AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ \mathbf{2} & \mathbf{5} & \mathbf{0} \\ \mathbf{3} & \mathbf{6} & \mathbf{0}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right] \)
and \( C=\left[\begin{array}{lll}3 & 2 & 1 \\ 1 & 2 & 3 \\ 7 & 8 & 9\end{array}\right], \) Then evaluate
\( \boldsymbol{A B}-\boldsymbol{B C} \)
Subject: Maths
Find \( \boldsymbol{A}, \) if \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{2} \\ \mathbf{0} & \mathbf{9}\end{array}\right] \) and \( \boldsymbol{A}- \)
\( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & -\mathbf{6} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \)
Subject: Physics
Complete the table choosing the right
term from the list given in brackets: \( \left(10^{9}\right. \)
micro, \( \left.\mathbf{d}, \mathbf{1 0}^{-\mathbf{9}}, \mathbf{m i} \| \mathbf{i}, \mathbf{m}, \mathbf{M}\right) \)
\begin{tabular}{lll} 
Factor & Prefix & Symbol \\
\( 10^{-1} \) & deci & \\
\( 10^{-6} \) & & \( \mu \) \\
& giga & G \\
\( 10^{6} \) & mega & \\
\hline
\end{tabular}
Subject: Maths
Vivekbhai bought a TV for Rs \( 16,000 . \) Rs 200 was spent on transportation and labour. For earning 12 \% profit, what price should it be sold?
A. \( R s 30,144 \)
B. \( R s 18,144 \)
c. \( R s 20,144 \)
D. None of these
Subject: Maths
The length of a chord of a circle of
radius \( 10 \mathrm{cm} \) is \( 12 \mathrm{cm} \). Find the
distance of the chord from the centre of
the circle
A. \( 6 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)
Subject: Chemistry
What is the formula of ammonium
aquapentafluoronickelate(IV)?
\( \mathbf{A} \cdot\left[\operatorname{Ni}\left(N H_{3}\right)\left(H_{2} O\right) F_{5}\right]^{+1} \)
B . \( \left[N i\left(N H_{3}\right)\left(H_{2} O\right) F_{5}\right] \)
\( \mathbf{c} \cdot\left(N H_{4}\right)_{2}\left[N i\left(H_{2} O\right) F_{5}\right] \)
D. \( N H_{4}\left[N i\left(H_{2} O\right) F_{5}\right] \)
Subject: Chemistry
Assertion
Primary benzylic halides are more reactive than primary alkyl halides
towards \( S_{N} 1 \) reaction
Reason
Reactivity depends upon the nature of the nucleophile and the solvent
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: Biology
Assertion
Acraniata is a group of organisms which do not have distinct cranium.
Reason
It includes small marine forms without
head
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
A man walks \( 20 \mathrm{m} \) at an angle of \( 60^{\circ} \) east of north. How far towards north has
he traveled?
A . \( 10 m \)
в. 20m
\( \mathrm{c} \cdot 10 \sqrt{3} m \)
D. \( 10 / \sqrt{3} m \)
Subject: Maths
\( \tan \theta=-2, \theta \epsilon(0, \pi) \) then which of the
following is correct
This question has multiple correct options
A \( \cdot \sin \theta=\frac{-2}{\sqrt{5}} \)
B. \( \sin \theta=\frac{2}{\sqrt{5}} \)
\( ^{\mathrm{C}} \cdot \cos \theta=\frac{-1}{\sqrt{5}} \)
D. \( \cos \theta=\frac{1}{\sqrt{5}} \)
Subject: Physics
A proton and an electron are accelerated by same potential difference starting from rest have de-
Brogile wavelength \( \lambda_{p} \) and \( \lambda_{e^{*}} \)
A \( \cdot \lambda_{e}=\lambda_{p} \)
B . \( \lambda_{0}<\lambda_{p} \)
c. \( \lambda_{e}>\lambda_{p} \)
D. none of these
Subject: Chemistry
Kohlrausch's Law states that at:
A. infinite dilution, each ion makes the definite contribution to the conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
B. infinite dilution, each ion makes a definite contribution to an equivalent conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
C. finite dilution, each ion makes the definite contribution to an equivalent conductance of an electrolyte whatever be the nature of the other ion of the electrolyte.
