AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion
Static frictional force is self adjusting, for the given two surfaces.
Reason
Sliding frictional force between two given solid surfaces is independent of
surface area of contact
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
A square of side \( 16 \mathrm{cm} \) is reduced by a scale factor 0.5 Find the area of the
image
A \( \cdot 16 \mathrm{cm}^{2} \)
В. \( 32 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 64 c m^{2} \)
D. \( 1024 \mathrm{cm}^{2} \)
Subject: Chemistry
\( 56 g \) of nitrogen and \( 8 g \) of hydrogen gas are heated in a closed vessel. At
equilibrium \( 34 g \) of ammonia is present. The equilibrium number of moles of nitrogen, hydrogen and ammonia are respectively:
\( \mathbf{A} \cdot 1,2,2 \)
в. 2,2,1
c. 1,1,2
D. 2,1,2
Subject: Maths
Two roads are represented by the
equations \( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{6} \) and \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{8} \)
An inspection bungalow has to be so constructed that it is at a distance of
100 from each of the roads. Possible
location of the bungalow is given by :
This question has multiple correct options
A \( \cdot(100 \sqrt{2}+1,7) \)
в. \( (1-100 \sqrt{2}, 7) \)
c. \( (1,7+100 \sqrt{2}) \)
D. \( (1,7-100 \sqrt{2}) \)
Subject: Maths
If \( 2 \sinh ^{-1}\left(\frac{a}{\sqrt{1-a^{2}}}\right)=\log \left(\frac{1+X}{1-X}\right) \)
then \( X= \)
\( A \)
B.
c. \( \sqrt{1-a^{2}} \)
D. \( \frac{1}{\sqrt{1-a^{2}}} \)
Subject: Maths
If \( a, b, c \) are the roots of the equation
\( \boldsymbol{x}^{3}+\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}+\boldsymbol{r}=\boldsymbol{0}, \) form the
equation whose roots are \( a-\frac{1}{b c}, b-\frac{1}{c a}, c-\frac{1}{a b} \)
Subject: Chemistry
Which of the following represents
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O N a+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
\( \mathbf{c} \cdot 2 C H_{3} C O O H+2 N a \rightarrow C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)
Subject: Chemistry
Combination of
\( \boldsymbol{P t}(\boldsymbol{I} \boldsymbol{V}), \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{C l}^{-}, \boldsymbol{K}^{+} \) result in the
formation of \( x \) complexes and one such
complex is \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{4} . \boldsymbol{x} \) is :
Subject: Chemistry
When \( H_{2} O_{2} \) is added to an acidified
solution of \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C} \boldsymbol{r}_{2} \boldsymbol{O}_{7} \)
A. solution turns green due to formation of \( C r_{2} O_{3} \)
B. solution turns yellow due to formation of \( K_{2} \) Cr \( O_{4} \).
c. a deep blue-violet colored compound \( C r O\left(O_{2}\right)_{2} \) is formed
D. solution gives green ppt. of \( \operatorname{Cr}(O H)_{3} \)
Subject: Physics
I wo lathtical roas one and two each on
mass M and length L are performing
general plane motion on the horizontal
plane as shown in the figure if \( V \) is
velocity of center of mass of both the
rods and \( \omega \) is the angular speed about
the certical axis then angular momentum of rod 1 in the frame of
reference of center of mass of rod 2 at
the given instant will be
\( ^{\mathbf{A}} \cdot\left(M v \frac{3 L}{2}+\frac{M L^{2}}{12} \omega\right)(-k) \)
B \( \cdot\left(M v \frac{3 L}{2}\right)(-k) \)
\( ^{\mathbf{C}} \cdot\left(\frac{M L^{2}}{12} \omega\right)(-K) \)
D \( \cdot\left(M v \frac{3 L}{4}\right)(-k) \)
Subject: Chemistry
Assertion: The fluorine has lower
reactivity.

