AP POLYCET 2024 Question Paper: Download Set D Question Paper with Answer Key PDF

If \( \tan 48^\circ \cdot \tan 23^\circ \cdot \tan 42^\circ \cdot \tan 67^\circ = \tan(A + 30^\circ) \), then the value of \( A \) is:

• (1) 30°
• (2) 45°
• (3) 60°
• (4) 15°

If \( a \sin 45^\circ = b \csc 30^\circ \), then the value of \( \frac{a^4}{b^4} \) is:

• (1) 1
• (2) 2
• (3) 3
• (4) 2\(^3\)

If \( \sin^2 \theta + \csc^2 \theta = 6 \), then \( \sin \theta + \csc \theta = \dots \)

• (1) \( \sqrt{3} \)
• (2) \( \sqrt{2} \)
• (3) \( 2\sqrt{2} \)
• (4) \( \sqrt{5} \)

A tree is broken by wind, its upper part touches the ground at a point 10 meters from the foot of the tree and makes an angle of 45° with the ground. Then, what is the entire height of the tree?

• (1) 15 m
• (2) 20 m
• (3) \( 10(1 + \sqrt{2}) \) m
• (4) \( 10(1 + \sqrt{3}/2) \) m

If two towers of heights \( h_1 \) and \( h_2 \) subtend angles of 30° and 60° respectively at the midpoint of the line joining their feet, then the ratio of \( h_1 : h_2 \) is:

• (1) \( 2:1 \)
• (2) \( 1:2 \)
• (3) \( 3:1 \)
• (4) \( 1:3 \)

If the probability of guessing the correct answer to a question is \( \frac{x}{12} \) and the probability of not guessing the correct answer is \( \frac{5}{8} \), then the value of \( x \) is:

• (1) \( 4:5 \)
• (2) 4
• (3) \( 1:2 \)
• (4) 0.5

A box contains 24 balls of which \( x \) are red, \( 2x \) are white, and \( 3x \) are blue. A ball is selected at random. What is the probability that the selected ball is not red?

• (1) \( \frac{1}{6} \)
• (2) \( \frac{1}{2} \)
• (3) \( \frac{1}{3} \)
• (4) \( \frac{5}{6} \)

Two dice are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is more than 10?

• (1) \( \frac{1}{36} \)
• (2) \( \frac{1}{12} \)
• (3) \( \frac{1}{26} \)
• (4) \( \frac{1}{13} \)

2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from the remaining pack. What is the probability of getting a black card?

• (1) \( \frac{22}{52} \)
• (2) \( \frac{22}{46} \)
• (3) \( \frac{24}{52} \)
• (4) \( \frac{24}{46} \)

The average of the observations 10, 20, 65, 102, 108, 115 is:

• (1) 50
• (2) 70
• (3) 60
• (4) 40

If 35 is removed from the data \( 30, 34, 35, 36, 37, 38, 39, 40 \), then the median increases by:

• (1) 2
• (2) 1.5
• (3) 1
• (4) 0.5

The modal class of the following frequency distribution is:

• (1) 80-100
• (2) 0-20
• (3) 60-80
• (4) 40-60

If the mode and mean of a data are 24 and 60 respectively, then the median of the data is:

• (1) 49
• (2) 48
• (3) 47
• (4) 46

The upper limit of the median class of the following frequency distribution is:

• (1) 110
• (2) 90
• (3) 130
• (4) 70

\( \frac{140}{210} \) is a:

• (1) terminating decimal
• (2) non-terminating and repeating decimal
• (3) non-terminating and non-repeating decimal
• (4) None of the above

The remainder when the square of any prime number greater than 3 is divided by 6 is:

• (1) 1
• (2) 2
• (3) 3
• (4) 4

Which of the following statements is not correct?

• (1) The sum of a rational number and an irrational number is an irrational number.
• (2) The sum of two irrational numbers need not be an irrational number.
• (3) The product of a non-zero rational number and an irrational number is an irrational number.
• (4) The product of two irrational numbers is always an irrational number.

The HCF of 306 and 657 is:

• (1) 10
• (2) 8
• (3) 9
• (4) 7

The value of \( \log_2 32 \) is:

• (1) 2
• (2) 32
• (3) 5
• (4) 0

If \( A = \{1, 2, \{3, 4\}, 5\} \), then which of the following is incorrect?

• (1) \( \{3, 4\} \in A \)
• (2) \( \{3, 4\} \subset A \)
• (3) \( \{3, 4\} \subset A \)
• (4) None of these

If A and B are the two sets containing 3 and 6 elements respectively, then what can be the maximum number of elements in \( A \cup B \)?

• (1) 9
• (2) 10
• (3) 11
• (4) 12

The number of subsets of the set \( A = \{p, q\} \) is:

• (1) 2
• (2) 4
• (3) 3
• (4) 0

Which of the following is a polynomial?