D. infinite dilution each ion makes the definite
contribution to an equivalent conductance of an electrolyte depending on the nature of the other ion of the electrolyte.
Subject: Chemistry
Assertion
Carbon and its compounds used as fuels for most applications.
Reason
When carbon is heated in presence of excess of air or oxygen, it forms carbon dioxide. During its formation, a large amount of heat and light are released.
Further, once ignited, carbon and its
compounds keep on burning without needing additional heat energy.
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 solid right circular wax cone of height \( 12 \mathrm{cm} \) and radius \( 4 \mathrm{cm} \) is melted and
smaller wax cones of height \( 4 \mathrm{cm} \) and
radius \( 2 \mathrm{cm} \) are made The number of
smaller cones will be
\( A \cdot 48 \)
B. 18
\( c \cdot 24 \)
D. 36
Subject: Chemistry
Which is correct relation?
\( \mathbf{A} \cdot A_{e q \cdot(K O O C \cdot C O O N a)}=\frac{1}{2} \lambda_{K^{+}}+\frac{1}{2} \lambda_{N a^{+}}+\frac{1}{2} \lambda_{O X^{2}} \)
B. \( A_{e q .(\text {KOOC} \cdot \text {COONa})}=\lambda_{K^{+}}+\lambda_{N a^{+}}+\lambda_{O X^{2-}} \)
C \( \cdot A_{\text {eq. }(\text { KOOC } \cdot \text { COON } a)}=\lambda K^{+}+\lambda_{N a^{+}}+\frac{1}{2} \lambda_{O X^{2}-} \)
D. \( A_{e q .(\text {KOOC} \cdot \text {COONa})}=\frac{1}{2} \lambda_{K^{+}}+\frac{1}{2} \lambda_{N a^{+}}+\lambda_{O X^{2}} \)
Subject: Physics
When the forward bias voltage of a diode is changed froth \( 0.6 ~ V \) to \( 0.7 ~ V \)
the current changes from \( 5 m A \) to
15 m \( A \). Then its forward bias resistance
is:
\( \mathbf{A} \cdot 0.01 \Omega \)
в. \( 0.1 \Omega \)
c. \( 10 \Omega \)
D. \( 100 \Omega \)
Subject: Physics
A body cools from a temperature \( 3 T \) to
\( 2 T \) in 10 minutes. The room
temperature is \( T . \) Assume that
Newton's law of cooling is applicable. The temperature of the body at the end
of next 10 minutes will be
A \( \cdot \frac{7}{4} T \)
в. \( \frac{3}{2} T \)
c. \( \frac{4}{3} T \)
D. \( T \)
Subject: Maths
\( \ln \) a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is \( 1 / 3 \& \) the probability that he copies the answer is \( 1 / 6 . \) The probability that his answer is correct given that he copied it, is \( 1 / 8 . \) Find the probability that he knew the answer to the question given that he correctly answered it. If expressed in the form of \( a / b \) (simplest form), \( b-a=? \)
Subject: Maths
Evaluate \( \int \frac{x^{5} d x}{\sqrt{\left(1+x^{3}\right)}}= \)
A. \( \frac{2}{3} \sqrt{\left(1+x^{3}\right)+\left(x^{2}+2\right)} \)
B. \( \frac{2}{9} \sqrt{\left(1+x^{3}\right)-\left(x^{3}-4\right)} \)
c. \( \frac{2}{9} \sqrt{\left(1+x^{3}\right)\left(x^{3}+4\right)} \)
D. \( \frac{2}{3} \sqrt{\frac{\left(1+x^{3}\right)^{3}}{3}-\left(1+x^{3}\right)} \)
Subject: Chemistry
In the preparation of \( C a O \) from \( C a C O_{3} \)
using the equilibrium \( C a C O_{3}(s) \rightleftharpoons \) \( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}) \boldsymbol{K}_{p} \) is expressed as:
\( \log \boldsymbol{K}_{p}=\mathbf{7 . 2 8 2}-\frac{\mathbf{8 5 0 0}}{\boldsymbol{T}} \)
for complete decomposition of \( C a C O_{3} \)
the temperature in celsius to be used is:
A . 1167
в. 894
c. 8500
D. 850
Subject: Physics
A boy is \( 1.8 m \) tall and can see his
image in a plane mirror fixed on a wall.