Reason: \( \boldsymbol{F}-\boldsymbol{F} \) bond has low bond
dissociation energy
A. Both assertion and reason are true and the reason is a correct explanation of the assertion
B. Both assertion and reason are true but reason is not a correct explanation of the assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Assertion is false but the reason is true
Subject: Biology
Match the following. \begin{tabular}{ccc|c} 
& List I & & List II \\
\( \mathrm{i} \) & Deforestation & \( \mathrm{a} \) & Urbanization \\
\( \mathrm{ii} \) & Natural cause \( \mathrm{of} \) deforestation & \( \mathrm{b} \) & Cutting of forests \\
iii & Man-made cause of deforestation & \( \mathrm{c} \) & Droughts
\end{tabular}
\( \mathbf{A} \)
\( 1-b \) , \( \|-a,\| I-c \)
\( B \cdot I-a,\|-b,\| I-C \)
\( \mathbf{C} \cdot \mid-\mathrm{c},\|-\mathrm{a},\|-\mathrm{b} \)
D. \( |-b,||-c,|||- \)
Subject: Chemistry
Assertion
Ortho and para-nitrophenols can be separated by steam distillation.
Reason

Ortho isomer associates through intermolecular hydrogen bonding while Para isomer associates through
intramolecular hydrogen bonding.
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
A parabola has \( x \) - axis as its axis, \( y \) axis as its directrix and \( 4 a \) as its latus
rectum. If the focus lies to the left side
of the directrix then the equation of the parabola is
\( \mathbf{A} \cdot y^{2}=4 a(x+a) \)
B \( \cdot y^{2}=4 a(x-a) \)
C \( \cdot y^{2}=-4 a(x+a) \)
D \( \cdot y^{2}=4 a(x-2 a) \)
Subject: Maths
The area enclosed between the curves
\( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{y}=|\boldsymbol{x}| \boldsymbol{i} \boldsymbol{s} \)
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{1}{6} \)
\( D \)
Subject: Chemistry
Fill up the following with suitable terms.
(i) Activation energy \( = \) Threshold
energy -
(ii) Half-life period of zero order reaction
\( = \)
(iii) Average rate of reaction \( = \)
(iv) Instantaneous rate of reaction \( = \)
A \( \cdot \) potential energy, \( \frac{0.693}{k}, \frac{d x}{d t}, \frac{\Delta[A]}{\Delta t} \)
B. Energy of reactants, \( \frac{1}{k}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)
C. Energy of reaction, \( \frac{\log k}{t}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)
Derage kinetic energy of reactants, \( \frac{a}{2 k}, \frac{\Delta[A]}{\Delta t}, \frac{d x}{d t} \)
Subject: Biology
Assertion
Under conditions of high light intensity
and limited \( C O_{2} \) supply,
photorespiration has a useful role in
protecting the plants from photooxidative damage.
Reason
If enough \( C O_{2} \) is not available to utilize
light energy for carboxylation to proceed, the excess energy may not cause damage to plants.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts ona
particle and displaces it form initial position \( \overrightarrow{x_{1}}=(3 \hat{i}+4 \hat{j}) m \) to final position \( \overrightarrow{x_{2}}=(2 \hat{i}+3 \hat{j}) m, \) then work
done by force, is
\( \mathbf{A} \cdot-19 J \)
в. \( -5 . J \)
c. \( 12 J \)
D. \( 19 J \)
Subject: Physics
A rod of length L lies along the \( x \) -axis with its left end at the origin. It has a nonuniform charge density \( \boldsymbol{\lambda}=\boldsymbol{\alpha} \boldsymbol{x} \)
where \( \alpha \) is a positive constant. What are
the units of \( \boldsymbol{\alpha} \) ?
