JEECUP 2024 Group A Polytechnic Question Paper Available: Download Solution PDF with Answer Key

SECTION-I
MATHEMATICS

Question 1:

The perimeter of an equilateral triangle whose area is \( 4\sqrt{3} \, cm^2 \) is equal to:

• (A) 20 cm
• (B) 10 cm
• (C) 15 cm
• (D) 12 cm

\(\tan 3A - \tan 2A \cdot \tan A\) is equal to:

• (A) \(\tan 3A - \tan 2A - \tan A\)
• (B) \(\tan 3A + \tan 2A + \tan A\)
• (C) \(\tan 3A \cdot \tan 2A - \tan A\)
• (D) None of these

The value of \( \sqrt[3]{72.9} \) is:

• (A) 5.625
• (B) None of these
• (C) 5.652
• (D) 5.265

If 7 is the mean of 5, 3, 0.5, 4.5, \( a \), 8.5, 9.5, then the value of \( a \) is:

• (A) 49
• (B) 18
• (C) 31
• (D) 12

The value of \( \sin \theta + \cos(90^\circ + \theta) + \sin(180^\circ - \theta) + \sin(180^\circ + \theta) \) is:

• (A) 0
• (B) -1
• (C) 1
• (D) \( \frac{1}{2} \)

The volume of a cuboid is \( x^3 - 7x + 6 \), then the longest side of the cuboid is:

• (A) None of these
• (B) \( x - 1 \)
• (C) \( x + 3 \)
• (D) \( x - 2 \)

If \( 5\sqrt{5} \times 5^3 \div 5^{-3/2} = 5^a \), then the value of \( a \) is:

• (A) 8
• (B) 5
• (C) 6
• (D) 4

The value of \( \frac{\sqrt{1 + \sin x}}{1 - \sin x} \) is:

• (A) \( \tan x - \sec x \)
• (B) \( \sec x - \tan x \)
• (C) \( \sec x \cdot \tan x \)
• (D) \( \sec x + \tan x \)

If \( 2^x = 5^{y} = 10^{-z} \), then the value of \( \left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right) \) is:

• (A) 3
• (B) 5
• (C) 0
• (D) -2

The volume of the cylinder is \( 448 \pi \, cm^3 \) and height 7 cm. Then its lateral surface area is:

• (A) 259 cm\(^2\)
• (B) 352 cm\(^2\)
• (C) 252 cm\(^2\)
• (D) None of these

The value of \( \tan 15^\circ \) is:

• (A) \( 2 - \sqrt{3} \)
• (B) \( \frac{2}{\sqrt{3}} \)
• (C) \( \frac{1}{2 \sqrt{3}} \)
• (D) \( 2 + \sqrt{3} \)

The value of \( \frac{\cos 20^\circ \cos 70^\circ - \sin 20^\circ}{\sin 70^\circ} \) is:

• (A) \( \infty \)
  %Option (B) None of these
• (C) 1
• (D) 0

Ravi can do \( \frac{3}{4} \) of a work in 12 days. In how many days Ravi can finish the \( \frac{1}{2} \) work?

• (A) 7 days
• (B) None of these
• (C) 8 days
• (D) 6 days

The L.C.M. of \( 12x^2 y^3 z^2 \) and \( 18x^4 y^3 z^3 \) is:

• (A) \( 21xy z \)
• (B) \( 36x^4 y^3 z^3 \)
• (C) \( 24x^4 y^2 z^2 \)
• (D) \( 32x^4 yz^3 \)

The vertices of a triangle are \( (4, 6), (2, -2) \), and \( (0, 2) \). Then the coordinates of its centroid must be:

• (A) \( (2, 3) \)
• (B) \( (1, 2) \)
• (C) \( (-2, 2) \)
• (D) \( (2, 2) \)

Use the following figure to find \( x^\circ \) and \( y^\circ \):

• (A) \( x = 50^\circ, y = 30^\circ \)
• (B) \( x = 30^\circ, y = 50^\circ \)
• (C) \( x = 50^\circ, y = 60^\circ \)
• (D) \( x = 55^\circ, y = 65^\circ \)

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is:

• (A) 1 : 6
• (B) 1 : 2
• (C) 1 : 4
• (D) 1 : 8

The compound interest on Rs. 24,000 compounded semi-annually for \( 1 \frac{1}{2} \) years at the rate of 10% per annum is:

• (A) Rs. 3,783
• (B) Rs. 3,774
• (C) Rs. 3,583
• (D) Rs. 3,780

The sum of two numbers is 11 and their product is 30, then the numbers are:

• (A) 8, 3
• (B) 7, 4
• (C) 6, 5
• (D) 9, 2

In figure \( \angle BAP = 80^\circ \) and \( \angle ABC = 30^\circ \), then \( \angle AQC \) will be:

• (A) 55°
• (B) 110°
• (C) 50°
• (D) 65°

Two straight lines \( 3x - 2y = 5 \) and \( 2x + ky + 7 = 0 \) are perpendicular to each other. The value of \( k \) is:

• (A) \( \frac{1}{3} \)
• (B) \( \frac{4}{3} \)
• (C) \( \frac{3}{2} \)
• (D) 3

A Verandah of area 90 m\(^2\) is around a room of length 15 m and breadth 12 m. The width of the verandah is:

• (A) 1.5 m
• (B) 2 m
• (C) 2.5 m
• (D) 1 m

If points \( (5, 5) \), \( (10, k) \), and \( (-5, 1) \) are collinear, then the value of \( k \) is:

• (A) 9
• (B) 6
• (C) 8
• (D) 7

The value of \( \log_5 \left( \frac{1}{125} \right) \) is:

• (A) 5
• (B) 3
• (C) -3
• (D) 0

In the given figure, the value of \( \angle DEC \) is:

• (A) 65°
• (B) 75°
• (C) 55°
• (D) 45°

The factor of \( a^4 b^4 - 16c^4 \) is:

• (A) \( (a^2 b^2 - 4c^2)(ab + 2c)(ab - 4c) \)
• (B) \( (a^2 b^2 - 4c^2)(ab + 2c)(ab + 4c) \)
• (C) \( (a^2 b^2 + 4c^2)(ab + 2c)^2 \)
• (D) \( (a^2 b^2 - 4c^2)(ab + 2c)^2 \)

The quadratic equation, whose roots are \( \frac{4 + \sqrt{7}}{2} \) and \( \frac{4 - \sqrt{7}}{2} \), is:

• (A) \( 4x^2 + 16x + 9 = 0 \)
• (B) \( 4x^2 - 16x - 9 = 0 \)
• (C) \( 4x^2 - 16x + 9 = 0 \)
• (D) \( 4x^2 + 16x - 9 = 0 \)

A train passes a telegraph post in 40 seconds moving at a rate of 36 km/h. Then the length of the train is:

• (A) 400 m
• (B) 395 m
• (C) 500 m
• (D) 450 m

If the side of the cube is 6 cm, then the diagonal of the cube is:

• (A) \( 3\sqrt{2} \, cm \)
• (B) \( 6\sqrt{3} \, cm \)
• (C) \( 6\sqrt{2} \, cm \)
• (D) \( 2\sqrt{3} \, cm \)

Angles of a triangle are in ratio 1 : 5 : 12, the biggest angle of this triangle is:

• (A) 60°
• (B) 120°
• (C) 90°
• (D) 45°

If \( \sin x + \sin^2 x = 1 \), then the value of \( \cos^2 x + \cos^4 x \) is:

• (A) 1
• (B) -1
• (C) 2
• (D) 0

The value of \( \log \frac{14}{15} - \log \frac{3}{25} - \log \frac{7}{9} \) is:

• (A) 2
• (B) 3
• (C) 0
• (D) 1

The solution of the equation \( y^{\frac{2}{3}} - 2y^{\frac{1}{3}} = 15 \) is:

• (A) 25, 27
• (B) 27, -125
• (C) 25, -27
• (D) 125, -27

If \( \tan(A + B) = \sqrt{3} \) and \( \cos(A - B) = \frac{\sqrt{3}}{2} \), the values of \( A \) and \( B \) are:

• (A) \( 40^\circ, 20^\circ \)
• (B) \( 15^\circ, 30^\circ \)
• (C) \( 45^\circ, 15^\circ \)
• (D) \( 60^\circ, 30^\circ \)

The HCF of two polynomials \( p(x) = 4x^2 (x^2 - 3x + 2) \) and \( q(x) = 12x(x - 2)(x^2 - 4) \) is \( 4x(x - 2) \). The LCM of these polynomials is:

• (A) \( 4x(x - 2) \)
• (B) \( 12x^2 (x^2 - 3x + 2) (x^2 + 4) \)
• (C) \( x^2(x^2 - 3x + 2)(x^2 - 4) \)
• (D) \( 12x^2 (x^2 - 3x + 2) (x^2 - 4) \)

The value of \( \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} \) is:

• (A) \( \sqrt{5}(2 + \sqrt{2}) \)
• (B) \( \sqrt{5}(5 + \sqrt{2}) \)
• (C) \( \sqrt{5}(1 + \sqrt{2}) \)
• (D) \( \sqrt{3}(3 + \sqrt{2}) \)

Find the equation of the line passing through the two points \( (3, 5) \) and \( (-4, 2) \):

• (A) \( 3x - 7y + 26 = 0 \)
• (B) \( 3x + 7y + 26 = 0 \)
• (C) \( 7x - 3y + 26 = 0 \)
• (D) \( 3x - 7y + 62 = 0 \)

The area of the circle whose circumference is equal to the perimeter of a square of side 11 cm is:

• (A) 134 cm\(^2\)
• (B) 124 cm\(^2\)
• (C) 144 cm\(^2\)
• (D) 154 cm\(^2\)

The perpendicular distance between two parallel lines \( 3x + 4y - 6 = 0 \) and \( 6x + 8y + 7 = 0 \) is equal to:

• (A) 19/5 unit
• (B) 10/19 unit
• (C) 19/2 unit
• (D) 19/10 unit

The length of sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. The area of the triangle is:

• (A) 764 cm\(^2\)
• (B) 864 cm\(^2\)
• (C) 664 cm\(^2\)
• (D) 684 cm\(^2\)

The earth makes a complete rotation about its axis in 24 hours. What angle will it turn in 3 hours 20 minutes?

• (A) None of these
• (B) 50°
• (C) 120°
• (D) 130°

If \( A = 4x + \frac{1}{x} \), then the value of \( A + \frac{1}{A} \) is:

• (A) \( \frac{1}{4x^3 + x} \)
• (B) \( 4x^2 + 1 \)
• (C) \( x \)
• (D) \( \frac{x}{4x^2 + 1} \)

The median of the following data 25, 34, 31, 23, 22, 26, 35, 29, 20, 32 is:

• (A) 22.5
• (B) 29.5
• (C) 30.5
• (D) 27.5

Find the value of the complementary angle of \( 75^\circ \):

• (A) \( 85^\circ \)
• (B) \( 15^\circ \)
• (C) \( 30^\circ \)
• (D) \( 45^\circ \)

If \( \tan \theta + \sin \theta = m \) and \( \tan \theta - \sin \theta = n \), then the value of \( m^2 - n^2 \) is:

• (A) \( \sqrt{mn} \)
• (B) \( 2\sqrt{mn} \)
• (C) \( 4mn \)
• (D) \( \sqrt{mn} \)

The value of \( \left( x - \frac{2}{x} \right) \left( x^2 + 2 + \frac{4}{x^2} \right) \) is equal to:

• (A) \( x^3 + 2x + \frac{4}{x} - 8 \)
• (B) \( x^3 - \frac{8}{x^3} \)
• (C) \( x^3 + \frac{8}{x^3} \)
• (D) \( x^3 - \frac{8}{x^2} \)

The value of \( x (\log y - \log z) \times y (\log z - \log x) \) is equal to:

• (A) 0
• (B) 3
• (C) 5
• (D) 1

A and B can do a piece of work in 72 days. B and C in 120 days and A and C in 90 days. In what time can A alone do it?

• (A) 110 days
• (B) 120 days
• (C) 60 days
• (D) 55 days

If \( \left( x + \frac{1}{x} \right) = \sqrt{3} \), then the value of \( \left( x^3 + \frac{1}{x^3} \right) \) will be:

• (A) \( 3(\sqrt{3} + 1) \)
• (B) \( \sqrt{3} \)
• (C) 0
• (D) \( 3(\sqrt{3} - 1) \)

If \( \sqrt{3}x - 2 = 2\sqrt{3} + 4 \), then the value of \( x \) is:

• (A) \( 1 + \sqrt{3} \)
• (B) \( 2(1 + \sqrt{3}) \)
• (C) \( 1 - \sqrt{3} \)
• (D) \( 2(1 - \sqrt{3}) \)

SECTION -II
PHYSICS

Question 51:

Two resistances combine in series order to provide 50 ohms resultant resistance, and when they combine in parallel order, they provide 8 ohms resultant resistance. Then the value of each resistance is:

• (A) 21 ohm and 29 ohm
• (B) 10 ohm and 40 ohm
• (C) 20 ohm and 30 ohm
• (D) 15 ohm and 35 ohm

A ball is released from the top of a tower of height \( h \) meters. It takes \( T \) seconds to reach the ground. What is the position of the ball above the ground in \( T/5 \) seconds?