His eyes are \( 1.6 m \) from the floor level
The minimum length of the mirror to see his full image is-
A \( .0 .9 m \)
B. \( 0.85 m \)
\( c .0 .8 m \)
D. Can't be determined
Subject: Chemistry
\( \ln H_{2}-O_{2} \) fuel cell a reaction occuring
at cathode is:
A. \( 2 H_{2} O+O_{2}+4 e^{-} \rightarrow 4 O H^{-} \)
В. \( 2 H_{2}+O_{2} \rightarrow 2 H_{2} O(l) \)
\( \mathrm{c} \cdot H^{+}+O H^{-} \rightarrow H_{2} \mathrm{O} \)
D. \( H^{+}+e^{-} \rightarrow \frac{1}{2} H_{2} \)
Subject: Maths
What will be the height of a cuboid
whose volume is \( 275 \mathrm{cm}^{3} \) and base area
is \( 25 \mathrm{cm}^{2} ? \)
\( A \cdot 10 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( c \cdot 9 \mathrm{cm} \)
D. None of these
Subject: Maths
If the sum of the coefficients of \( x^{2} \) and
coefficients of \( x \) in the expansion of
\( (1+x)^{m}(1-x)^{n} \) is equal to \( -m, \) then
the value of \( 3(n-m) \) is
(Note \( : \boldsymbol{m}, \boldsymbol{n} \text { are distinct }) \)
Subject: Maths
Solve \( \left(2 x-10 y^{3}\right) \frac{d y}{d x}+y=0 \)
A \( \cdot x=-2 y^{3}+c y^{-2} \)
B . \( x=2 y^{3}+c y^{-2} \)
c. \( x=2 y^{3}+c y^{2} \)
D. None of these
Subject: Physics
Assertion
There are two neutral points on a horizontal board when a magnet is held vertically on the board
Reason
At the neutral point the net magnetic field due to the magnetic and magnetic field of the earth is zero
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
Magnetic flux has the dimension
\( \mathbf{A} \cdot M L^{2} A^{-2} \)
B \( \cdot M L^{2} T^{-2} A^{-1} \)
\( \mathbf{C} \cdot M T^{-2} A^{-1} \)
D. \( M L^{2} T^{-2} A^{-2} \)
Subject: Maths
Let \( P(x) \) be a polynomial of degree 4
with \( \boldsymbol{P}(\mathbf{2})=-\mathbf{1}, \boldsymbol{P}^{\prime}(\mathbf{2})=\mathbf{0}, \boldsymbol{P}^{\prime \prime}(\mathbf{2})=\mathbf{2} \)
\( \boldsymbol{P}^{\prime \prime \prime}(2)=-12 \) and \( \boldsymbol{P}^{i v}(2)=24, \) The
value of \( \boldsymbol{P}^{\prime \prime}(1) \) is
Subject: Physics
A lens having focal length \( \boldsymbol{f} \) and
aperture of diameter \( d \) forms an image \( \boldsymbol{d} \)
of intensity \( I . \) Aperture of diameter \( \frac{\mathrm{u}}{2} \) in central region of lens is covered by a
black paper. Focal length of lens and
intensity of image now will be respectively.
