n^{2}, \) which \( n t h \) term is \( t_{n}=5+6 n n \in \)
\( N \)
A \( \cdot \frac{n\left(4 n^{2}-1\right) c^{2}}{6} \)
B. \( 3 n^{2}+8 n \)
c. \( \frac{n\left(4 n^{2}-1\right) c^{2}}{3} \)
D. \( \frac{n\left(4 n^{2}+1\right) c^{2}}{6} \)
Subject: Chemistry
In case of Hall's process applied on
reduction of \( A l_{2} O_{3} \) to \( A l \) can be done by
using:
A. Cathode - Al, Anode - Graphite
B. Cathode - Graphite, Anode - Graphite
c. cathode - Graphite, Anode - steel
D. Cathode - Steel, Anode - Graphite
Subject: Maths
Let \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be two independent events.
The probability that both \( \boldsymbol{E} \) and \( \boldsymbol{F} \)
happens is \( 1 / 6 \) and the probability that neither \( \boldsymbol{E} \) nor \( \boldsymbol{F} \) happens is \( \mathbf{1} / \mathbf{3} \). Then This question has multiple correct options
A \( \cdot P(E)=1 / 2, P(F)=1 / 3 \)
B . \( P(E)=1 / 2, P(F)=1 / 6 \)
C \( \cdot P(E)=1 / 6, P(F)=1 / 2 \)
D \cdot \( P(E)=1 / 3, P(F)=1 / 2 \)
Subject: Maths
\( D \) and \( F \) are mid-points of sides \( A B \)
and \( A C \) of a triangle \( A B C . \) A line
through \( F \) and parallel to \( A B \) meets
\( B C \) at point \( E . \) Then \( B D F E \) is a :
A. rhombus
B. parallelogram
c. rectangle
D. data insufficient
Subject: Physics
A body of weight \( W_{1} \) is suspended from
the celling of a room through a chain of
weight \( W_{2} \) The earth pulls the chain by a force equal to:
\( A \cdot W_{2} \)
B. \( \left(W_{1}+W_{2}\right) / 2 \)
\( \mathbf{c} \cdot\left(W_{1}+W_{2}\right) \)
D. \( W_{1} \times W_{2} \)
Subject: Chemistry
Which of the following does not truly represent the property indicated against it?
A. \( B r_{2}<C l_{2}<F_{2} \) : Oxidising power
B. \( B r<C l<F \) : Electronegativity
c. \( B r<F<C l \) : Electron affinity
D. \( B r_{2}<C l_{2}<F_{2}: \) Bond energy
Subject: Physics
In a region of space, the electric field is given by \( \overrightarrow{\boldsymbol{E}}=\mathbf{8} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} . \) The electric
flux through a surface of area 100 units in the xy plane is :
A. 800 units
B. 300 units
c. 400 units
D. 1500 units
Subject: Biology
Assertion
UV radiation cause photo dissociation
of ozone into \( O_{2} \) and 0 thus causing
damage to stratospheric ozone layer.
Reason
Ozone hole is resulting in global warming and climatic change.
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: Chemistry
Which of the following is not a disproportionation reaction?
A. Cannizzaro reaction
B. Decomposition of \( H_{2} O_{2} \) to \( H_{2} O \) and \( O_{2} \)
c. Decomposition of ozone to \( O_{2} \)
D. Decomposition of \( K C l O_{3} \) to \( K C l O_{4} \) and \( K C l \)
Subject: Maths
Which one of the following is a
quadratic polynomial?
A \( \cdot x^{2}+3 \)
B. \( x^{3}+x^{2}+4 \)
\( \mathbf{c} \cdot 2 x^{4}+4 x^{3}+3 x^{2}+6 \)
D. None of the above
Subject: Chemistry
Assertion : 20 gm of argon (atomic mass of \( A r=40) \) occupies volume of
\( 22400 c m^{3} \) at STP.
Reason : 20 gm of Neon (atomic mass of
\( N e=20) \) occupies a volume of
\( 22400 c m^{3} \) at STP.
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.
