AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Complexes formed in the following
methods are:
(1) Mond's process for purification of nicke
(II) Removal of unreacted AgBr from photographic plate
(III) Removal of lead poisoning from the
body
A \( \cdot \) ।. \( N i(C O)_{4}, \) II. \( \left[A g(C N)_{2}\right]^{-}, \) ॥I. \( [P b(E D T A)]^{2} \)
B . I. \( N i(C O)_{4}, \) II. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3-}, \) ॥I. \( [P b(E D T A)]^{2} \)
c. ।. \( N i(C O)_{6}, \) ॥. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3-}, \) ॥I. \( [P b(E D T A)]^{4} \)
D. I. \( N i(C O)_{6}, \) II. \( \left[A g\left(S_{2} O_{3}\right)\right]^{-}, \) III. \( [P b(E D T A)]^{2} \)
Subject: Chemistry
The IUPAC name of \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right] \) is:
A. potassium tetracyanonickelate (II)
B. potassium tetracyanato nickelate (III)
c. potassium tetracyanatonickel (II)
D. potassium tetracyanonickel (III)
Subject: Physics
Two coils connected in parallel having
resistances \( 300 \Omega \) and \( 200 \Omega a t 20^{0} C \)
and temperature coefficient of resistivity \( 0.001 K^{-1} \) and \( 0.006 K^{-1} \)
respectively.The effective temperature coefficient of the combination is
A. \( 0.007 K^{-1} \)
B . \( 0.004 K^{-1} \)
D. \( 0.003 K^{-1} \)
Subject: Maths
The total \( \operatorname{cost} C_{(x)} \) and the total revenue \( R_{(x)} \) associated with production and
sale of \( x \) units of an item are given by
\( C(x)=0.1 x^{2}+30 x+1000 \) and
\( R(x)=0.2 x^{2}+36 x-100 . \) Find the
marginal cost and the marginal revenue when \( x=20 \)
Subject: Physics
A dip needle shows angle of dip \( \theta \) when
the dip circle is placed in magnetic meridian. Now, the dip circle is rotated
by an angle \( \alpha \) and the apparent angle of
dip at this place is \( \theta^{\prime} \), then
\( \left(\tan \theta^{\prime} / \tan \theta\right) \) is :
A . \( 1 / \cos \alpha \)
B. \( 1 / \sin \alpha \)
\( c \cdot \cos \alpha \)
D. sina
Subject: Physics
Average distance of the earth from the
sun is \( L_{1} . \) If one year of the earth \( =D \)
days, one year of another planet whose
average distance from the sun is \( L_{2} \) will
be
\( ^{\mathrm{A}} \cdot_{D}\left(\frac{L_{2}}{L_{1}}\right)^{1 / 2} \) days
B. \( \quad D\left(\frac{L_{2}}{L_{1}}\right)^{3 / 2} \) days
\( ^{\mathbf{C}} \cdot_{D}\left(\frac{L_{2}}{L_{1}}\right)^{2 / 3} \) days
D. \( D\left(\frac{L_{L}}{L_{1}}\right) \) days
Subject: Chemistry
In which of the following complex ion, the central metal ion is in a state of
\( s p^{3} d^{2} \) hybridisation?