A \( \cdot f \) and \( \frac{I}{4} \)
B. \( \frac{3 f}{4} \) and \( \frac{I}{4} \)
c. \( f \) and \( \frac{3 I}{4} \)
D. \( _{f \text { and }} \frac{I}{2} \)
Subject: Chemistry
Assertion
In the coagulation of negatively charged arsenic sulphide sol, the coagulating power decreases in the order \( A l^{3+}> \)
\( \boldsymbol{B} \boldsymbol{a}^{2+}>\boldsymbol{N} \boldsymbol{a}^{+} \)
Reason
Generally, greater the valency of coagulating ion, the greater is its power
of coagulation.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct
Subject: Chemistry
For a given reaction:
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \rightarrow \boldsymbol{3} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \)
Subject: Physics
A wire having a linear density of 0.05 \( \mathrm{gm} / \mathrm{cm} \) is stretched between two rigid supports with a tension of \( 4.5 \times 10^{7} \)
dynes. It is observed that the wire resonates at a frequency of 420 cycles/sec. The next higher frequency at which the same wire resonates is 490
cycles/sec. The length of wire is approximately
A. \( 314 \mathrm{cm} \)
B. 254 cm
c. \( 214 \mathrm{cm} \)
D. 354 cm
Subject: Chemistry
What is chemical equilibrium?
A. A state of balance in a reaction where the forward and reverse reaction speed is equal and the concentrations of the products and reactants remain unchanged.
B. Equilibrium involving chemicals.
C. A state of balance in a reaction where the forward and reverse reaction speed is unequal
D. Equilibrium between two substances that does not involve a change in the chemical makeup of a substance.
E. A state where the reaction is unbalanced
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{x}^{2} / 2 . \) If the graph of \( \boldsymbol{f}(\boldsymbol{x}) \)
is translated 2 units up and 3 units left and the resulting graph is that of \( g(x) \) \( \operatorname{then} g(1 / 2)= \)
A .
B . \( -1 / 8 \)
c. \( -2 / 8 \)
D. \( -33 / 8 \)
E . \( 13 / 8 \)
Subject: Maths
Inverse circular functions,Principal values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{aligned}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\pi+\tan ^{-1} \frac{x+y}{1-x y}, & x>1
\end{aligned}
\]
Solve
(a) \( \cos \left(2 \sin ^{-1} x\right)=1 / 9 \)
(b) \( \cos ^{-1}(3 / 5)-\sin ^{-1}(4 / 5)=\cos ^{-1} x \)
(c) If \( \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1, \) then
prove that \( x \) is equal to \( 1 / 5 \)
Subject: Physics
Two species of radioactive atoms are mixed in equal number. The disintegration constant of the first species is \( \lambda \) and of the second is \( \lambda / 3 \)
After a long time the mixture will behave as a species with mean life of
approximately:
A. \( 0.70 / \lambda \)
d
в. \( 2.10 / \lambda \)
c. \( 1.00 / \lambda \)
D. \( 0.52 / \lambda \)
Subject: Chemistry
\( P H_{3} \) and \( N H_{3} \) on separate reaction with bleaching powder produce respectively
A. P and \( N_{2} \)
B. \( P C l_{3} \) and \( N C l_{3} \)
c. \( P C l_{3} \) and \( N_{2} \)
D. \( P C l_{5} \) and \( N C l_{3} \)
Subject: Physics
The radius of the curved part of the wire is \( R=100 m m, \) the linear parts of the
wire are very long. Find the magnetic induction at the point \( O \) if the wire
carrying a current \( I=8.0 A \) has the
shape shown in figure.
A \( .0 .34 \mu T \)
в. \( 0.11 \mu T \)
c. \( 1.1 \mu T \)
D. \( 34 \mu \) 7
Subject: Chemistry
The oxidation state of oxygen of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in the final products when it reacts with
\( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{O}_{3} \) is :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. - -
Subject: Physics
A hemisphere and a solid cone have a
common base. The center of mass of the
common structure coincides with the
centre of the common base. If \( \boldsymbol{R} \) is the
radius of hemisphere and \( h \) is height of
the cone then:
A \( \cdot \frac{h}{R}=\sqrt{3} \)
в. \( \frac{h}{R}=\frac{1}{\sqrt{3}} \)
c. \( \frac{h}{R}=3 \)
D. \( \frac{h}{R}=\frac{2}{\sqrt{3}} \)
Subject: Maths
For \( |z-1|=1, \) find \( \tan \left[\arg \frac{((z-1)}{\left.\left.\left(2-2 \frac{i}{z}\right)\right)\right]}\right. \)
\( \mathbf{A} \cdot i \)
B.