• (A) \( 25 \, h m \)
• (B) \( \frac{h}{25} \, m \)
• (C) \( 24 \, h m \)
• (D) \( \frac{24h}{25} \, m \)

In an L-C-R circuit, 100 volt alternating voltage is applied between end points. In the circuit, inductive reactance is \( X_L = 20 \, \Omega \), capacitive reactance is \( X_C = 20 \, \Omega \), and resistance is \( R = 5 \, \Omega \). The impedance of the circuit will be:

• (A) 20 ohm
• (B) 5 ohm
• (C) 15 ohm
• (D) 45 ohm

The capacitance of a capacitor is \( 3 \, \mu F \). If \( 108 \, \mu C \) charge is available in it, then what will be the potential difference between the plates?

• (A) 324 volt
• (B) 224 volt
• (C) 36 volt
• (D) 24 volt

One proton enters in a magnetic field of \( 2500 \, N/Amp-m \) intensity with velocity of \( 4 \times 10^5 \, m/sec \) in parallel of the field. The force exerted on the proton will be:

• (A) 0 N
• (B) \( 4.8 \times 10^{-10} \, N \)
• (C) \( 0.48 \times 10^{-10} \, N \)
• (D) \( 4.8 \times 10^{-10} \, N \)

100 gm of water at \( 60^\circ C \) is added to 180 gm of water at \( 95^\circ C \). The resultant temperature of the mixture is:

• (A) \( 80^\circ C \)
• (B) \( 82.5^\circ C \)
• (C) \( 77.5^\circ C \)
• (D) \( 85^\circ C \)

Two unlike parallel forces of 2 N and 16 N act at the ends of a uniform rod of 21 cm length. The point where the resultant of these two forces acts at a distance of .............. from the greater force.

• (A) 4 cm
• (B) 3 cm
• (C) 2 cm
• (D) 1 cm

Magnetic flux of a 20-turn coil is reduced to zero from 0.3 weber in one second. Then the induced e.m.f between the terminals of the coil is:

• (A) 1.5 V
• (B) 6 V
• (C) 2.5 V
• (D) 3 V

The electric field strength at a point in an electric field is 30 N/C. Find the force experienced by a charge of 20 C at that point.

• (A) 600 N
• (B) 30 N
• (C) 20 N
• (D) 300 N

A particle is moving along a circular track of radius 1 m with a uniform speed. The ratio of the distance covered and the displacement in half revolution is:

• (A) 1 : 1
• (B) \( \pi : 1 \)
• (C) 2 : \( \pi \)
• (D) \( \pi : 2 \)

A car of mass 2000 kg is moving with a velocity of 18 km/h. Work done to stop this car is:

• (A) \( 2.5 \times 10^6 \) joules
• (B) \( 2.5 \times 10^5 \) joules
• (C) \( 2.5 \times 10^4 \) joules
• (D) \( 2.5 \times 10^3 \) joules

If the radius of Earth shrinks by 4% and mass of Earth unchanged, then the value of acceleration due to gravity will be changed by:

• (A) 16%
• (B) 8%
• (C) 2%
• (D) 4%

A spherical mirror and a thin spherical lens each have a focal length of \( -15 \, cm \). The nature of the mirror and lens will be:

• (A) Both concave
• (B) Mirror convex and lens concave
• (C) Mirror concave and lens convex
• (D) Both convex

A stone is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of \( 10 \, m/s^2 \), with what velocity and after what time will it strike the ground?

• (A) 20 m/s, 2 s
• (B) 10 m/s, 20 s
• (C) 10 m/s, 2 s
• (D) 20 m/s, 20 s

A sound wave has a frequency of 500 Hz and wavelength 80 cm. How long will it take to travel 1 km?