• (1) \( x^2 - 6\sqrt{x} + 2 \)
• (2) \( \frac{5}{x^2 - 3x + 1} \)
• (3) \( 5x^2 - 3x + \sqrt{2} \)
• (4) \( 2x^2 - \frac{5}{x} + 3 \)

If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( f(x) = 6x^2 + x - 2 \), then the sum of the zeroes is:

• (1) \( \frac{1}{6} \)
• (2) \( -\frac{1}{6} \)
• (3) \( \frac{1}{3} \)
• (4) \( \frac{1}{2} \)

If the zeroes of the quadratic polynomial \( ax^2 + bx + c \) (where \( c \neq 0 \)) are equal, then:

• (1) \( c \) and \( a \) have opposite signs
• (2) \( c \) and \( a \) have the same signs
• (3) \( b^2 \neq 4ac \)
• (4) None of these

If \( \alpha, \beta, \gamma \) are the roots of \( 4x^3 - 6x^2 + 7x + 3 = 0 \), then the value of \( \alpha\beta + \beta\gamma + \gamma\alpha \) is:

• (1) \( -\frac{7}{4} \)
• (2) \( \frac{7}{4} \)
• (3) \( \frac{2}{3} \)
• (4) \( \frac{3}{2} \)

SECTION-II:PHYSICS

Question 51:

Formation of dew and fog is due to the process of:

• (1) melting
• (2) freezing
• (3) evaporation
• (4) condensation

40 g of water at 40°C is added to 10 g of water at 80°C. The final temperature of the mixture is:

• (1) 48°C
• (2) 40°C
• (3) 120°C
• (4) 64°C

A light ray bends away from normal when it travels from:

• (1) air to water
• (2) water to air
• (3) water to glass
• (4) air to glass

If \( v_1 \) and \( v_2 \) are the speeds of light in the two media of refractive indices \( n_1 \) and \( n_2 \) respectively, then:

• (1) \( \frac{v_1}{v_2} = \frac{n_1}{n_2} \)
• (2) \( \frac{v_1}{v_2} = \frac{n_2}{n_1} \)
• (3) \( \frac{v_1}{v_2} = \frac{n_1^2}{n_2^2} \)
• (4) \( \frac{v_1}{v_2} = \frac{n_2^2}{n_1^2} \)

The speed of light in vacuum is \( c \). The speed of light in a medium of refractive index \( \frac{4}{3} \) is:

• (1) \( \frac{c}{3} \)
• (2) \( \frac{c}{4} \)
• (3) \( \frac{4c}{3} \)
• (4) \( \frac{3c}{4} \)

The stars appear twinkling. The principle involved in it is:

• (1) refraction
• (2) reflection
• (3) total internal reflection
• (4) dispersion

A rectangular tank of depth 4 m is full of water of refractive index \( \frac{4}{3} \). When viewed from the top, the bottom of the tank is seen at a depth of:

• (1) 3 m
• (2) 2 m
• (3) 1.33 m
• (4) 1 m

A convex lens gives a virtual image when the object is placed on the principal axis at:

• (1) at infinity
• (2) at the centre of curvature
• (3) between focal point and optic centre
• (4) between the focal point and centre of curvature

Irrespective of the position of the object on the principal axis, a concave lens always forms an image of nature:

• (1) real, invert
• (2) real, erect
• (3) virtual, erect
• (4) Does not form any image

The lens which is bounded by one-curved surface is:

• (1) biconvex
• (2) biconcave
• (3) plano-concave
• (4) concavo-convex

If 25 cm each is the object and image distances due to convex lens, then its focal length is:

• (1) 50 cm
• (2) 25 cm
• (3) 15 cm
• (4) 12.5 cm

The angle between paraxial rays and principal axis is:

• (1) 0°
• (2) 45°
• (3) 90°
• (4) 83°

Splitting of white light into VIBGYOR colours is called:

• (1) scattering
• (2) dispersion
• (3) total internal reflection
• (4) refraction

The light which has the maximum angle of deviation is:

• (1) red
• (2) yellow
• (3) violet
• (4) green

Blue colour of the sky is due to the scattering of light by the atmospheric molecules of:

• (1) \( H_2O \)
• (2) \( CO_2 \)
• (3) \( H_2 \)
• (4) \( N_2 \) and \( O_2 \)

The power of a lens of focal length 20 cm is:

• (1) 5 D
• (2) 0.2 D
• (3) 1 D
• (4) 2 D

In hypermetropia defect, the image is formed:

• (1) beyond the retina
• (2) before the retina
• (3) on the retina
• (4) Does not form an image

For a normal human-eye, 2.5 cm is the distance between:

• (1) eye-lens and cornea
• (2) eye-lens and retina
• (3) retina and cornea
• (4) retina and object

In old age, the value of least distance of distinct vision shifts to:

• (1) larger value
• (2) smaller value
• (3) Does not change
• (4) None of these

Electric power is the product of current and:

• (1) resistance
• (2) charge
• (3) velocity
• (4) potential difference

Three resistors each of 4 \(\Omega\), 0.4 \(\Omega\), and 0.04 \(\Omega\) are connected in series combination. Their equivalent resistance is:

• (1) 4 \(\Omega\)
• (2) 4.44 \(\Omega\)
• (3) 4 \(\Omega\)
• (4) 0.44 \(\Omega\)

Pick the correct answer from the following two statements:

• (a) Ohm's law is applicable to semiconductors.
• (b) Ohm's law is applicable to metallic conductors.
• (1) Only (a) is true
• (2) Only (b) is true
• (3) Both (a) and (b) are true
• (4) Both (a) and (b) are false

6 watt \(\times\) second =

• (1) 6 volt
• (2) 6 ohm
• (3) 6 joule
• (4) 6 coulomb

The relationship between current and voltage is established by the scientist:

• (1) Faraday
• (2) Oersted
• (3) Kirchhoff
• (4) Ohm

The electrical energy (in kWh) consumed in operating a bulb of 40 W for 5 hours a day in a month of 30 days is

• (1) 12
• (2) 6
• (3) 3
• (4) 1.5

Which of the following is not a measuring function of a multimeter?

• (1) Charge
• (2) Current
• (3) Voltage
• (4) Resistance

If \( R \) is the resistance of a conductor of length \( l \), then:

• (1) \( R \propto \frac{1}{l} \)
• (2) \( R \propto l \)
• (3) \( R \propto \sqrt{l} \)
• (4) \( R \) is independent of \( l \)

Two currents 3 mA and 5 mA are flowing towards the junction in a circuit and three currents 1 mA, 1.5 mA, and \( x \) are flowing away. The value of \( x \) (in mA) is:

• (1) 8
• (2) 10.5
• (3) 2.5
• (4) 5.5

1 tesla =

• (1) \( 1 \, weber \)
• (2) \( \frac{1 \, weber}{metre} \)
• (3) \( \frac{1 \, weber}{metre^2} \)
• (4) \( \frac{1 \, watt}{metre^2} \)

The phenomenon of electromagnetic induction involves the process of

• (1) charging a body
• (2) heating a coil
• (3) producing induced current in a coil
• (4) preventing damages due to overload

If \( \Delta \Phi \) and \( \Delta t \) are the change in magnetic flux and time respectively, then the induced EMF is:

• (1) \( \frac{\Delta \Phi}{\Delta t} \)
• (2) \( \frac{\Delta \Phi}{\Delta t} \)
• (3) \( \Delta \Phi \cdot \Delta t \)
• (4) \( \frac{\Delta t}{\Delta \Phi} \)

A freely suspended needle of a magnetic compass comes to rest along the geographic.

• (1) \( North-east direction \)
• (2) \( East-west direction \)
• (3) \( South-east direction \)
• (4) \( North-south direction \)

An increase in magnetic flux through a coil of 100 turns in 0.1 s is 0.001 Wb. The maximum induced EMF generated in the coil is:

• (1) \( 1 \, V \)
• (2) \( 10 \, V \)
• (3) \( 0.1 \, V \)
• (4) \( 100 \, V \)

The magnetic force acting on a moving charge in a magnetic field is the product of three quantities namely:

• (1) charge, speed, electromotive force
• (2) charge, magnetic flux, magnetic flux density
• (3) charge, speed, magnetic flux density
• (4) charge, speed, current

An auto driver started an auto rickshaw with the help of pulling a rope. The device used by him to convert mechanical energy into electrical energy is:

• (1) multimeter
• (2) transformer
• (3) dynamo
• (4) voltmeter

Faraday's laws of electromagnetic induction is a consequence of:

• (1) conservation of mass
• (2) conservation of linear momentum
• (3) conservation of angular momentum
• (4) conservation of energy

The C.G.S. unit of heat energy is:

• (1) joule
• (2) kelvin
• (3) dioptre
• (4) calorie

If \( 27^\circ C + x = 300 \, K \), then the value of \( x \) is:

• (1) 0 K
• (2) 327 K
• (3) 273 K
• (4) 300 K

The pair of substances which have the same value of specific heat is:

• (1) copper, aluminium
• (2) zinc, iron
• (3) ice, kerosene oil
• (4) water, ice

During the process of conversion from liquid to solid, the internal energy of the water:

• (1) increases
• (2) decreases
• (3) remains constant
• (4) None of these

SECTION-III:CHEMISTRY

Question 91:

1s² 2s² 2p⁶ 3s² 3p⁶ (2,8,8) configuration is related to

(1) P³⁻

(2) Cl⁻

(3) S²⁻

(4) All of these

Lithium, sodium, and ______ are Doberiener's triads.