E. Both assertion and reason are incorrect.
Subject: Physics
A body ties to a string of length \( \boldsymbol{L} \) is
revolved in a vertical circle with
minimum velocity, when the body
reaches the upper most point the string
breaks and the body moves under the influence of the gravitational field of
earth along a parabolic path. The
horizontal range \( A C \) of the body will be:
A \( . x=L \)
B. \( x=2 L \)
C \( . x=2 \sqrt{2 L} \)
\( \mathbf{D} \cdot x=\sqrt{2 L} \)
Subject: Physics
A moving coil galvanometer has a coil with 175 turns and area \( 1 \mathrm{cm}^{2} \). It uses a
torsion band of torsion constant \( 10^{-6} \mathrm{N} \)
\( \mathrm{m} / \mathrm{rad} . \) The coil is placed in a magnetic field B parallel to its plane. The coil
deflects by \( 1^{\circ} \) for a current of \( 1 \mathrm{mA} \). The value of \( \mathrm{B}(\text { in } \text { Telsa }) \) is approximately.
A \( \cdot 10^{-3} \)
B . \( 10^{-1} \)
\( c \cdot 10^{-4} \)
D. \( 10^{-2} \)
Subject: Chemistry
\( H_{3} P O_{4} \) is a tri basic acid and one of its
salt is \( N a H_{2} P O_{4} . \) What volume in ml of
1M NaOH solution should be added to
\( 12 g \) of \( N a H_{2} P O_{4} \) to convert it into
\( N a_{3} P O_{4} ? \)
Subject: Chemistry
Sulphur reacts with chlorine in 1: 2
ratio and forms \( X . \) hydrolysis of \( X \) gives
a sulphur compound \( Y \). What is the
hybridization state of central atom in the compound?
\( A \cdot s p^{3} \)
B \( \cdot s p^{2} \)
\( c \cdot s p \)
D. \( d s p^{2} \)
Subject: Biology
Q Type your question
opuion gıven below:
\( \mathbf{A} \)
b-iv, c-iii, d\( a-i i \)
B. a-i, b-iv, c-iii, d-ii
c. a-iii, b-iv, c-i, d-ii
D. \( a-i i i \) b-ii, c-i, d-iv
Subject: Maths
Find the area of the triangle formed by the midpoints of the sides of \( \Delta A B C \) where \( \boldsymbol{A}=(\mathbf{3}, \mathbf{2}), \boldsymbol{B}=(-\mathbf{5}, \mathbf{6}) \) and \( \boldsymbol{C}= \)
(8,3)
Subject: Chemistry
Four reactions that take place in the blast furnace to produce iron are shown. Which reaction is used to keep the furnace hot?
A. \( C+O_{2} \rightarrow C O_{2} \)
в. \( C O_{2}+C \rightarrow 2 C O \)
c. \( F e_{2} O_{3}+3 C \rightarrow 2 F e+3 C O \)
D. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
Subject: Physics
If the angle of dip at a certain place is
\( 45^{\circ} \) then the horizontal component \( \boldsymbol{H} \)
vertical component \( V \) and total
intensity \( I \) of earth's magnetic field have the correct relationship given by :
A. \( H=\sqrt{2} V \)
В. \( I=\sqrt{2} V \)
\( \mathbf{c} \cdot H=2 V \)
D. \( H=\sqrt{2} H \)
Subject: Maths
\( A B \) is chord of a circle with centre \( O \)
and radius \( 17 \mathrm{cm} . \) If \( O M \perp A B \) and
\( \boldsymbol{O} \boldsymbol{M}=\mathbf{8} \mathrm{cm} . \) The length of chord \( \boldsymbol{A B} \) is
A . \( 12 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)
Subject: Chemistry