• (A) 2.5 seconds
• (B) 25 seconds
• (C) 25 minutes
• (D) 2.5 minutes

In a simple pendulum experiment, a student calculates the value of \( g = 9.92 \, m/s^2 \), but the standard value of \( g \) is \( 9.80 \, m/s^2 \). Then the percentage error in the calculation of \( g \) is:

• (A) 1.42%
• (B) 1.32%
• (C) 1.12%
• (D) 1.22%

A charge of 10 coulomb is brought from infinity to a point \( P \) near a charged body and in this process 200 joules of work is done. Electric potential at point \( P \) is:

• (A) 10 V
• (B) 100 V
• (C) 200 V
• (D) 20 V

Heat (in calorie) required to increase the temperature from \( 10^\circ C \) to \( 20^\circ C \) of 6 kg copper is the same as the heat (in calorie) required to increase the temperature from \( 20^\circ C \) to \( 100^\circ C \) of 3 kg lead. If the specific heat of copper is 0.09, then the specific heat of lead will be:

• (A) 0.033
• (B) 0.022
• (C) 0.044
• (D) 0.055

\( V_V, V_R, V_G \) are the velocities of violet, red, and green light respectively, in a glass prism. Which among the following is a correct relation?

• (A) \( V_V < V_R < V_G \)
• (B) \( V_V = V_R = V_G \)
• (C) \( V_V < V_G < V_R \)
• (D) \( V_V > V_R > V_G \)

The gravitational force between two masses kept at a certain distance is \( P \) Newton. The same two masses are now kept in water and the distance between them is the same. The gravitational force between these two masses in water is \( Q \) Newton. Then:

• (A) \( P > Q \)
• (B) None of these
• (C) \( P = Q \)
• (D) \( P < Q \)

100 joules of heat is produced each second in a 4 ohm resistance. Potential difference across the resistor is:

• (A) 40 V
• (B) 100 V
• (C) 20 V
• (D) 50 V

An object of 4.0 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?

• (A) +25 cm
• (B) +25.5 cm
• (C) -35.5 cm
• (D) -37.5 cm

An object is placed in front of a convex lens of focal length 12 cm. If the size of the real image formed is half the size of the object, then the distance of the object from the lens is:

• (A) 48 cm
• (B) 36 cm
• (C) 26 cm
• (D) 30 cm

A body weighs 75 gm in air, 51 gm when completely immersed in an unknown liquid and 67 gm when completely immersed in water. Find the density of the unknown liquid:

• (A) 4 gm/cm\(^3\)
• (B) 6 gm/cm\(^3\)
• (C) 8 gm/cm\(^3\)
• (D) 3 gm/cm\(^3\)

A wooden block of mass 6 kg is pulled across a rough surface by a 54 N force against a friction force \( F \). The acceleration of the block is \( 6 \, m/s^2 \). Then the value of friction force \( F \) is:

• (A) 36 N
• (B) 54 N
• (C) 18 N
• (D) 9 N

SECTION- III
CHEMISTRY

Question 76:

Electronic configuration of copper can be represented as:

• (A) \( [Ar] 4s^1 3d^{10} \)
• (B) \( [Ar] 4s^2 3d^9 \)
• (C) \( [Ar] 4s^2 3d^9 4p^1 \)
• (D) \( [Ar] 4s^2 3d^{10} 4p^1 \)

Which among the following pairs are not having the same number of total electrons?

• (A) \( Na^+ \) and \( Al^{3+} \)
• (B) \( O^{2-} \) and \( F^- \)
• (C) \( Mg^{2+} \) and Ar
• (D) \( P^{3-} \) and Ar

The half-life period of a radioactive element is 150 days. After 600 days, 1 gm of the element will be reduced to:

• (A) \( \frac{1}{32} \, gm \)
• (B) \( \frac{15}{16} \, gm \)
• (C) \( \frac{1}{8} \, gm \)
• (D) \( \frac{1}{16} \, gm \)

The number of molecules present in 2.8 g of nitrogen is:

• (A) \( 6.023 \times 10^{22} \)
• (B) \( 6.023 \times 10^{21} \)
• (C) \( 6.023 \times 10^{20} \)
• (D) \( 6.023 \times 10^{23} \)

The common name of 2-Butanone is:

• (A) Acetone
• (B) Butyraldehyde
• (C) Acetic anhydride
• (D) Ethyl Methyl Ketone