\( c \cdot-i \)
D. -
Subject: Chemistry
1 mole of \( N O \) and 1 mole of \( O_{3} \) are
taken in \( 10 L \) vessel and heated. At
equilibrium, \( 50 \% \) of \( N O \) (by mass)
reacts with \( O_{3} \) according to the equation:
\( N O(g)+O_{3(g)} \rightleftharpoons N O_{2(g)}+O_{2(g)} \)
What will be the equilibrium constant for this reaction?
\( A \)
B. 2
\( c .3 \)
D.
Subject: Physics
Match the columns
\( \begin{array}{ll}\text { A } & \text { B } \\ \text { i) } h \text { image }=h \text { object } & \text { a) } M<1 \\ \text { ii) } h \text { image }>h \text { object } & \text { b) } M>1 \\ \text { iii) } h \text { image }<h \text { object } & \text { c) } M=1\end{array} \)
\( \mathbf{A} \cdot i-a, i i-c, i i i-b \)
B \( . i-b, i i-a, i i i-c \)
\( \mathbf{c} \cdot i-c, i i-b, i i i-a \)
D. \( i-a, i i-b, i i i-c \)
Subject: Chemistry
A mixture of \( C_{3} H_{8} \) and \( C H_{4} \) exerts a
pressure of \( 320 \mathrm{mm} \) Hg at temperature \( \boldsymbol{T}(\boldsymbol{K}) \) in a \( \boldsymbol{V} \) litre flask. On complete combustion, gaseous mixture contains
\( C O_{2}, \) only and exerts a pressure of 448 \( \mathrm{mm} \) Hg under identical condition.
Hence, mole fraction of \( C_{3} H_{8} \) in the mixture is :
A . 0.2
B. 0.8
c. 0.25
D. 0.75
Subject: Chemistry
For the combustion reaction at \( 298 K \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\mathbf{1} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}(\boldsymbol{s}) \)
Which of the following alternative is
correct?
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. \( \Delta \)Hand\( \Delta U \) bear no relation with each other
Subject: Biology
Match List I with List II and select the
correct option.
List 1
A. Adrenalin
1. Myxoedema
B.
2. Accelerates heart Hyperparathyroidism beat
C. Oxytocin
3. Salt-water balance
D. Hypothyroidism
4. Childbirth
E. Aldosterone
5. Demineralisation
A. A- 2, B- 5, C- 4, D-1, E-3
B. A- 3, B-4, C- 5, D-3, E-2
C. \( A-5, B-3, C-2, D-4, E-1 \)
D. \( A-2, B-3, C-4, D-5, E-1 \)
E . A- 5, B- 3, C- 4, D- 2, E-1
Subject: Chemistry
Arrange the following compounds in the increasing order of homolytic \( (\boldsymbol{C}-\boldsymbol{C}) \)
bond dissociation energy.
I. Propane
II. Ethane
III. 2,2 -Dimethyl propane
IV. 2-Methyl propane
\( A \cdot((11)<(11)<(11)<(1) \)
B. (II) <(I) <(IV) <(III)
\( c \cdot(\| I)<(\mid V)<(\mid)<(||) \)
\( D \cdot(1)<(\| 1)<(11)<(1 V) \)
Subject: Chemistry
The standard reduction potential at
\( 25^{\circ} \mathrm{C} \) of the reaction \( 2 H_{2} O+2 e^{-} \rightleftharpoons \)
\( H_{2}+2 \stackrel{\ominus}{O} H \) is \( -0.8277 \mathrm{V} . \) The
equilibrium constant for the reaction \( 2 H_{2} O \rightleftharpoons H_{3} O^{\oplus}+\stackrel{\ominus}{O} \) at \( 25^{\circ} C \) is:
A \( \cdot K_{w}=9.35 \times 10^{-15} \)
В. \( K_{w}=9.83 \times 10^{-15} \)
C . \( K_{w}=9.14 \times 10^{-15} \)
D. None of these
Subject: Physics
Work done in stretching a wire through \( 1 \mathrm{mm} \) is \( 2 J . \) What amount of work will
be done for elongating another wire of same material, with half the length and
double the radius of cross section, by 1 \( \mathrm{mm} ? \)
A .2
в. 4
c. 8 J
D. 16
Subject: Maths
The scores obtained by 50 students in
an examination is tabulated as shown
below.