\( \boldsymbol{S}_{N^{1}} \) reactivity of the following halides,
(i) \( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C} \boldsymbol{B r} \)
(ii) \( \left(C_{6} H_{5}\right)_{2} C H B r \)
(iii) \( \left(C_{6} H_{5}\right)_{2} C\left(C H_{3}\right) B r \)
(iv) \( \left(C H_{3}\right)_{2} C H B r \) will be in the order:
\( \mathbf{A} \cdot i v>i>i i>i i i \)
в. \( i i>i> \) iii \( > \) iv
\( \mathbf{c} \cdot i>i i i>i i>i v \)
D. \( i i i>i i>i>i v \)
Subject: Physics
A heavy steel ball of mass greater than \( 1 \mathrm{kg} \) moving with a speed of \( 2 \mathrm{m} / \mathrm{s} \) collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision
the ping pong ball moves approximately
with a speed
A. \( 2 m / s \)
в. \( 4 m / s \)
c. \( 2 \times 10^{4} m / s \)
D. \( 2 \times 10^{3} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If the equation \( a x^{2}-6 x y+y^{2} 2 g x+ \)
\( 2 f y+c=0 \) represents a pair of line
whose slopes are \( m \) and \( m^{2}, \) then sum
of all possible values of \( a \) is-
A . 17
в. -19
c. 19
D. -17
Subject: Physics
The isotopes present in naturally occurring uranium are
\( (i) U-235 \)
\( (i i) U-236 \)
\( (i i i) U-238 \)
\( (i v) U-232 \)
A \( .(i) \) and \( (i i i) \)
B. \( (i) \) and \( (i i) \)
c. \( (i i) \) and \( (i i i) \)
D. (iv) and (ii)
Subject: Chemistry
\( E^{0} \) for the cell, \( Z n\left|Z n^{2+}_{(a q)}\right|\left|C u^{2+}_{(a q)}\right| C u \) is
\( 1.10 V \) at \( 25^{0} C . \) The equilibrium constant
for \( Z n+C u^{2+}_{(a q)} \rightarrow Z n^{2+}_{(a q)}+C u \) the cell
reaction is of the order of :
A \( \cdot 10^{-37} \)
B. \( 10^{37} \)
D. \( 10^{17} \)
Subject: Chemistry
Which of the following pairs of compounds is isoelectronic and isostructural?
A. \( I F_{3}, X e F_{2} \)
в. \( B e C l_{2}, X e F_{2} \)
\( \mathbf{c} \cdot \operatorname{TeI}_{2}, X e F_{2} \)
D. \( I B r_{2}^{-}, X e F_{2} \)
Subject: Maths
Differentiate the following function with
respect to \( x \)
\( \boldsymbol{x}^{-4}\left(\boldsymbol{3}-\boldsymbol{4} \boldsymbol{x}^{-\boldsymbol{5}}\right) \)
A . \( -12 x^{-6}+36 x^{-10} \)
B. \( -12 x^{-5}+36 x^{-11} \)
c. \( -12 x^{-5}+36 x^{-10} \)
D. \( -12 x^{5}+36 x^{-10} \)
Subject: Chemistry
Which of the following species has been oxidized?
\( M g(O H)_{2(a q)}+2 N a_{(s)} \rightarrow M g_{(s)}+ \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}_{(a q)} \)
A. \( M g^{+2} \)
в. \( N a \)
\( \mathrm{c} . M g \)
D. \( O H^{-} \)
Subject: Chemistry
In which of the following species the
interatomic bond angle is \( 109^{\circ} 28^{\prime} ? \)
A \( \cdot N H_{3},\left(B F_{4}\right)^{-1} \)
B . \( \left(N H_{4}\right)^{+}, B F_{3} \)
c. \( N H_{3}, B F_{3} \)
D. \( \left(N H_{2}\right)^{-1}, B F_{3} \)
Subject: Biology
How many of the following plants given below possess open (X) and closed vascular bundles (Y) respectively? Brassica, Tulipa, Capsicum, Gloriosa, Nicotiana, Aloe, Cicer, Asparagus, Petunia, Colchicum, Sesbania, Zea.