A \( \cdot \frac{C}{m^{2}} \)
в. \( \frac{c}{m^{1}} \)
\( \mathrm{c} \cdot \mathrm{Cm} \)
D. \( C m^{2} \)
Subject: Physics
The change in the gravitational potential energy when a body of mass \( \mathrm{m} \) is raised to a height \( n R \) above the surface of the Earth is (Here R is the
radius of the earth)
A \( \cdot\left(\frac{n}{n+1}\right) \) mgR
в. \( \left(\frac{n}{n-1}\right) \) тg \( R \)
c. \( n m g R \)
D. \( \frac{m g R}{n} \)
Subject: Maths
Select the missing number from the
given matrix:
\( \begin{array}{ccc}5 & 2 & 4 \\ 4 & 4 & 7 \\ 2 & 5 & 3 \\ 18 & 30 & ?\end{array} \)
A . 43
B. 42
\( c .33 \)
D. 32
Subject: Maths
\( \mathrm{f}\left[\begin{array}{l}\mathbf{4} \\ \mathbf{1} \\ \mathbf{3}\end{array}\right] \boldsymbol{A}=\left[\begin{array}{lll}-\mathbf{4} & \mathbf{8} & \mathbf{4} \\ -\mathbf{1} & \mathbf{2} & \mathbf{1} \\ -\mathbf{3} & \mathbf{6} & \mathbf{3}\end{array}\right], \) if \( \boldsymbol{A}= \)
\( \boldsymbol{a} \quad \boldsymbol{b} \quad \boldsymbol{c}] \)
Find \( a+b+c \)
Subject: Biology
The empirical formula of a hydrocarbon is \( C H_{3} . \) It's molecular weight is 30
What is molecular formula of the
compound.
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{10} \)
Subject: Chemistry
In which of the following reactions (I) is behaving like an electrophile?
(1)
(2) \( \mathrm{Br}_{2} \)
\[
+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \stackrel{\mathrm{CCl}_{4}}{\longrightarrow}
\]
\( (2) \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \quad+\mathrm{H}-\mathrm{Br} \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \)
(4)
\( A \)
\( B .2 \)
\( c \cdot 3 \)
\( D \cdot 4 \)
Subject: Physics
How much heat energy is released when
\( 5.0 g \) water at \( 42^{\circ} C \) changes into ice at
\( 0^{\circ} \mathrm{C} ? \) Take specific heat capacity of
water \( =4.2 J g^{-1}, \) specific latent heat of
fusion of ice \( =336 J g^{-1} \)
\( \mathbf{A} \cdot 21 J \)
B. \( 4200 J \)
c. \( 42 J \)
D . 2562 \( J \)
Subject: Chemistry
For the reaction: \( C a C O_{3}(s) \rightleftharpoons \operatorname{CaO}(s)+ \)
\( C O_{2}(g) . K_{p}=1 \) atm at \( 927^{0} \mathrm{C} . \) If \( 20 \mathrm{g} \) of
\( \mathrm{CaCO}_{3} \) were kept in a 10 liter vessel at
\( 927^{0} \mathrm{C}, \) then calculate percentage of
\( C a C O_{3} \) remaining at equilibrium:
Subject: Physics
For both pure and doped silicon,
calculate the probability that a state at
the bottom of the silicon conduction
band is occupied?
\( A \cdot 5.20 \times 10^{-2} \)
B . \( 1.40 \times 10^{-2} \)
c. \( 10.5 \times 10^{-2} \)
D. \( 14 \times 10^{-2} \)
Subject: Maths
A survey regarding the height (in cm) of
51 girls of class \( X \) of a school was
conducted and the following data was
obtained:
\( \begin{array}{ll}\text { Height in } \mathrm{cm} & \text { Number of Girls } \\ \text { Less than } 140 & 4 \\ \text { Less than } 145 & 11 \\ \text { Less than } 150 & 29 \\ \text { Less than } 155 & 40 \\ \text { Less than } 155 & 46 \\ \text { Less than } 165 & 51\end{array} \) Find the median height.