The IUPAC name of

• (A) 3-Methyl-1-Pentyne
• (B) 3-Methyl-4-Pentyne
• (C) 2-Ethyl-2-Propyne
• (D) 3-Methyl-5-Pentyne

Essential constituent of an amalgam is:

• (A) an alkali
• (B) Silver
• (C) Mercury
• (D) an alkali metal

Equivalent weight of a dibasic acid is 12. Its molecular weight is:

• (A) 6
• (B) 12
• (C) 24
• (D) 48

In the following reaction: \[ SO_2 + 2H_2S \rightarrow 3S + 2H_2O \]
Which of the following statements is correct?

• (A) Sulphur is reduced and oxygen is oxidised
• (B) Sulphur is both oxidised and reduced
• (C) Sulphur is oxidised and Hydrogen is reduced
• (D) Hydrogen is oxidised and Sulphur is reduced

Which of the following types of drugs reduces fever?

• (A) Analgesic
• (B) Antibiotic
• (C) Tranquilizers
• (D) Antipyretic

Hydrocarbon used for welding purposes is:

• (A) Ethene
• (B) Ethyne
• (C) Ethane
• (D) Benzene

An example of thermosetting plastic is:

• (A) Polyethylene
• (B) All of these
• (C) Bakelite
• (D) P.V.C.

Which of the following order of ionic radii is correctly represented?

• (A) \( H^- > H^+ > H \)
• (B) \( Na^+ > F^- > O^{2-} \)
• (C) \( F^- > O^{2-} > Na^+ \)
• (D) \( Al^{3+} < Mg^{2+} < N^{3-} \)

Amount of copper deposited on the cathode of an electrolytic cell containing copper sulphate solution by the passage of 2 amperes for 30 minutes (At. mass of Cu = 63.5):

• (A) 1.184 gm
• (B) 0.2214 gm
• (C) 2.214 gm
• (D) 0.1184 gm

Which catalyst is used in oxidizing \( NH_3 \) in Ostwald's process?

• (A) Pt
• (B) FeO
• (C) \( V_2O_5 \)
• (D) Molybdenum

Real gas behaves like an ideal gas at:

• (A) None of these
• (B) Low temperature
• (C) High temperature
• (D) High pressure

The rate of diffusion of a gas is \( r \) and its density is \( d \), then under similar conditions of pressure and temperature:

• (A) \( r \propto d \)
• (B) \( r \propto \sqrt{d} \)
• (C) \( r \propto \frac{1}{d} \)
• (D) \( r \propto \frac{1}{\sqrt{d}} \)

Among the following, which is an ionic hydride?

• (A) BH\(_3\)
• (B) PH\(_3\)
• (C) MgH\(_2\)
• (D) SiH\(_4\)

Detergents are the salt of:

• (A) Carboxylic acid and Sulphonic acids or alkyl hydrogen sulphates both
• (B) Carboxylic acid
• (C) Sulphonic acids or alkyl hydrogen sulphates
• (D) None of these

Hardness of water is due to the presence of:

• (A) Sodium and Potassium salt
• (B) Calcium and magnesium salt
• (C) Lead and copper salt
• (D) None of these

In which of the following compounds does the oxidation number of oxygen equal +2?

• (A) \( F_2O \)
• (B) \( Na_2O_2 \)
• (C) \( K_2O \)
• (D) \( O_3 \)

\( F_2C = CF_2 \) is a monomer of:

• (A) Nylon-6
• (B) Buna-S
• (C) Teflon
• (D) Glyptol

10.0 gm \( CaCO_3 \) on heating gave 5.6 gm of \( CaO \) and 4.4 gm of \( CO_2 \), given data support the law of:

• (A) Multiple proportion
• (B) Constant proportion
• (C) Law of conservation of mass
• (D) All of these

Cracking is a process used for change in:

• (A) Higher molecular weight alkane to lower molecular weight alkane
• (B) Ketones to aldehydes
• (C) Alkanes to aromatic hydrocarbons
• (D) Alcohols to aldehydes

An organic compound contains carbon = 38.71%, Hydrogen = 9.67% and Oxygen. The empirical formula of the compound would be:

• (A) \( CH_3O \)
• (B) \( CH_4O \)
• (C) \( CH_2O \)
• (D) \( CHO \)