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

SECTION–I
(Mathematics)

Question 1:

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) 22
• (2) 46
• (3) 24
• (4) 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

140 divided by 210 is:

• (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) \( 2x^2 - \frac{5}{x^3} + 3 \)

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

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

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 \(\alpha\), \(\beta\), and \(\gamma\) 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) \(\frac{3}{2}\)

The pair of linear equations \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) has a unique solution, then

• (1) \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
• (2) \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
• (3) \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
• (4) \(\frac{a_1}{a_2} = \frac{b_1}{b_2}\)

Nimra went to a bank to withdraw ₹2,000. She asked the cashier to give her ₹50 and ₹100 notes only and she got 30 notes in all. How many notes of ₹50 and ₹100 respectively did she receive?

• (1) 20, 10
• (2) 15, 15
• (3) 10, 20
• (4) None of these

If 2 is a root of the equation \(x^2 - px + q = 0\) and \(p^2 = 4q\), then the other root is

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

The ratio of the sum and product of the roots of the quadratic equation \(7x^2 - 12x + 18 = 0\) is

• (1) 7:12
• (2) 7:18
• (3) 3:2
• (4) 2:3

If the area of a rectangle is 112 m² and its length is 6 m more than the breadth, then the breadth of the rectangle is

• (1) 8 m
• (2) 14 m
• (3) 10 m
• (4) 12 m

Find the 10th term of the arithmetic progression 5, 1, -3, -7, ....

• (1) 31
• (2) -31
• (3) 30
• (4) -30

The sum of the first 10 terms of the arithmetic progression 34, 32, 30, .... is

• (1) 200
• (2) 225
• (3) 250
• (4) 275

The 12th term of the geometric progression (G.P.) \(2, 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, ...\) is

• (1) \(\frac{1}{2^9}\)
• (2) \(\frac{1}{2^8}\)
• (3) \(\frac{1}{2^{11}}\)
• (4) \(\frac{1}{2^{10}}\)

Which of the following is a geometric progression?

• (1) \(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, ...\)
• (2) \(-2, -4, -12, ...\)
• (3) \(3, 4, 6, 12, ...\)
• (4) \(x, 1, x^2, ...\)

The coordinates of the point \(P\) which is equidistant from the three vertices of the triangle \(\Delta OAB\) as shown in the figure is

• (1) \((x, y)\)
• (2) \((y, x)\)
• (3) \(\left(\frac{x}{2}, \frac{y}{2}\right)\)
• (4) \(\left(\frac{y}{2}, \frac{x}{2}\right)\)

In what ratio Y-axis divides the line segment joining the points \(P(-4, 2)\) and \(Q(8, 3)\)?

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

If the centroid of a triangle formed by the points \((a,b)\), \((b,c)\), and \((c,a)\) is at the origin, then \(a^3 + b^3 + c^3\) is

• (1) \(abc\)
• (2) 0
• (3) \(a + b + c\)
• (4) \(3abc\)

If the points \((1,2)\), \((-1,k)\), and \((2,3)\) are collinear, then the value of \(k\) is

• (1) 0
• (2) -1
• (3) 1
• (4) 2

If the slope of the line joining the points \((4,2)\) and \((3,-k)\) is -2, then the value of \(k\) is

• (1) -3
• (2) 4
• (3) 3
• (4) -4

In the following figure, if \(DE \parallel BC\), then \(x = \)

• (1) \(\sqrt{3}\)
• (2) \(\sqrt{7}\)
• (3) \(\sqrt{6}\)
• (4) \(\sqrt{5}\)

\(\triangle ABC \sim \triangle DEF\), the area of \(\triangle ABC = 9 \, cm^2\) and the area of \(\triangle DEF = 16 \, cm^2\). If \(BC = 2 \, cm\), then \(EF =\)

• (1) 2.8 cm
• (2) 4.2 cm
• (3) 2.5 cm
• (4) 4.1 cm

In \(\triangle ABC\), \(DE \parallel BC\), \(AD/DB = 3/5\) and \(AC = 5.6 \, cm\), then \(AE =?\)

• (1) 3 cm
• (2) 5 cm
• (3) 2:1
• (4) 7 cm

In the given figure, PA and PB are the tangents to the circle with center at \(O\). If \(\angle APB = 36^\circ\), then \(\angle AOB = \)

• (1) \(72^\circ\)
• (2) \(134^\circ\)
• (3) \(144^\circ\)
• (4) \(154^\circ\)

The area of the shaded region in the given figure is

• (1) \(4\pi \, sq. units\)
• (2) \(16 - 4\pi \, sq. units\)
• (3) \(16 - \pi \, sq. units\)
• (4) None of these

In the given figure, the radius of each outer circle is \(a\), then the radius of the inner circle is

• (1) \( \sqrt{2} + 1 \)
• (2) \(a(\sqrt{2} + 1)\)
• (3) \( \sqrt{2} - 1 \)
• (4) \(a(\sqrt{2} - 1)\)

If the length, breadth, and height of a cuboid are 8 cm, 3 cm, and 4 cm respectively, then the total surface area of the cuboid is

• (1) 48 cm²
• (2) 72 cm²
• (3) 136 cm²
• (4) 108 cm²

If the volume of a cylinder is 500 m³ and the area of its base is 25 m², then its height (in m) is

• (1) 20
• (2) 15
• (3) 50
• (4) 30

If \(\sec \theta + \tan \theta = k\), then \(\sec \theta - \tan \theta = ?\)

• (1) \(k\)
• (2) \(\frac{1}{k}\)
• (3) \(k^2\)
• (4) \(\frac{1}{k^2}\)

If \(\sin \alpha + \sin \beta + \sin \gamma = 3\), then \(\cos \alpha + \cos \beta + \cos \gamma = ?\)

• (1) 0
• (2) 1
• (3) 2
• (4) 3

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) \(30^\circ\)
• (2) \(45^\circ\)
• (3) \(15^\circ\)
• (4) \(60^\circ\)

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

• (1) 1
• (2) 2
• (3) 3
• (4) 4

If \(\sin^2 \theta + \cos^2 \theta = 6\), then \(\sin \theta + \cos \theta = ?\)

• (1) \(3\sqrt{2}\)
• (2) \(\sqrt{2}\)
• (3) \(4\)
• (4) \(\sqrt{6}\)

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) \(10(1 + \frac{\sqrt{3}}{2})\) m
• (4) 10 \(\left( 1 + \frac{\sqrt{2}}{2} \right)\) 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

SECTION–II
(Physics)

Question 51:

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) \(1 \, weber/meter\)
• (3) \(1 \, weber/meter^2\)
• (4) \(1 \, watt/meter^2\)

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) \(\sqrt{\frac{\Delta \Phi}{\Delta t}}\)
• (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

direction. It points towards

• (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 water

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

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 \(4/3\) 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 \(4/3\). 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

• (1) at infinity
• (2) at the centre of curvature
• (3) between the 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, inverted
• (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 a 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) \(H_2 O\)
• (2) CO₂
• (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) 4.8 \( \Omega \)
• (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

SECTION–III
(Chemistry)

Question 91:

What is the structural formula of simplest ketone?

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