AP POLYCET 2023 Question Paper: Download Set C Question Paper with Answer Key PDF

Question 16:

If one card is drawn at random from a well-shuffled deck of 52 playing cards, then the probability of getting a non-face card is:

• (1) \( 3 \)
• (2) \( 10 \)
• (3) \( 13 \)
• (4) \( 4 \)

A lot consists of 144 ball pens of which 20 are defective and the others are good. Rafai will buy a pen if it is good but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is:

• (1) \( \frac{5}{36} \)
• (2) \( \frac{20}{36} \)
• (3) \( \frac{31}{144} \)
• (4) \( \frac{36}{144} \)

A bag contains 3 red balls and 5 black balls. If a ball is drawn at random from the bag, then the probability of getting a red ball is:

• (1) \( \frac{1}{3} \)
• (2) \( \frac{3}{8} \)
• (3) \( \frac{5}{8} \)
• (4) \( \frac{3}{5} \)

If the mean of the following frequency distribution is 15, then the value of \( y \) is:

• (1) \( 8 \)
• (2) \( 10 \)
• (3) \( 12 \)
• (4) \( 9 \)

If the difference between mode and mean of a data is \(k\) times the difference between the median and mean, then the value of \(k\) is:

• (1) 2
• (2) 3
• (3) Cannot be determined
• (4) None of these

The median of the first 10 prime numbers is:

• (1) 11
• (2) 12
• (3) 13
• (4) 14

For the given data with 50 observations, the 'less than ogive' and the 'greater than ogive' intersect at the point (15.5, 20). The median of the data is:

• (1) 15.5
• (2) 20
• (3) 15
• (4) 14.5

The modal class for the following frequency distribution is: \[ \begin{array}{|c|c|} \hline x (Class Interval) & Frequency (f)

• (1) \( 10 - 20 \)
• (2) \( 20 - 30 \)
• (3) \( 50 - 60 \)
• (4) \( 30 - 40 \)

After how many decimal places, the decimal expansion of the rational number \[ \frac{23}{2^2 \times 5^2} \]
will terminate?

• (1) 1
• (2) 2
• (3) 3
• (4) 4

The sum of the exponents of the prime factors in the prime factorization of 156 is:

• (1) 2
• (2) 3
• (3) 4
• (4) 6

For any natural number \( n \), \( n^9 \) cannot end with which of the following digits?

• (1) 1
• (2) 2
• (3) 3
• (4) None of these

If the LCM of 12 and 42 is \( 10m + 4 \), then the value of \( m \) is:

• (1) 1
• (2) 5
• (3) 4
• (4) 8

The value of \( \frac{1}{\log_{60} 60} + \frac{1}{\log_{60} 60} \) is:

• (1) 2
• (2) 1
• (3) 0
• (4) 60

Which of the following collections is not a set?

• (1) The collection of natural numbers between 2 and 20
• (2) The collection of numbers which satisfy the equation \( x^2 - 5x + 6 = 0 \)
• (3) The collection of prime numbers between 1 and 100
• (4) The collection of all brilliant students in a class

If \( P = \{3m : m \in \mathbb{N}\} \) and \( Q = \{3m : m \in \mathbb{N}\} \) are two sets, then

• (1) \( P \subset Q \)
• (2) \( Q \subset P \)
• (3) \( P = Q \)
• (4) \( P \cup Q = N \)

If \( A \) and \( B \) are disjoint sets and \( n(A) = 4 \), \( n(A \cup B) = 7 \), then the value of \( n(B) \) is:

• (1) 3
• (2) 4
• (3) 5
• (4) 7

If the sum and product of the zeroes of a quadratic polynomial are 3 and 10, respectively, then the polynomial is:

• (1) \( x^2 - 3x - 10 \)
• (2) \( x^2 - 3x + 10 \)
• (3) \( x^2 + 3x - 10 \)
• (4) \( x^2 + 3x + 10 \)

If \( x = 2 \) is a factor of the polynomial \( x^3 - 6x^2 + ax - 8 \), then the value of \( a \) is:

• (1) 10
• (2) 12
• (3) 14
• (4) 18

If \( \alpha, \beta, \gamma \) are the zeroes of the cubic polynomial \( 2x^3 - x^2 - 13x + 6 \), the value of \( \alpha \beta \gamma \) is:

• (1) \( \frac{1}{2} \)
• (2) \( -3 \)
• (3) \( 13 \)
• (4) \( 2 \)

The number of zeroes of the polynomial shown in the graph is:

• (1) 0
• (2) 1
• (3) 2
• (4) None of these

The pair of linear equations \( x + 2y = 5 \) and \( 3x + 12y = 10 \) has:

• (1) no solution
• (2) two solutions
• (3) unique solution
• (4) infinitely many solutions

In a competitive examination, 1 mark is awarded for each correct answer, and \( \frac{1}{2} \) mark is deducted for each wrong answer. If a student answered 120 questions and got 90 marks, then the number of questions that the student answered correctly is:

• (1) 90
• (2) 100
• (3) 110
• (4) None of these

Which of the following is not a quadratic equation?