\( \begin{array}{ll}\text { Score } & \text { Number of students } \\ \text { below 10 } & 3 \\ \text { below 20 } & \text { 7 } \\ \text { below 30 } & \text { 13 } \\ \text { below 40 } & \text { 22 } \\ \text { below 50 } & \text { 32 } \\ \text { below 60 } & \text { 40 } \\ \text { below 70 } & \text { 46 } \\ \text { below 80 } & \text { 50 }\end{array} \) Find the median score
Subject: Chemistry
The percentage of \( S e \) in peroxidase
anhydrous enzyme is \( 0.5 \% \) by weight (atomic weight \( =\mathbf{7 8 . 4} \) ). Then minimum
molecular weight of peroxidase anhydrous enzyme is:
A \( \cdot 1.568 \times 10^{4} \)
B . \( 1.568 \times 10^{3} \)
c. 15.68
D. \( 3.136 \times 10^{4} \)
Subject: Maths
If \( \vec{a}+\vec{b} \perp \vec{a} \) and \( |\vec{b}|=\sqrt{2}|\vec{a}| \), then?
\( \mathbf{A} \cdot(2 \vec{a}+\vec{b} \| \vec{b} \vec{b} \)
B . \( (2 \vec{a}+\vec{b}) \perp \vec{b} \)
c. \( (2 \vec{a}-\vec{b}) \perp \vec{b} \)
D. \( (2 \vec{a}+\vec{b}) \perp \vec{a} \)
Subject: Maths
A value of \( x \) satisfying the equation \( x^{2}+b^{2}=(a-x)^{2} \) is:
A \( \cdot \frac{b^{2}+a^{2}}{2 a} \)
в. \( \frac{b^{2}-a^{2}}{2 a} \)
c. \( \frac{a^{2}-b^{2}}{2 a} \)
D. \( \frac{a-b}{2} \)
Subject: Physics
A particle moves according to the equation \( \boldsymbol{x}=\boldsymbol{\alpha} \boldsymbol{t}^{3}+\boldsymbol{\beta} \boldsymbol{t}^{2} \). Find
instantaneous acceleration at any time
\( \mathbf{A} \cdot 6 \alpha+2 \beta \)
B. \( 3 \alpha t+2 \beta \)
\( \mathbf{c} \cdot 3 \alpha t+\beta \)
D. \( 6 \alpha t+2 \beta \)
Subject: Maths
John bought a car for a certain sum of money. He spent \( 10 \% \) of the cost on
repairs and sold the car for a profit of
Rs. 11000. How much did he spend on
repairs, if he made a profit of \( 20 \% ? \)
A. Rs. 4000
B. Rs. 4400
c. Rs. 5000
D. Rs. 5500
Subject: Maths
If \( \vec{r}=3 \vec{i}+2 \vec{j}-5 \vec{k}, \vec{a}=2 \vec{i}-\vec{j}+\vec{k} \)
\( \vec{b}=\vec{i}+3 \vec{j}-2 \vec{k} \) and \( \vec{c}=-2 \vec{i}+\vec{j}-3 \vec{k} \)
such that \( \vec{r}=\lambda \vec{a}+\mu \vec{b}+\nu \vec{c} \) then
A \( \cdot \mu, \frac{\lambda}{2}, \nu \) are in \( A P \)
B. \( \lambda, \mu, \nu \) are in \( A P \)
c. \( \lambda, \mu, \nu \) are in \( H P \)
D. \( \mu, \lambda, \nu \) are in \( G P \)
Subject: Physics
Two vectors are necessarily mutually perpendicular when
\( \mathbf{A} \cdot \vec{A}+\vec{B}=\overrightarrow{0} \)
\( \mathbf{B} \cdot \vec{A}-\vec{B}=\overrightarrow{0} \)
\( \mathbf{c} \cdot \vec{A} \times \vec{B}=\overrightarrow{0} \)
D . \( \vec{A} . \vec{B}=0 \)
Subject: Maths
Given that \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x} \boldsymbol{g}(\boldsymbol{x})}{|\boldsymbol{x}|}, \boldsymbol{g}(\mathbf{0})= \)
\( \boldsymbol{g}^{\prime}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f} \) is continuous at \( \boldsymbol{x}=\mathbf{0} \)
the value of \( f^{\prime}(0) \) is
Subject: Maths
The equation of the plane, which bisects the line joining the points (1,2,3) and (3,4,5) at right angles is?