\( \mathbf{A} \cdot\left[C o F_{6}\right]^{3-} \)
B \cdot \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e(C N)_{6}\right]^{3} \)
D \cdot \( \left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Physics
A system is shown in the figure. A man
a standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is
\( 2 m / s \) downwards. The velocity of the
block will be: [Assume that the block
does not rotate \( ] \)
A. \( 3 m / s \)
B. \( 2 m / s \)
c. \( \frac{1}{2} m / s \)
D. \( 1 \mathrm{m} / \mathrm{s} \)
Subject: Physics
The surface tension of soap solution is \( 0.03 N / m . \) The work done in blowing to
from a soap bubble of surface area
\( 40 c m^{2},(\text { in } J), \) is
A \( \cdot 1.2 \times 10^{-4} \)
B. \( 2.4 \times 10^{-4} \)
c. \( 12 \times 10^{-4} \)
D. \( 24 \times 10^{-4} \)
Subject: Physics
The number of turns in an air core
solenoid of length \( 25 \mathrm{cm} \) and radius 4 \( \mathrm{cm} \) is \( 100 . \) Its self inductance will be
A \( \cdot 5 \times 10^{-4} H \)
в. \( 2.5 \times 10^{-4} H \)
c. \( 5.4 \times 10^{-3} H \)
D . \( 2.5 \times 10^{-3} \mathrm{H} \)
Subject: Maths
What is the perimeter of the triangle with vertices \( \boldsymbol{A}(-\mathbf{4}, \mathbf{2}), \boldsymbol{B}(\mathbf{0},-\mathbf{1}) \) and
\( C(3,3) ? \)
A. \( 7+3 \sqrt{2} \)
B. \( 10+5 \sqrt{2} \)
c. \( 11+6 \sqrt{2} \)
D. \( 5+10 \sqrt{2} \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{\sin \left(x^{g}\right)}{x}(g=g r a d) \)
A \( \cdot \frac{\pi}{180} \)
в. \( \frac{\pi}{90} \)
c. \( \frac{\pi}{100} \)
D. \( \frac{\pi}{200} \)
Subject: Maths
If \( S_{n}=\sum_{r=0}^{n} \frac{1}{n} \) and \( t_{n}=\sum_{r=0}^{n} \frac{r}{n}, \) then
\( \frac{\boldsymbol{t}_{\boldsymbol{n}}}{\boldsymbol{s}_{\boldsymbol{n}}}= \)
A \( \cdot \frac{1}{2} n \)
в. \( \frac{1}{2} n-1 \)
c. \( n-1 \)
D. \( \frac{2 n-1}{2} \)
Subject: Chemistry
I.U.P.A.C name for \( \boldsymbol{F e}(\boldsymbol{C O})_{2}(\boldsymbol{\sigma}- \)
\( \left.\boldsymbol{C}_{5} \boldsymbol{H}_{5}\right)\left(\boldsymbol{\pi}-\boldsymbol{C}_{5} \boldsymbol{H}_{5}\right) \) complex
A . Dicarbonyl ( \( \eta^{5} \) - cyclopentadienyl) (cyclopentadienyl)ferrate(II)
B. Dicarbony! ( \( \eta^{5} \) - cyclopentadiene) (cyclopentadiencyl)iron(II)
C. Dicarbonyl ( \( \eta^{5} \) - cyclopentadienyl) ( \( \eta^{5} \) cyclopentadienyl)iron(II)
D. Dicarbonyl ( \( \eta^{5} \) - cyclopentadieny!) (cyclopentadienyl)iron(II)
Subject: Physics
Body is projected vertically with velocity \( 10 \mathrm{m} / \mathrm{s} \) on reaching the ground, change in its velocity is(upwards direction is taken as positive)
\( A \cdot 20 \mathrm{m} / \mathrm{s} \)
B. \( -20 \mathrm{m} / \mathrm{s} \)
c. zero
D. none
Subject: Physics
A soild sphere of radius \( \boldsymbol{R}_{1} \) and volume
charge density \( \rho=\frac{\rho_{0} o}{r} \) is enclosed by a
hollow sphere of radius \( R_{2} \) with
negative surface charge density \( \sigma \), such
that the total charge in the system is
zero. \( \rho_{0} \) is a positive constant and \( r \) is the distance from the center of the
sphere.Then the ratio \( \boldsymbol{R}_{2} / \boldsymbol{R}_{1} \) is
\( A \cdot \sigma / \rho_{o} \)
B. \( \sqrt{2 \sigma} / \rho_{o} \)
c. \( \sqrt{\rho_{-} o} / \quad 2 \sigma \)
D. \( \rho_{o} / \sigma \)
Subject: Physics
What is the pressure \( 200 \mathrm{m} \) below the surface of the ocean if the sp. gravity of sea water is 1.03: [Atmospheric
pressure \( \left.=1.013 \times 10^{5} N / m^{2}\right] \)
A \( .21 .2 \times 10^{5} N / m^{2} \)
B . \( 20.4 \times 10^{5} N / m^{2} \)
C \( .40 \times 10^{4} N / m^{2} \)
D . \( 21.2 \times 10^{6} N / m^{2} \)
Subject: Maths
\( \ln \) a \( \triangle A B C \) in which \( A C=5 \mathrm{cm} \) and