Subject: Physics
Two circular coils made up of identical
wires of length \( 40 \mathrm{cm} \) have respectively 8 and 4 turns and the current flowing through the second coil is 4 times
greater than in the first coil. The ratio of magnetic induction at their centres is :
A . 2: 3
B. 3:
\( c \cdot 1: \)
D. 1: 2
Subject: Chemistry
The correct order of acidic strength of
oxy - acids of chlorine is:
\( \mathbf{A} \cdot H C l O<H C l O_{2}<H C l O_{3}<H C l O_{4} \)
B \( \cdot H C l O_{4}<H C l O_{3}<H C l O_{2}<H C l O \)
\( \mathbf{c} \cdot H C l O>H C l O_{4}>H C l O_{3}>H C l O_{2} \)
D. \( H C l O_{4}<H C l O_{2}>H C l O_{3}>H C l O \)
Subject: Maths
The complex number system, denoted
by \( C, \) is the set of all ordered pairs of
real numbers (that is, \( \boldsymbol{R} \times \boldsymbol{R} \) ) with the
operation (denoted by \( \times \) ) which satisfy
multiplication
\( \mathbf{A} \cdot(a, b) \times(c, d)=(a c+b d, b c-a d) \)
B. \( (a, b) \times(c, d)=(a c-b d, b c+a d) \)
C \( .(a, b) \times(c, d)=(a+c, b+d) \)
D. None of these
Subject: Chemistry
If the EMF of a cell :
\( \boldsymbol{M}\left|\boldsymbol{M}^{2+}(\mathbf{0 . 0 2} \boldsymbol{M}) \| \boldsymbol{H}^{+}(\mathbf{0 . 1} \boldsymbol{M})\right| \boldsymbol{H}_{2} \)
\( a t m) \)
at \( 25^{\circ} \mathrm{C} \) is \( 0.81 \mathrm{V} \). Find the standard
reduction potential of \( M \)
(Write a value to the nearest integer. If an answer is negative then write its
magnitude)
Subject: Physics
The equation of a progressive wave is given by \( \boldsymbol{y}=\mathbf{1 0} \sin (\mathbf{5} \boldsymbol{t}-\boldsymbol{x}) . \) The wave
gets reflected from a open boundary The equation of the reflected wave is
A \( . y=10 \sin (5 t-x) \)
B. \( y=-10 \sin (5 t-x) \)
c. \( y=10 \sin (5 t+x) \)
D. \( y=10 \sin (5 t+x+\pi) \)
Subject: Maths
On simplification the product of given expression \( \left(x-\frac{1}{x}\right)\left(x+\frac{1}{x}\right)\left(x^{2}+\frac{1}{x^{2}}\right) \)
A \( \cdot x^{3}-\frac{1}{x^{3}} \)
в. \( x^{3}+\frac{1}{x^{3}} \)
c. \( x^{4}-\frac{1}{x^{4}} \)
D. \( x^{4}+\frac{1}{x^{4}} \)
Subject: Physics
The heat energy required to raise the
temperature of of a
substance through is
called its specific heat capacity.