\( A \cdot X=6, Y=6 \)
B. \( x=4, Y=8 \)
c. \( x=5, Y=7 \)
D. \( x=9, Y=3 \)
Subject: Physics
In a transformer, the number of turns in
the primary coil is 140 and that in the secondary coil is \( 280 . \) If the current in the primary coil is \( 4 A \), then that in the secondary coil is
\( A \cdot 4 A \)
B. 2 A
\( c \cdot 6 A \)
D. 10 A
Subject: Maths
Using determinants show that points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}) \) and \( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \)
are col-linear.
Subject: Chemistry
Complete the following reactions:
(i) \( C_{6} H_{5} N H_{2}+C H C l_{3}+ \)
alc.KOH\( \longrightarrow \)
(ii) \( C_{6} H_{5} N_{2} C l+H_{3} P O_{2}+H_{2} O \rightarrow \)
(iii) \( C_{6} H_{5} N H_{2}+H_{2} S O_{4}(\text { conc. }) \rightarrow \)
(iv) \( C_{6} H_{5} N_{2} C l+C_{2} H_{5} O H \rightarrow \)
\( (v) C_{6} H_{5} N H_{2}+B r_{2}(a q) \rightarrow \)
\( (v i) C_{6} H_{5} N H_{2}+\left(C H_{3} C O\right)_{2} O \rightarrow \)
\( \left(\text { vii) } C_{6} H_{5} N_{2} C l \frac{(i) H B F_{4}}{(i i) N a N O_{2} / C u, \Delta}\right. \)
Subject: Physics
If \( \oint_{s} \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s}=\boldsymbol{0} \) over surface, then
A. the electric field inside the surface and on it is zero
B. the electric field inside the surface is necessarily uniform
C . all charges must necessarily be outside the surface
D. all of these
Subject: Maths
Let \( \boldsymbol{f}:(e, \infty) \rightarrow \boldsymbol{R} \) be a function
defined by \( f(x)=\log (\log (\log x)), \) the
base of the logarithm being \( e \). Then
A. \( f \) is one-one and onto
B. \( f \) is one-one but not onto
\( c . f \) is onto but not one-one
D. the range of \( f \) is equal to its domain
Subject: Maths
Let \( \boldsymbol{O}= \) Set of odd natural numbers \( = \)
\( \{1,3,5,7,9, \dots\} \) and \( E=\operatorname{set} \) of even
natural numbers \( =\{2,4,6,8,10, \dots \dots .\} \)
Then show that \( 3 \in E \)
Subject: Physics
Assertion : The acceleration due to
gravity on the moon is one-sixth that on
the earth.
Reason : The law of gravitation is the
same on both the moon and the earth.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false
Subject: Maths
Calculate the coefficient of range for the
following data.
\begin{tabular}{lll} 
No. of wards & 1 & 2 \\
\hline
\end{tabular} 3 \begin{tabular}{r}
4 \\
\hline
\end{tabular}
No. of
\[
32 \quad 57
\]
\( 28 \quad 96 \)
nouses
Subject: Physics
A sphere of radius \( R \), density \( D \) and
specific heat \( S \) is heated to temperature \( \theta \) and surrounding is at
temperature \( \theta_{0} . \) Its rate of fall of temperature will be proportional to
A. \( D S / R \)
в. \( R / D S \)
\( \mathrm{c} .1 / R D S \)
D. \( R D S \)
Subject: Maths
In the series \( 20,18,16, \ldots \ldots \ldots,-2 \) is the
term
\( \mathbf{A} \cdot 10^{t h} \)
B. \( 11^{\text {th }} \)
\( \mathbf{c} \cdot 12^{t h} \)
D. \( 13^{\text {th }} \)
Subject: Chemistry
Assertion
Hydrides of group 13 elements are Lewis acids whereas hydrides of group \( 15-17 \) elements are Lewis bases
Reason
Group 13 hydrides have few electrons
whereas group \( 15-17 \) hydrides have excess electrons which are present as
lone pairs
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
\( \int \frac{7^{2 x+3} \sin ^{2} 2 x+\cos ^{2} 2 x}{\sin ^{2} 2 x}=\frac{7^{2 x+3}}{2 \log 7}- \)
\( \frac{(\cot x+x)}{b} \cdot \) Find \( b \)
Subject: Physics
A radioactive element X disintegrates successively as under:
\( \boldsymbol{X} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{1} \stackrel{\boldsymbol{\beta}}{\rightarrow} \boldsymbol{X}_{2} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{3} \stackrel{\gamma}{\rightarrow} \boldsymbol{X}_{4} \)
If the atomic number and atomic mass.