\( \angle B A C=60^{\circ} \) and \( B C-A B=1.2 \mathrm{cm} \)
The, \( A B \) is
A . 3.18
в. 4.32
\( c .5 .12 \)
D. None of these
Subject: Maths
In January 1990 the world's population
was 5.3 billion. Assuming a growth rate
of 2 percent per year, the world's
population, in billions, for \( t \) years after
1990 can be modeled by the equation \( P=5.3(1.02)^{t} . \) With the help of the
model, calculate the growth in
population from January 1995 to
January 1996
A .106,000,000
B . 114,700,000
c. 117,000,000
D. 445,600,000
E . 562,700,000
Subject: Physics
Assertion
A number 2.746 rounded off to three
significant figures is \( 2.75, \) while the number 2.743 would be 2.74
Reason
In rounding off the uncertain digits, the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5 and is left unchanged if the latter is less than 5
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 balls of mass \( m_{1} \) and \( m_{2} \) where
\( m_{2}=0.5 m_{1}, \) undergo head on collision
as shown in figure.
If \( \boldsymbol{v}_{3}=\mathbf{0 . 5} \boldsymbol{v}_{1} \) value of \( \boldsymbol{v}_{4} \) is
fter collision
A \( \cdot v_{4}=v_{1}+v_{2} \)
B \( \cdot v_{4}=v_{1}+2 v_{2} \)
\( \mathbf{c} \cdot v_{4}=2 v_{1}+v_{2} \)
\( \mathbf{D} \cdot v_{4}=2 v_{1}+3 v_{2} \)
Subject: Chemistry
What will be the volume of the air that
will be expelled from a vessel of
\( 300 \mathrm{cm}^{3} \) when it is heated from \( 27^{\circ} \mathrm{C} \) to
\( 37^{\circ} \mathrm{C} \) at the constant pressure will be :
A \( \cdot 310 \mathrm{cm}^{3} \)
В. \( 290 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 10 \mathrm{cm}^{3} \)
D. \( 37 \mathrm{cm}^{3} \)
Subject: Physics
A bar magnet \( 20 \mathrm{cm} \) in length is placed with its south pole towards geographic north. The neutral points are situated at a distance of \( 40 \mathrm{cm} \) from centre of the
magnet. If horizontal component of earth's field \( 3.2 \times 10^{-5} T, \) then pole
strength of magnet is :
\( A \cdot 5 \mathrm{Am} \)
B. 10 Am
c. \( 45 \mathrm{Am} \)
D. 20 Am
Subject: Chemistry
Identify the incorrect statement
A. The \( S-S-S \) bond angles in the \( S_{8} \) and \( S_{6} \) rings are
the same
B. Rhombic and monoclinic sulphur have \( S_{8} \) molecules
\( \mathrm{C} \cdot S_{2} \) is paramagnetic like oxygen
D. \( S_{8} \) ring has a crown shape
Subject: Physics
An oil drop has a charge \( -9.6 \times 10^{-19} C \)
and mass \( 1.6 \times 10^{-15} \) gm. When
allowed to fall, due to air resistance
force it attains a constant velocity. Then if a uniform electric field is to be
applied vertically to make the oil drop ascend up with the same constant speed, which of the following are correct. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{2}\right) \) (Assume that the
magnitude of resistance force is same in both the cases)
This question has multiple correct options
A. The electric field is directed upward
B. The electric field is directed downward
c. The intensity of electric field is \( \frac{1}{3} \times 10^{2} N C^{-} \)
D. The intensity of electric field is \( \frac{1}{6} \times 10^{5} \mathrm{NC}^{-1} \)
Subject: Physics
The de Broglie wavelength of an electron
in a metal at \( 27^{\circ} \mathrm{C} \) is \( \left(\text {Given } \boldsymbol{m}_{e}=\right. \)
\( \mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, \boldsymbol{k}_{\boldsymbol{B}}=\mathbf{1 . 3 8} \times \)
\( \left.10^{-23} J K^{-1}\right) \)
A \( \cdot 6.2 \times 10^{-9} \mathrm{m} \)
В. \( 6.2 \times 10^{-10} \mathrm{m} \)
\( \mathbf{c} \cdot 6.2 \times 10^{-8} m \)
D. \( 6.2 \times 10^{-7} m \)
Subject: Physics
Assertion
Statement 1: When static friction acts,
there is no loss of mechanical energy.