A. water, \( 10^{\circ} \mathrm{C} \)
B. hot, \( 10^{\circ} \mathrm{C} \)
C . one gram, \( 1^{\circ} \mathrm{C} \)
D. none of the above
Subject: Maths
Find \( \boldsymbol{X} \) and \( \boldsymbol{Y}, \) if \( \boldsymbol{2}\left[\begin{array}{ll}\mathbf{1} & \boldsymbol{3} \\ \boldsymbol{0} & \boldsymbol{x}\end{array}\right]+\left[\begin{array}{ll}\boldsymbol{y} & \boldsymbol{0} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right]= \)
\( \left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right] \)
Subject: Chemistry
\( 92 U^{238} \) by successive radioactive decays changes to \( _{82} P b^{206} \). A sample of uranium ore was analysed and found to contain \( 1.0 g U^{238} \) and \( 0.1 g P b^{206} \) has accumulated due to decay of uranium, find out the age of ore. \( t_{1 / 2} \) for \( U^{238}= \) \( 4.5 \times 10^{9} y e a r \)
Subject: Physics
Figure. shows the \( P-V \) plot of an ideal
gas taken through a cycle \( A B C D A \). The
part \( A B C \) is a semi-circle and \( C D A \) is
half of an ellipse. Then
This question has multiple correct options
A. the process during the path \( A \rightarrow B \) is isothermal
B. heat flows out of the gas during the path \( B \rightarrow C \rightarrow \)
c. work done during the path \( A \rightarrow B \rightarrow C \) is zero
D. positive work is done by the gas in the cycle \( A B C D A \)
Subject: Chemistry
The correct order of hybridization of the central atom in the following species is:
\( N H_{3},\left[P t C l_{4}\right]^{2-}, P C l_{5} \) and \( B C l_{3} \)
B . \( s p^{3}, d s p^{2}, d s p^{3}, s p^{2} \)
C \( \cdot d s p^{2}, s p^{2}, s p^{3}, d s p^{3} \)
D. \( d s p^{2}, s p^{3}, s p^{2}, d s p^{3} \)
Subject: Physics
If a body mass \( 36 g m \) moves with \( \mathrm{S}, \mathrm{H}, \mathrm{M} \)
of amplitude \( A=13 \) and period \( T= \)
12 \( \sec \) At a time \( t=0 \) the displacement
is \( x=+13 c m . \) The shortest time of
passage from \( \boldsymbol{x}=+\mathbf{6 . 5} \mathrm{cm} \) to \( \boldsymbol{x}=-\mathbf{6 . 5} \)
is
\( A \cdot 4 \sec \)
B. 2 sec
\( c \cdot 6 \sec \)
D. 3 sec
Subject: Chemistry
Which of the following oxide(s) of iron would be obtained on prolonged reaction of iron with steam?
A. FeO
в. \( F e_{2} O_{3} \)
\( \mathbf{c} \cdot F e_{3} O_{4} \)
D. \( F e_{2} O_{3} \) and \( F e_{3} O_{4} \)
Subject: Biology
Which of the following statement(s) is (are) true about heart?
A. Left atrium receives oxygenated blood from different parts of body while right atrium receives deoxygenated blood from lungs.
B. Left ventricle pumps oxygenated blood to different body parts while right ventricle pumps deoxygenated blood to lungs.
C. Left atrium transfers oxygenated blood to right ventricle which sends it to different body parts.
D. Right atrium receives deoxygenated blood from different parts of the body while left ventricle pumps oxygenated blood to different parts of the body.
\( E . \) Both \( B \) and \( D \)
Subject: Maths
The perimeters of a circular field and a square field are equal. If the area of the square field is \( 12100 m^{2} \), then the area
of the circular field will be
A. \( 15500 m^{2} \)
В. \( 15400 m^{2} \)
c. \( 15200 m^{2} \)
D. \( 15300 m^{2} \)
Subject: Chemistry
The standard heat of combustion of
solid boron is equal to:
A. \( \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
(2)
B \( \cdot \frac{1}{2} \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathbf{c} \cdot 2 \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathbf{D} \cdot-\frac{1}{2} \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
Subject: Maths
If the tangent to the curve \( y=x \log x \) at
\( (c, f(x)) \) is parallel to the line-segment
joining \( \boldsymbol{A}(\mathbf{1}, \boldsymbol{0}) \) and \( \boldsymbol{B}(\boldsymbol{e}, \boldsymbol{e}), \) then \( \mathbf{c}=\ldots \)
A \( \cdot \frac{e-1}{e} \)
B. \( \log \frac{e-1}{e} \)
c. \( \frac{1}{e^{1-e}} \)
D. \( \frac{1}{e^{e-1}} \)
Subject: Physics
A uniform wire of length \( l=5 \pm 0.05 \mathrm{cm} \)
and radius \( r=0.5 \pm 0.005 \mathrm{cm} \) has
mass \( \boldsymbol{m}=\mathbf{0 . 4}+\mathbf{0 . 0 0 4 g} . \) The maximum
percentage error in its density is
\( A \)
B. 2
\( c \cdot 4 \)
D. 5.8
Subject: Biology
Assertion
Glycolysis takes place in the cytoplasm.