Number of \( X \) are 72 and \( 180 . \) What are
the corresponding values for \( \boldsymbol{X}_{\mathbf{4}} \)
A .69,176
B. 69,172
c. 71,176
D. 71,172
Subject: Physics
A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic
energy, \( \boldsymbol{E}_{\mathbf{0}} \). The minimum energy of
explosion will be
\( \mathbf{A} \cdot 6 E_{0} \)
в. \( \frac{4 E_{0}}{3} \)
c. \( 4 E_{0} \)
D. \( 8 E_{0} \)
Subject: Chemistry
Which one among the following is not
correct as per indicated property?
\( \mathbf{A} \cdot B r_{2}<C l_{2}<F_{2}(\text { Oxidising power }) \)
B. \( B r_{2}<F_{2}<C l_{2} \) (Electron gain enthalpy)
\( \mathbf{c} \cdot B r_{2}<C l_{2}<F_{2}(\text { Electronegativity }) \)
\( \mathbf{D} \cdot B r_{2}<C l_{2}<F_{2}(\text { Bond energy }) \)
Subject: Chemistry
The ether that undergoes electrophilic
substitution reaction is :
A. \( C H_{3} O C_{2} H_{5} \)
в. \( C_{6} H_{5} O C H_{3} \)
\( \mathbf{c} \cdot C H_{3} O C H_{3} \)
D. \( C_{2} H_{5} O C_{2} H_{5} \)
Subject: Chemistry
Given the species \( N_{2}, C O, N O^{+} \) and
\( C N^{-} \) which of the following statements
are true for this :
(I) All the species are diamagnetic
(II) All the species are isostructural
(III) All the species have identical bond order
(IV) More than one species have zero dipole moment
A. I, II and III
B. ।, ॥, III and IV
c. III and IV
D. I and II
Subject: Chemistry
The various types of hydrides and
examples of each type are given below. Hydride types Compounds
\( (A) \) Electron deficient
\( (i) L i H \)
\( (B) \) Saline
\( (i i) C H_{4} \)
\( (C) \) Electron precise
\( (i i i) N H_{3} \)
\( (D) \) Interstitial
\( (i v) B_{2} H_{6} \)
\( (\boldsymbol{E}) \) Electron rich
\( (\boldsymbol{v}) \boldsymbol{C r} \boldsymbol{H} \)
Choose the correct matching from the codes given below.
A \( \cdot(A)-(i i),(B)-(i v),(C)-(v),(D)-(i i i),(E)-(i) \)
B. \( (A)-(i v),(B)-(i),(C)-(i i),(D)-(v),(E)-(i i i) \)
C. \( (A)-(i v),(B)-(i i i),(C)-(v),(D)-(i i),(E)-(i) \)
D. \( (A)-(v),(B)-(i i i),(C)-(i v),(D)-(i i),(E)-(i) \)
E \( .(A)-(i v),(B)-(v),(C)-(i),(D)-(i i),(E)-(i i i) \)
Subject: Chemistry
A jar contains 30 mL of glycerine (whose mass is37.8 \( g \) ) and 60 mL of corn syrup (whose mass is \( 82.8 \mathrm{g} \) ). Which liquid is on top? Show your work, and explain your
answer.