Reason
Statement 2: When kinetic friction acts
between two bodies, there is loss of
mechanical energy.
A. Both Statements1 and 2 are true and Statement 2 is the correct explanation of Statement 1
B. Both Statements 1 and 2 are true, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is true but Statement 2 is false
D. Statement 1 is false but Statement 2 is true
Subject: Physics
A car with a vertical windsheld moves in
a rain storm at a speed of \( 40 \mathrm{km} / \mathrm{hr} \) The rain drops fall vertically with constant speed of \( 20 m / s . \) The angle at
which rain drops strike the windsheild
is
A. \( \tan ^{-1} \frac{5}{9} \)
в. \( \tan ^{-1} \frac{9}{5} \)
c. \( \quad \) tan \( ^{-1} \frac{3}{2} \)
D. \( \tan ^{-1} \frac{2}{3} \)
Subject: Biology
Which one of the following statements in regard to the excretion by the human kidneys is correct?
A. Ascending limb of loop of Henle is impermeable to electrolytes.
B. Descending limb of Loop of Henle is impermeable to water
c. Distal convoluted tubule is incapable of reabsorbing \( H C O_{3}^{-} \)
D. Nearly 99 per cent of the glomerular filtrate is reabsorbed by the renal tubules
Subject: Biology
Dinitrophenol (DNP) allows hydrogen ions to leak across a membrane which
can harm the \( H^{+} \) gradient. Select the
correct statement.
A. It would permit a greater growth rate, since the cell would no longer have to spend energy pumping \( H^{+} \) across the membrane
B. It would permit a greater growth rate, because the equalization of \( H^{+} \) on both sides of a membrane would help the cell cope with an acidic environment.
c. If the cell was a neuron, it would have no impact, because the charge difference on the surface of the neuron membrane is based on \( N a^{+} \) and \( K^{+}, \) not on
\( H^{+} \)
D. The cell would lose the bulk of its energy production because of DNP's interference with chemiosmosis
E. It would slow the growth rate slightly, but the cell would compensate by maintaining the function of proton pumps
Subject: Physics
Four positive charges \( (2 \sqrt{2}-1) Q \) are
arranged at the four corner of a square. Another charge q is placed at the centre of the square. Resulting force acting on each corner charge is zero if q is :
A \( \cdot \frac{-7 Q}{4} \)
в. \( \frac{-4 Q}{7} \)
\( c \cdot-Q \)
D. \( -(\sqrt{2}+1) Q \)
Subject: Physics
A thin circular ring of area \( A \) is held
perpendicular to a uniform magnetic
field of induction \( B \). A small cut is
made in the ring and a galvanometer is connected across the ends such that
the total resistance of the circuit is \( \boldsymbol{R} \)
When the ring suddenly squeezed to
zero area, the charge flowing through the galvanometer is :
A \( \cdot \frac{B R}{A} \)
\( \mathbf{B} \cdot(A B) / R \)
c. \( A B R \)
D \cdot \( \left(E^{2} A\right) / R^{2} \)
E . none
Subject: Chemistry
A primary amine \( \{\mathrm{B} \) ), on treatment with
a solution of \( A u C l_{3} \) in conc. \( H C l \) yields
a compound whose formula would be?