Reason

Enzymes for glycolysis are found in the
cytoplasm.
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
A trust fund has Rs. 30,000 that must
be invested in two different types of bonds. The first bond pays \( 5 \% \) interest per year, and the second bond pays \( 7 \% \) interest per year. Using matrix multiplication, determine how to divide
Rs. 30,000 among the two types of bonds. If the trust fund must obtain an
annual total interest of
A) Rs. 1800
B) Rs. 2000
Subject: Maths
Find the values of \( c \) that satisfy the MVT
for integrals on [-2,3]
\( \boldsymbol{f}(\boldsymbol{t})=\mathbf{8} \boldsymbol{t}+\boldsymbol{e}^{-\boldsymbol{3} \boldsymbol{t}} \)
В. \( c=-0.0973 \)
c. \( c=1.0973 \)
D. \( c=0.0973 \)
Subject: Maths
A sum of Rs. 1000 is lent to be returned
in 11 monthly installments of Rs. 100 each, interest being simple. The rate of interest
A \( \cdot g \frac{1}{11} \% \)
B. \( 10 \% \)
c. \( 11 \% \)
D. \( 21 \frac{9}{11} \% \)
Subject: Maths
Consider the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cl}\frac{\tan k x}{x}, & x<0 \\ 3 x+2 k^{2}, & x \geq 0\end{array} . \) What is the non- \right.
zero value of k for which the function is
continuous at \( \boldsymbol{x}=\mathbf{0} ? \)
A . \( 1 / 4 \)
B. \( 1 / 2 \)
c. 1
D.
Subject: Maths
A unit radial vector \( \hat{r} \) makes angles of
\( \boldsymbol{\alpha}=\mathbf{3 0}^{o} \) relative to the \( \boldsymbol{x} \) -axis, \( \boldsymbol{\beta}=\mathbf{6 0}^{\circ} \)
relative to the \( y \) -axis, and \( \gamma=90^{\circ} \)
relative to the \( z- \) axis. The vector \( \hat{r} \) can
be written as:
A \( \cdot \frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j} \)
B. \( \frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j} \)
c. \( \frac{\sqrt{2}}{3} \hat{i}+\frac{1}{\sqrt{3}} \hat{j} \)
D. none of these
Subject: Maths
If \( x \) is \( 90 \% \) of \( y, \) then what percent of \( x \) is
\( \boldsymbol{y} ? \)
A \( .90 \% \)
B. \( 190 \% \)
c. \( _{101} \frac{1}{9} \% \)
D. \( 111 \frac{1}{9} \% \)
Subject: Chemistry
Which of the following relation is not correctly matched with the formula?
A \( \cdot \ln \) case of association, \( \alpha=\frac{i-1}{\frac{1}{n}-1} \)
B. \( _{\text {In case of dissociation, } \alpha}=\frac{i-1}{n+1} \)
\( i \frac{n_{B}}{n_{A}+n_{B}} \)
Devation in boiling point, \( \Delta T=K_{b} \times \frac{W_{B} \times 1000}{M_{B} \times W_{A}} \)
Subject: Chemistry
When metal XX is treated with sodium
hydroxide, a white ppt. of AA is obtained
which is soluble in excess
of NaOHNaOH to form soluble
complex BB.Compound AA is soluble in dilute HCIHCl to form compound CC.The compound AA when strongly heated gives compound DD which is used to
extract metals.