• (1) \( x^3 - x^2 = 0 \)
• (2) \( (x - 1)^2 - 3(x - 2) = 0 \)
• (3) \( (x + 2)^2 - 3x - 3 = 0 \)
• (4) \( (x - 2)(x - 1)(x - 3) = 0 \)

If one root of the quadratic equation \( ax^2 + bx + c = 0 \) is \( \alpha \), the other root is:

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

If the sum and product of the roots of the quadratic equation \( kx^2 + 6x + k = 0 \) are equal, then the value of \( k \) is:

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

If the numbers \( n - 3, 4n - 2, 5n + 1 \) are in arithmetic progression, then the value of \( n \) is:

• (1) 2
• (2) 3
• (3) 4
• (4) None of these

In an arithmetic progression, the 25th term is 70 more than the 15th term, then the common difference is:

• (1) 5
• (2) 6
• (3) 7
• (4) 8

Which term of the geometric progression \( 2, 2, \sqrt{2}, 4, \ldots \) is 128?

• (1) 11th
• (2) 12th
• (3) 13th
• (4) 14th

If the geometric progressions \( 162, 54, 18, \ldots \) and \( \frac{2}{81}, \frac{27}{9}, \ldots \) have their \( n \)-th term equal, then the value of \( n \) is:

• (1) 3
• (2) 4
• (3) 5
• (4) 6

The points \( A(-5,0), B(5,0), C(0,4) \) are the vertices of which triangle?

• (1) A right-angled triangle
• (2) An equilateral triangle
• (3) An isosceles triangle
• (4) A scalene triangle

The X-axis divides the line joining the points \( A(2, -3) \) and \( B(5, 6) \) in the ratio:

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

If four vertices of a parallelogram are \( (-3, -1), (a, b), (3, 1) \), and \( (4, 3) \), then the ratio of \( a \) and \( b \) is:

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

If the centroid of the triangle formed by the points \( (3, -5), (-7, 4) \) and \( (10, -4) \) is the point \( (k, -1) \), then the value of \( k \) is:

• (1) 2
• (2) 2.5
• (3) 3
• (4) 4

If \( AM \) and \( PN \) are the altitudes of two similar triangles \( \triangle ABC \) and \( \triangle PQR \), and \( \frac{AB}{PQ} = \frac{4}{9} \), then \( \frac{AM}{PN} = \frac{16}{81} \), then the value of \( k \) is:

• (1) 3
• (2) 4
• (3) 2
• (4) 5

SECTION II : PHYSICS

Question 51:

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

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

Question 52:

If \(i_1\) and \(i_2\) are the angle of incidence and angle of emergence due to a prism respectively, then at the angle of minimum deviation

• (1) \(i_1 < i_2\)
• (2) \(i_1 = i_2\)
• (3) \(i_1 > i_2\)
• (4) None of these

The minimum focal length of the eye-lens of a healthy human being is

• (1) 25 cm
• (2) 2.5 cm
• (3) 25.0 cm
• (4) 1 cm

Volt per ampere is called

• (1) watt
• (2) ohm
• (3) coulomb
• (4) joule

The device which maintains a constant potential difference between its ends is called

• (1) battery
• (2) multimeter
• (3) ammeter
• (4) electric bulb

Two resistors of 0.4 \(\Omega\) and 0.6 \(\Omega\) are connected in parallel combination. The equivalent resistance is:

• (1) 1 \(\Omega\)
• (2) 0.5 \(\Omega\)
• (3) 1.2 \(\Omega\)
• (4) 0.24 \(\Omega\)

The junction law proposed by Kirchhoff is based on:

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

The materials which have a large number of free electrons and offer low resistance are called:

• (1) semiconductors
• (2) conductors
• (3) insulators
• (4) None of these

A fuse is made up of:

• (1) thin wire of high melting point
• (2) thin wire of low melting point
• (3) thick wire of high melting point
• (4) thick wire of low melting point

If the specific resistance of a wire of length 2 m and area of cross-section 1 mm\(^2\) is \( 10^{-2} \, \Omega \, m \), then calculate the resistance:

• (1) \( 2 \, \Omega \)
• (2) \( 2 \times 10^{-2} \, \Omega \)
• (3) \( 2 \, \Omega \)
• (4) \( 2 \times 10^{2} \, \Omega \)

An evidence for the motion of charge in the atmosphere is provided by:

• (1) rainbow
• (2) mirage
• (3) thunder
• (4) lightening

The electric energy (in kWh) consumed in operating a bulb of 60 W for 10 hours a day is:

• (1) 6
• (2) 2
• (3) 36
• (4) 12

The scientific demonstration of H.C. Oersted is related to the study of:

• (1) electric discharge through air
• (2) relationship between voltage and current
• (3) magnetic effect of current
• (4) refraction of light

Pick the correct answer from the following two statements:

(a) Within a bar magnet, magnetic field lines travel from south pole to north pole.

(b) Outside a bar magnet, magnetic field lines travel from north pole to south pole.

• (1) Both (a) and (b) are true
• (2) Both (a) and (b) are false
• (3) Only (a) is true
• (4) Only (b) is true

Weber is the S.I. unit of:

• (1) magnetic pole strength
• (2) magnetic moment
• (3) magnetic flux
• (4) magnetic flux density

The magnetic force acting on a straight wire of length \( l \) carrying a current \( I \) is placed perpendicular to the uniform magnetic field \( B \) is:

• (1) \( I B l \)
• (2) \( I B / l \)
• (3) \( I B l^2 \)
• (4) \( \sqrt{I B l} \)