\( \mathbf{A} \cdot(B H)^{+} \cdot A u C l_{4}^{-} \)
B \( \cdot\left(B H_{2}\right)^{+} \cdot A u C l_{4}^{-2} \)
\( \mathbf{c} \cdot(B H)^{+} \cdot H A u C l_{4} \)
D. \( B . A u C l_{4} \)
Subject: Physics
Assertion
Statement 1:The current density \( \bar{J} \) at any point in ohmic resistor is in direction of electric field \( \bar{E} \) at that point.
Reason
Statement \( 2: A \) point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
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
For the given reaction the equilibrium expression
\( \mathbf{2} \boldsymbol{A}_{(\boldsymbol{g})}+\boldsymbol{B}_{(\boldsymbol{g})} \Leftrightarrow \mathbf{3} \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{D}_{(\boldsymbol{g})} \)
\( \mathbf{A} \cdot[A]^{2}[B][D] \)
В. \( \frac{[C]^{3}[D]}{\left.[A]^{2}[] B\right]} \)
c. \( \frac{[2 C][D]}{[2 A][B]} \)
D. \( \frac{[D]}{[A]^{2}[B]} \)
E \( \cdot \frac{[A]^{2}[B]}{[C]^{3}[D]} \)
Subject: Physics
Q Type your question
the surface of Mars it is \( 4.0 m s^{-2} . A 60 \)
kg passenger goes from the Earth to the
Mars in a spaceship moving with a constant velocity. Neglect all other
objects in the sky. Which part of figure
best represents the weight (net gravitational force) of the passenger as
a function of time.??
\( A \)
B. B
\( c \cdot c \)
\( D \)
Subject: Physics
An electric tea kettle has two electric
heating coils. When one of the coil is switched on the tea begins to boil in 6 minutes. When the other is switched on
the boiling begins in 8 minutes If both the coils are now arranged in series and switched on, boiling starts in
A . \( 24 / 7 \) minutes
B. 12 minutes
c. 14 minutes
D. 4 minutes
Subject: Chemistry
Given are two figures of Daniell cell(X) and (Y). Study the figures and mark the incorrect statement from the following.
A . In fig( \( (x) \) ) electrons flow from \( Z n \) rod to \( C u \) rod hence current flows from \( C u \) to \( Z n\left(E_{\text {ext}}<1.1 \mathrm{V}\right) \)
B. In fig (Y), electrons flow from \( C u \) to \( Z n \) and current flows from \( Z n \) to \( C u\left(E_{e x t}>1.1 \mathrm{V}\right) \)
\( c . \ln \operatorname{fig}(x), Z n \) dissolves at anode and \( C u \) deposits at cathode
D. In fig ( \( \gamma \) ), \( Z n \) is deposited at \( C u \) and \( C u \) is deposited at \( z_{n} \)
Subject: Physics
thin shells of uniformly distributed
positive charge \( Q \) and radius \( d \) are
located a distance \( 10 d \) from each other.
A positive point charge \( q \) is placed
inside one of the shells at a distance
\( d / 2 \) from the center, on the line
connecting the centers of the two shells,
as show in the figure. What is the net
force on the charge \( q ? \)
A \( \cdot \frac{Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the left
B. \( \frac{Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the right
c. \( \frac{362 Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the left
D. \( \frac{360 Q q}{361 \pi \varepsilon_{0} d^{2}} \) to the right
Subject: Chemistry
Assertion
Rusting of iron is considered an
oxidation reaction
Reason
Rust is another name for iron oxide
which occurs when iron is exposed to
oxygen and moisture for a long period of
time. Overtime the oxygen combines with the metal at atomic level forming a compound called an oxide. Rust forms
when iron undergoes oxidation. The
main catalyst for the rusting process is
water.
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 specie(s) has/have a tetrahedral structure?