Compound \( D \) is :
\( \mathbf{A} \cdot A l_{2} O_{3} \)
в. \( C u O \)
c. \( H g O \)
D. \( M g O \)
Subject: Maths
Construct a quadrilateral \( P Q R S \) where \( \boldsymbol{P Q}=\mathbf{4} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{6} \boldsymbol{c m}, \boldsymbol{R} \boldsymbol{S}= \)
\( \mathbf{5} c m \cdot \boldsymbol{P} \boldsymbol{S}=\mathbf{5} . \mathbf{5} \boldsymbol{c m} \) and \( \boldsymbol{P} \boldsymbol{R}=\mathbf{7} \boldsymbol{c m} \)
Subject: Maths
A family of lines is given by \( (1+ \)
\( 2 \lambda) x+(1-\lambda) y+\lambda=0, \lambda \) being the
parameter. The line belonging to this family at the maximum distance from
the point (1,4) is
A. \( 4 x-y+1=0 \)
B. \( 33 x+12 y+7=0 \)
c. \( 12 x+33 y=7 \)
D. none of these
Subject: Maths
Assertion
Points \( \boldsymbol{P}(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}), \sin \beta) \) and
\( \boldsymbol{R}(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})), \) where
\( \beta=\frac{\pi}{4}+\frac{\alpha}{2} \) are non-collinear.
Reason
Three given points are non-collinear if they form a triangle of non-zero area.
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 the Reason is correct
Subject: Chemistry
By dissolving 13.6 g of a substance in 20 \( g \) of water, the freezing point decreased
by \( 3.7^{\circ} \mathrm{C} \). Calculate the molecular mass
of the substance.
(Molal depression constant for water = \( 1.863 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \) )
Subject: Maths
Which of the following list of numbers
does form an AP?
A. \( 2,4,8,16, \dots \)
В \( \cdot 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots \)
c. \( 0.2,0.22,0.222,0.2222, \ldots \)
D. \( 1,3,9,27, \ldots \)
Subject: Maths
\( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x \)
A. \( \cot x+\frac{x \csc x}{x \cos x-\sin x}+c \)
в. \( \frac{\sin x-x \cos x}{x \sin x+\cos x}+c \)
c. \( -\cot x+\frac{x \csc x}{x \cos x-\sin x}+c \)
D. \( \cot x-\frac{x \csc x}{x \cos x-\sin x}+c \)
Subject: Maths
Consider the equation \( 2+\mid x^{2}+4 x+ \)
\( \mathbf{2} \mid=\boldsymbol{m}, \boldsymbol{m} \epsilon \boldsymbol{R} \) so that the given
equation has three solutions is:
\( A \cdot\{4\} \)
B \( \cdot\{2\} \)
\( c \cdot\{1\} \)
\( D \cdot\{0\} \)
Subject: Physics
A ball is released from the top of height 'h' metres. It takes 't' seconds to reach
the ground. Where is the ball at the time t/2 \( s ? \)
A \( \cdot \operatorname{At}\left(\frac{h}{4}\right) \) from the ground
B. \( \operatorname{At}\left(\frac{h}{2}\right) \) from the ground
c. \( \operatorname{At}\left(\frac{3 h}{4}\right) \) from the ground
D. Depends upon mass and volume of the bal
Subject: Chemistry
Which one of the following is oxidised
by \( \mathrm{MnO}_{2} ? \)
A \( \cdot \mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}_{2}-\mathrm{OH} \)
B. \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \)
c. \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3} \)
D. \( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{OH} \)
Subject: Chemistry
Amongst \( N H_{3}, B e C l_{2}, C O_{2} \) and \( H_{2} O \)
the non-linear molecules are:
A. \( B e C l_{2} \) and \( H_{2} O \)
в. \( B e C l_{2} \) and \( C O_{2} \)
c. \( N H_{3} \) and \( H_{2} O \)
D. \( N H_{3} \) and \( C O_{2} \)
Subject: Maths
Evaluate \( \lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}},(a \neq 0) \)
A \( \cdot \frac{2}{3 \sqrt{3}} \)
B \( \cdot \frac{4}{3 \sqrt{3}} \)
c. \( \frac{5}{3 \sqrt{3}} \)
D. \( \frac{7}{3 \sqrt{3}} \)