A. glycerine
B. syrup
\( c . \) a and \( b \)
D. none of these
Subject: Maths
\( \mathbf{a}=\left|\begin{array}{ccc}\cos \theta / 2 & 1 & 1 \\ 1 & \cos \theta / 2 & -\cos \theta / 2 \\ -\cos \theta / 2 & 1 & -1\end{array}\right| \)
If the minimun of \( \Delta \) is \( m_{1} \) and
maximum of \( \Delta \) is \( m_{2}, \) then \( \left[m_{1}, m_{2}\right] \) are
related
A. [-4,-2]
B. [2, 4]
\( c \cdot[-4,0] \)
D. [0, 2]
Subject: Maths
If \( x y \) -plane and \( y z \) -plane divides the line segment joining \( A(2,4,5) \) and \( B(3,5,-4) \) in the ratio a:b and p:q respectively then value of \( \left(\frac{a}{b}, \frac{p}{q}\right) \) may be
A \( \cdot \frac{23}{12} \)
B. \( \frac{7}{5} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{21}{10} \)
Subject: Chemistry
Which of the following statement(s) is/are true or false?
\( S_{1}: \) In organometallic compounds, carbon is bonded to metals directly.
\( S_{2}: \) Complexes having \( d^{0} \) or \( d^{10} \) configuration of metal ions are always diamagnetic.
\( \boldsymbol{S}_{3}: \) Extra stability of metal carbonyls is
explained by synergic bonding.
\( S_{4}: \ln F e(C O)_{5}, \) the Fe-C bond
possesses both \( \sigma \) and \( \pi \) characteristics.
A. TTTT
B. TTFF
c. FTFT
D. FTTT
Subject: Physics
A particle of mass \( 5 \mathrm{kg} \) is free to slide on a smooth ring of radius \( r=20 \mathrm{cm} \) fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point 0 of the ring. Initially the particle is at rest at a point \( A \) of the ring such that \( \angle O C A \) \( =60^{\circ}, \mathrm{C} \) being the centre of the ring.
The natural length of the spring is also equal to \( r=20 \mathrm{cm} . \) After the particle is released, it slides down the ring, the contact force between the particle \( \& \) the ring becomes zero when it reaches the lowest position B. Determine the force constant of the spring.
Subject: Biology
In which one of the following, the BOD (Biochemical Oxygen Demand) of sewage (S), distillery effluent (DE), paper mill effluent (PE) and sugar mill effluent (SE) have been arranged in ascending order
\( A \cdot S E<S<P E<D E \)
B. SE <PE <S <DEE
c. \( P E<S<S E<D E \)
D. \( S<D E<P E<S E \)
Subject: Maths
ff \( \bar{a}, \bar{b}, \bar{c}, \bar{d} \) are the position vectors of four points \( \mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D} \) in a plane such that \( |\overline{\boldsymbol{a}}-\overline{\boldsymbol{d}}|=|\overline{\boldsymbol{b}}-\overline{\boldsymbol{d}}|=|\overline{\boldsymbol{c}}-\overline{\boldsymbol{d}}| \) then the
point \( \mathbf{D} \) is the \( \cdots \) of \( \Delta \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \)
A. centroid
B. circumcentre
c. orthocentre
D. incentre
Subject: Physics
A cube is shifted to a depth of \( 100 m \) is
alake. The change in volume is \( 0.1 \% \). The bulk modules of the material is nearly
\( \mathbf{A} \cdot 10 P a \)
в. \( 10^{4} P a \)
\( \mathbf{c} \cdot 10^{7} P a \)
D. \( 10^{9} \mathrm{Pa} \)
Subject: Physics
Given \( \vec{A}=2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}+\hat{j} . \) The
component of vector \( \overrightarrow{\boldsymbol{A}} \) along vector \( \overrightarrow{\boldsymbol{B}} \) is:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{3}{\sqrt{2}} \)
c. \( \frac{5}{\sqrt{2}} \)
D. \( \frac{7}{\sqrt{2}} \)
Subject: Chemistry
Assertion
(A) : Noble gases have very low boiling
points.
Reason
(R) : All noble gases have general
electronic configuration of \( \boldsymbol{n} \boldsymbol{s}^{2} \boldsymbol{n} \boldsymbol{p}^{6} \)
\( (\operatorname{except} H e) \)
A. Both (A) and (R) are true but (R) is correct explanation of (A)
B. (A) is false but (R) is true
c. (A) is true but (R) is false
D. Both (A) and (R) are true but (R) is not the correct explanation of (A)