This question has multiple correct options
A. \( B_{2} H_{6} \) (around each boron atom)
в. \( B_{3} N_{3} H_{6} \)
\( \mathbf{c} \cdot B H_{4}^{-} \)
D. \( A l C l_{4} \)
Subject: Maths
At what point \( p(x, y) \) of the curve \( y= \) \( e^{-|x|} \) should a tangent be drawn so that
area of the triangle bounded by the
tangent and the co-ordinate axes be
greatest?
\( \mathbf{A} \cdot(\pm e, 1) \)
B \( \cdot\left(\pm 1, \frac{1}{e}\right) \)
\( ^{c} \cdot\left(1, \pm \frac{1}{e}\right) \)
D \( \cdot(\pm 1, e) \)
Subject: Physics
An electron in the hydrogen atom jumps from excited state \( n \) to the ground state. The wavelength so emitted illuminates
a photosensitive material having work function 2.75 eV. If the stopping
potential of the photoelectron is \( 10 \mathrm{V} \) then the value of \( n \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
Fill in the blanks:
(i) \( \boldsymbol{C a}_{3} \boldsymbol{P}_{2}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{3} \boldsymbol{C a} \boldsymbol{C l}_{2}+ \)
\( p \)
\( - \)
(ii) \( P_{4}+3 N a O H+3 H_{2} O \rightarrow \)
\( q_{--}+3 N a H_{2} P O_{2} \)
(iii) \( P H_{4} I+K O H \rightarrow K I+H_{2} O+ \)
p, \( q \) and \( r \) respectively are:
A. \( P H_{3}, H_{3} P O_{3}, P I_{3} \)
в. \( P H_{3}, P H_{3}, P H_{3} \)
c. \( P C l_{3}, H_{3} P O_{4}, P H_{3} \)
D. \( P C l_{5}, P H_{3}, P_{4} O_{6} \)
Subject: Maths
The family of curves passing through (0,0) and satisfying the differential equation \( \left.\frac{\boldsymbol{y}_{2}}{\boldsymbol{y}_{1}}=1 \text { (where }\left(\boldsymbol{y}_{n}=\frac{\boldsymbol{d}^{n} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{n}}\right)\right) \)
is
A. \( y=k \)
в. \( y=k x \)
c. \( y=k\left(e^{x}+1\right) \)
D. \( y=k\left(e^{x}-1\right) \)
Subject: Chemistry
Cerium \( (z=58) \) is an important member of the Lanthanides. Which of
the following statements about cerium is incorrect?
A. The +3 oxidation state of cerium is more stable than the +4 oxidation state
B. The common oxidation states of cerium are +3 and +4
c. Cerium (IV) acts as an oxidizing agent
D. The +4 oxidation state of cerium is not known in solutions
Subject: Chemistry
Which among the following sequences is correct about the bond energy of \( C- \) \( C, C=C \) and \( C \equiv C \) bonds?
A. \( C \equiv C>C=C>C-C \)
в. \( C \equiv C<C=C<C-C \)
c. \( C=C>C \equiv C>C-C \)
D. \( C \equiv C>C-C>C=C \)
\( C \)
Subject: Maths
A manufacturer has three machine
operators \( A, B \) and \( C . \) The first operator \( A \) produces \( 1 \% \) defective items,
whereas the other two operators \( B \) and
\( C \) produce \( 5 \% \) and \( 7 \% \) defective items
respectively. \( A \) is on the job for \( 50 \% \) of
the time, \( B \) is on the job for \( 30 \% \) of the
time and \( C \) is on the job for \( 20 \% \) of the
time. A defective item is produced, what is the probability that it was produced
by \( \boldsymbol{A} \) ?