• (1) S
• (2) Ca
• (3) Cl
• (4) K

IV A group elements are called:

• (1) carbon family
• (2) chalcogen family
• (3) nitrogen family
• (4) boron family

An element X belongs to 2nd group and 3rd period. What is its valency?

• (1) 1
• (2) 2
• (3) 3
• (4) 4

Valence Bond Theory was proposed by:

• (1) Lewis
• (2) Kossel
• (3) Pauling
• (4) Bohr

Identify the correct statement.

• (1) By losing electron chlorine becomes cation
• (2) By losing electron chlorine becomes anion
• (3) By gaining electron chlorine becomes cation
• (4) By gaining electron chlorine becomes anion

An element \( X^{27} \) forms ionic compound. What is the charge on \( X \) in ionic compound?

• (1) +1
• (2) +2
• (3) +3
• (4) +4

Linus Pauling proposed the concept of:

• (1) ionic bond
• (2) hydrogen bond
• (3) hybridization
• (4) covalent bond

Electronic configuration of O\(^{-2}\) ion is

• (1) \( 1s^2, 2s^2, 2p^4 \)
• (2) \( 1s^2, 2s^2, 2p^5 \)
• (3) \( 1s^2, 2s^2, 2p^6 \)
• (4) \( 1s^2, 2s^2, 2p^3 \)

The number of electrons gained by non-metallic element is equal to its

• (1) valency
• (2) group number
• (3) bond angle
• (4) All of these

Reactivity increasing order of the following metals will be

• (1) K, Na, Ca
• (2) K, Ca, Na
• (3) Ca, Na, K
• (4) Na, K, Ca

Poling process is used to

• (1) concentrate the ore
• (2) reduce the ore
• (3) heat the ore with \( O_2 \)
• (4) purify the crude metal

Corrosion of silver results in the formation of

• (1) silver chloride
• (2) pure silver
• (3) silver nitrate
• (4) silver sulphide

During corrosion, a metal will

• (1) be oxidised
• (2) lose electrons
• (3) be reduced
• (4) (1) and (2)

Replacing one hydrogen from \( NH_3 \) by alkyl group will result in the formation of

• (1) aldehyde
• (2) ketone
• (3) amine
• (4) ester

What is the structural formula of simplest ketone?

Ethene and ethyne differ in the

• (1) number of carbons
• (2) number of bonds
• (3) number of hydrogens
• (4) (2) and (3)

Identify the dimethyl ether.

Saturated hydrocarbons contain

• (1) at least one double bond
• (2) at least one triple bond
• (3) all single bonds
• (4) at least one ionic bond

Aliphatic hydrocarbons are

• (1) closed chain hydrocarbons
• (2) acyclic hydrocarbons
• (3) open chain hydrocarbons
• (4) (2) and (3)

Which one of the following can be used as acid-base indicator to detect acidic or basic nature of solution?

• (1) Turmeric solution
• (2) Litmus
• (3) (1) and (2)
• (4) None of these

If pH of rain water is less than ____, then it is called acid rain.

• (1) 5.6
• (2) 7.6
• (3) 6.6
• (4) 8.6

Tooth enamel is made up of

• (1) calcium sulphate
• (2) calcium chloride
• (3) calcium phosphate
• (4) magnesium sulphate

What do you observe on pouring potassium hydroxide on red and blue litmus papers?

• (1) Red litmus remains red and blue litmus turns to red
• (2) Red litmus turns to blue and blue litmus remains blue
• (3) Red litmus becomes colorless and blue litmus remains blue
• (4) Red litmus turns to blue and blue litmus turns to red

The maximum number of electrons in M shell is

• (1) 2
• (2) 12
• (3) 18
• (4) 24

Which of the following orbitals does not exist?

• (1) \( 2p^6 \)
• (2) \( 3s^1 \)
• (3) \( 4f^{12} \)
• (4) \( 2d^3 \)

Niels Bohr received Nobel Prize in

• (1) Chemistry
• (2) Physics
• (3) Biochemistry
• (4) Biophysics

The number of degenerate orbitals present in 4d subshell is

• (1) 8
• (2) 10
• (3) 4
• (4) 5

The number of electrons in the valence shell of an element is called its

• (1) Atomic number
• (2) Valency
• (3) Mass number
• (4) Atomic mass

Strong ionic bond is formed between \underline{\hspace{2cm and \underline{\hspace{2cm group elements.

• (1) I A and II A
• (2) II A and VIII A
• (3) I A and VII A
• (4) I A and VIII A