A. \( x+y+z=0 \)
B. \( x+y-z=9 \)
c. \( x+y+z=9 \)
D. \( x+y-z+9=0 \)
Subject: Physics
A parallel plate capacitor consists of
two circular plates each of radius \( 12 \mathrm{cm} \)
and separated by \( 5.0 m m . \) The capacitor is being charged by an external source. The charging current is constant and is
equal to \( 0.15 A \). The rate of change of potential difference between the plates will be :
A. \( 8.173 \times 10^{7} V / s \)
В . \( 7.817 \times 10^{8} V / s \)
C \( .1 .873 \times 10^{9} \mathrm{V} / \mathrm{s} \)
D. \( 3.781 \times 10^{10} V / s \)
Subject: Maths
State true or false:
In triangle \( A B C, P \) is the mid-point of
side \( B C . \) A line through \( P \) and Parallel to \( C A \) meets \( A B \) at point \( Q ; \) and a line through \( Q \) and parallel to \( B C \) meets
median \( A P \) at point \( R \). Can it be
concluded that,
\( \boldsymbol{A P}=\boldsymbol{2} \boldsymbol{A} \boldsymbol{R} ? \)
A. True
B. False
Subject: Maths
Based on this information answer the
questions given below. A string of three English letters is formed as per the following rules:
(a) The first letter is any vowel.
(b) The second letter is \( \boldsymbol{m}, \boldsymbol{n} \) or \( \boldsymbol{p} \)
(c) If the second letter is \( m \) then the
third letter is any vowel which is different from the first letter.
(d) If the second letter is \( n \) then the
third letter is \( e \) or \( u \)
(e) If the second letter is \( p \) then the third
letter is the same as the first letter.
How many strings of letters can possibly be formed using the above
rules?
\( \mathbf{A} \cdot 40 \)
B . 45
c. 30
D. 35
Subject: Physics
An elevator is moving upwards with
constant acceleration. The dashed
curve in figure. shows the position y of the ceiling of the elevator as a function of time t. At the instant indicated by the
point \( P \) a bolt breaks loose and drops
from the ceiling. Which of the solid curves shown best describes the
position of the bolt as a function of time?
\( A \)
B.
\( c \)
D. IV
Subject: Physics
Two wave-fronts are emitted from
coherent sources of path difference between them is 2.1 micron. Phase
difference between the wave-fronts at
that point is \( 7.692 \pi . \) Wavelength of light emitted by sources will be :
в. 5400 月
c. \( 5460 \hat{h} \)
D. 5892 月
Subject: Chemistry
Calculate : \( K_{a} \) for \( H C N \) given
\( \boldsymbol{K}_{b}\left(\boldsymbol{C N}^{-}\right)=\mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{5}} \)
A \( \cdot 10^{-5} \)
В. \( 2 \times 10^{-7} \)
c. \( 4 \times 10^{-10} \)
D. None of these