Subject: Maths
A unit vector which make \( 45^{0} \) with
vector \( 2 i+2 j-k \) and angle of \( 60^{0} \) with
vector \( \boldsymbol{j}-\boldsymbol{k} \) is
A. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} k \)
в. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} j \)
c. \( \frac{1}{\sqrt{2}} i-\frac{1}{\sqrt{2}} j+\frac{1}{\sqrt{2}} j \)
D. none of the above
Subject: Maths
Dietician has to develop a special diet using two foods \( P \) and \( Q . \) Each packet (containing \( 30 g \) ) of food \( P \) contains 12
units of calcium, 4 units of iron, 6 units
of cholesterol and 6 units of vitamin \( A \)
while each packet of the same quality of food \( Q \) contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast
460 units of iron and almost 300 units
of cholesterol. How many packets of each food should be used to maximize
the amount of vitamin \( A \) in the diet?
What is the maximum amount of
vitamin A?
Subject: Physics
A gas has a molecular diameter of \( 0.1 \mathrm{m} \) It also has a mean free path of \( 2.25 \mathrm{m} \) What is its density?
A \( \cdot 10^{-3} \)
B . \( 10^{-2} \)
\( \mathbf{c} \cdot 10^{-4} \)
D. \( 10^{-5} \)
Subject: Chemistry
What mass of solid ammonium
carbonate \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C O O N} \boldsymbol{H}_{4}, \) when
vaporized at \( 273^{\circ} C, \) will have a volume
of 8.961 at \( 760 m m \) of pressure.
Assume that the solid completely
decomposes as
\( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C O O N} \boldsymbol{H}_{4}(\boldsymbol{s}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
A . \( 15.6 g \)
в. \( 5.2 g \)
c. \( 46.8 g \)
D. \( 7.8 g \)
Subject: Physics
Two charges \( q_{1}=12 \times 10^{-9} \mathrm{C} \) and \( q_{2}= \)
\( -12 \times 10^{-9} C \) are placed \( 10 c m \) apart. The
potential at a point \( 6 \mathrm{cm} \) from \( q_{1} \) on the
line joining the two charges is :
A. 3500 Volt
B. 900 Volt
c. \( 1800 V \) olt
D. -900 Volt
Subject: Physics
An object placed at a distance of \( 16 \mathrm{cm} \)
from a convex lens produces an image
of magnification \( \boldsymbol{m}(\boldsymbol{m}>\mathbf{1}) . \) If the
object is moved towards the lens by
\( 8 c m \) then again an image of magnification \( m \) is obtained. Find the numerical value of focal length of the
lens.
Subject: Maths
\( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\ldots+n \)
terms \( = \)
A. \( \frac{n(n+3)}{4} \)
в. \( \frac{n(n+3)}{5} \)
c. \( \frac{n(n+2)}{3} \)
D. \( \frac{n(n+5)}{6} \)
Subject: Maths
Suppose \( A \) is a matrix such that \( A^{2}= \)
\( \boldsymbol{A} \) and \( (\boldsymbol{I}+\boldsymbol{A})^{10}=\boldsymbol{I}+\boldsymbol{k} \boldsymbol{A}, \) find \( \boldsymbol{k} \)
Subject: Physics
On doping germanium with donor atoms of density \( 10^{17} \mathrm{cm}^{-3} \) its conductivity in \( m h o / c m \) will be
\( \left[\text { Given: } \mu_{e}=3800 \mathrm{cm}^{2} / V-s \text { and } n_{i}=\right. \)
\( \left.2.5 \times 10^{13} c m^{-3}\right] \)
A . 30.4
B. 60.8
c. 91.2
D. 121.6
Subject: Chemistry
The standard molar heat of formation
of ethane, \( C O_{2} \) and water are
respectively -21.1,-94.1 and -68.3 kcal. The standard molar heat of
combustion of ethane will be :
\( \mathbf{A} \cdot-372 \) kcal
B . 162 kcal
c. -240 kcal
D. 183.5 kcal
Subject: Biology
When we say a nephron is the structural and functional unit of the kidneys, we mean that
(P) The kidney is made up of many nephrons.
(Q) The filtration of blood that occurs in the kidneys is because of what the nephrons do.
(R) Urea formation occurs in the
nephrons.
A. Only P and Q
B. Only Q and R
c. only \( \mathrm{P} \) and \( \mathrm{R} \)
D. P, Q and R