KCET 2023 Mathematics Question Paper: Download Set C3 Question Paper with Answer Key PDF

Question 1:

Let f : R → R be defined by f(x) = 3x² − 5 and g : R → R by g(x) = 1/(x²+1) , then g(f(x)) is:

(A) (3x²-5)/(4+2x²-4)
(B) (3x²-5)/(9x⁴+30x²-2)
(C) (3x²-5)/(9x⁴-30x²+26)
(D) (3x²-5)/(6x+26)

Choose the correct answer from the options given below:

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

Question 2:

Let the relation R be defined in N by aRb if 3a + 2b = 27, then R is:

• (1) {(1, 12), (3, 9), (5, 6), (7, 3), (9,0)}
• (2) {(2, 1), (9, 3), (6, 5), (7, 3)}
• (3) {(1, 12), (3, 9), (5, 6), (7,3)}
• (4) {(0, 2), (1, 12), (3, 9), (5, 6), (7, 3)}

Question 3:

Let f(x) = sin(2x)+cos(2x) and g(x) = x²-1, then g(f(x)) is invertible in the domain:

• (1) x∈ [-π/2, π/2]
• (2) x ∈ [0, π/4]
• (3) x ∈ [-π/4, π/4]
• (4) x∈ [-π/8,π/8]

Question 4:

The contrapositive of the statement “If two lines do not intersect in the same plane then they are parallel" is:

• (1) If two lines are not parallel, then they do not intersect in the same plane.
• (2) If two lines are parallel, then they do not intersect in the same plane.
• (3) If two lines are not parallel, then they intersect in the same plane.
• (4) If two lines are parallel, then they intersect in the same plane.

Question 5:

The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is:

• (1) 250000
• (2) 255000
• (3) 50000
• (4) 252500

Question 6:

Let f : R → R and g : [0,∞) → R be defined by f(x) = x² and g(x) = √x. Which one of the following is not true?

• (1) (g∘f)(2) = 2
• (2) (g∘f)(-2) = 2
• (3) (g∘f)(4) = 2
• (4) (g∘f)(-4) = 4

Question 7:

If A and B are two matrices such that AB = B and BA = A, then A² + B² = (A + B)² – 2AB is:

• (1) AB
• (2) 2BA
• (3) A + B
• (4) 2AB

Question 8:

If A = [[2, -k], [2, 3-k]] is a singular matrix, then the value of 5k – k² is equal to:

• (1) -4
• (2) 6
• (3) 4
• (4) -6

Question 9:

The area of a triangle with vertices (-3,0), (3,0), (0,1) is 9 sq. units, the value of k is:

• (1) 9
• (2) -9
• (3) 3
• (4) -3

Question 10:

If A = [[1, a, a²], [1, b, b²], [1, c, c²]] and Δ1 = [[a, a, a²], [a, b, b²], [a, c, c²]], then:

• (1) Δ1 = 4
• (2) Δ1 = 3A
• (3) Δ1 = 3A
• (4) Δ1 = 3A

Question 11:

If sin⁻¹(2a/(1+a²)) + cos⁻¹((1-a²)/(1+a²)) = tan⁻¹(2x/(1-x²)), where a, x ∈ (0,1), then the value of x is:

• (1) 2a/(1+a²)
• (2) 2a/(1-a²)
• (3) 0
• (4) a/2

Question 12:

The value of cot⁻¹((√(1-sinx) + √(1+sinx))/(√(1-sinx) - √(1+sinx))) , where x ∈ (0, π/2) is:

• (1) π/4 - x/2
• (2) x/2
• (3) x/4
• (4) π

Question 13:

If x[[3, 2], [2, 1]] + y[[-1, 1], [-1, 5]] = [[15, 5], [15, 5]], then the values of x and y are:

• (1) x = −4, y = 3
• (2) x = 4, y = -3
• (3) x = 4, y = 3
• (4) x = −4, y = −3

Question 14:

If the function is y = f(x) = (x+2)/(x+2), then the point of discontinuity of the composite function y = f(f(x)) is:

• (1) 5/2
• (2) -5/2
• (3) -2
• (4) 2

Question 15:

If y = a sin x + b cos x, then y² + (dy/dx)² is:

• (1) function of x and y
• (2) constant
• (3) function of x
• (4) function of y

Question 16:

If f(x) = 1 + nx + (n(n-1)/2)x² + ... + xⁿ, then f'(1) is:

• (1) 2n - 1
• (2) 2n - 2
• (3) n * n!
• (4) nxⁿ⁻¹

Question 17:

If A = [[1, -tan(α/2)], [tan(α/2), 1]] and AB = I, then B is:

• (1) cos²(α/2)
• (2) sin²(α/2)
• (3) cos²(α/2) * A
• (4) cos²(α/2)

Question 18:

If u = sin⁻¹(2x/(1+x²)) and v = tan⁻¹(2x/(1-x²)), then du/dv is:

• (1) 1
• (2) 1/2
• (3) 2
• (4) x

Question 19:

The function f(x) = cot x is discontinuous on every point of the set:

• (1) {x = (2n + 1)π/2, n ∈ Z}
• (2) {x = nπ/2, n ∈ Z}
• (3) {x = nπ, n ∈ Z}
• (4) {x = 2nπ, n ∈ Z}

Question 20:

A particle moves along the curve x²/16 + y²/4 = 1. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is:

• (1) III or IV
• (2) II or III
• (3) I or III
• (4) II or IV

Question 21:

An enemy fighter jet is flying along the curve given by y = x² + 2. A soldier is placed at (3,2) and wants to shoot down the jet when it is nearest to him. Then the nearest distance is:

• (1) 2 units
• (2) √5 units
• (3) √3 units
• (4) √6 units

Question 22:

Evaluate the integral ∫₂⁸ (5√(10-x))/(5√x + 5√(10-x)) dx:

• (1) 4
• (2) 3
• (3) 5
• (4) 6

Question 23:

Evaluate the integral ∫ √(cosec x - sin x) dx:

• (1) 2 sin x + C
• (2) (sin x)/2 + C
• (3) cos x + C
• (4) √sin x + C

Question 24:

If f(x) and g(x) are two functions with g(x) = x − 3 and f(g(x)) = 8, then f(x) is:

• (1) x - 3
• (2) x + 3
• (3) x² - 3
• (4) x + 3

Question 25:

A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing when the radius is 5.2 cm is:

• (1) 5.05π cm²/sec
• (2) 5.2π cm²/sec
• (3) 5.2π cm²/sec
• (4) 27.4π cm²/sec

Question 26:

The distance s in meters travelled by a particle in t seconds is given by s = 2t³ – 3t⁴. The acceleration when the particle comes to rest is:

• (1) 12 m/sec²
• (2) 18 m/sec²
• (3) 3 m/sec²
• (4) 10 m/sec²

Question 27:

Evaluate the integral: ∫ (x tan x) / (sec x - csc x) dx

• (1) π/8
• (2) π/4
• (3) π/2
• (4) π²/4

Question 28:

Evaluate the integral ∫ √(5 - 2x + x²) dx:

(A) ^(x-1)/₂√5 - 2x + x² + 2 log |x − 1| + √5 – 2x + x² + C
(B) ^(x-1)/₂√5 – 2x + x² + 2log |x + 1| + √5 – 2x + x² + C
(C) ¹/₂√5 – 2x + x² + 4log |x + 1| + √5 – 2x + x² + C
(D) ¹/₂√5+ 2x + x² + 2 log |x-1| + √5 + 2x + x² + C

Question 29:

Evaluate the integral: ∫ ¹/_{(1+3 sin²x + 8 cos² x)} dx

• (1) 1/6 tan⁻¹(2 tan x) + C
• (2) 6 tan⁻¹(2tanx/3) + C
• (3) 1/3 (2 tan x + C)
• (4) tan⁻¹(2 tan x) + C

Question 30:

Evaluate the integral: ∫₋₂⁰ (x³ + 3x² + 3x + 3) cos(x + 1) dx

• (1) 4
• (2) 1
• (3) 0
• (4) 3

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KCET 2023 Paper Analysis May 20

KCET 2023 paper analysis May 20 is available here. Candidates can check KCET 2023 paper analysis by clicking on the link provided below.

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