Q1. If A is a square matrix of order 3 such that |A| = 5, then the value of |adj(2A)| is:
Correct Answer: Option A (| is:)
Explanation: Detailed explanation will be updated shortly.
ExamSpark CUET UG
Mock Test 10 Performance Solutions
Subject: Maths
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Q2. Let f(x) be a function defined as f(x) = {x² if x is rational; 1-x if x is irrational}. The value of f(f(√3 - 1)) is:
Correct Answer: Option A (4 - 2√3)
Explanation: Detailed explanation will be updated shortly.
Q3. The principal value of sin⁻¹(sin(7)) is:
Correct Answer: Option A (7)
Explanation: Detailed explanation will be updated shortly.
Q4. The integrating factor (I.F.) for the differential equation (1+y²)dx = (tan⁻¹y - x)dy is:
Correct Answer: Option A (e^(tan⁻¹x))
Explanation: Detailed explanation will be updated shortly.
Q5. A man, 2 meters tall, walks away from a 6-meter high lamppost at a speed of 3 m/s. The rate at which the tip of his shadow is moving away from the lamppost is:
Correct Answer: Option A (3 m/s)
Explanation: Detailed explanation will be updated shortly.
Q6. The value of the integral ∫ e^x * [ (x² + 1) / (x+1)² ] dx is:
Correct Answer: Option A (e^x * [ x / (x+1) ] + C)
Explanation: Detailed explanation will be updated shortly.
Q7. The area of the region lying between the curves |x| + |y| = 1 and x² + y² = 1/2 is:
Correct Answer: Option A (2 - π/2)
Explanation: Detailed explanation will be updated shortly.
Q8. The differential equation representing the family of circles that touch the y-axis at the origin is:
Correct Answer: Option A (x² + y² - 2xy(dy/dx) = 0)
Explanation: Detailed explanation will be updated shortly.
Q9. If a, b, c are three vectors such that |a|=1, |b|=2, |c|=3 and a+b+c=0, then the value of a·b + b·c + c·a is:
Correct Answer: Option A (7)
Explanation: Detailed explanation will be updated shortly.
Q10. The distance of the point P(1, 0, -2) from the point of intersection of the line (x-2)/3 = (y+1)/4 = (z-2)/12 and the plane x - y + z = 16 is:
Correct Answer: Option A (13)
Explanation: Detailed explanation will be updated shortly.
Q11. A random variable X has the following probability distribution: P(X=x) = k(x+1)² for x = 0, 1, 2. The value of P(X > 1) is:
Correct Answer: Option A (9/14)
Explanation: Detailed explanation will be updated shortly.
Q12. The corner points of the feasible region of an LPP are (0,10), (5,5), (15,20), and (0,25). For the objective function Z = px + qy, where p, q > 0, the condition on p and q so that the maximum of Z occurs at both (15,20) and (0,25) is:
Correct Answer: Option A (p = 3q)
Explanation: Detailed explanation will be updated shortly.
Q13. If ω is a non-real cube root of unity, then the matrix A = [[1, ω, ω²], [ω, ω², 1], [ω², 1, ω]] is:
Correct Answer: Option A (Invertible with |A| = 1)
Explanation: Detailed explanation will be updated shortly.
Q14. The function f(x) = x log(x) is strictly increasing in the interval:
Correct Answer: Option A ((0, 1/e))
Explanation: Detailed explanation will be updated shortly.
Q15. The sine of the angle between the line r = (i+2j-k) + λ(i-j+k) and the plane r · (2i-j+k) = 4 is:
Correct Answer: Option A (2√2 / 3)
Explanation: Detailed explanation will be updated shortly.
Q16. The value of tan[ (1/2) cos⁻¹(√5/3) ] is:
Correct Answer: Option A ((3 - √5) / 2)
Explanation: Detailed explanation will be updated shortly.
Q17. Two numbers are selected at random (without replacement) from the set {1, 2, 3, 4, 5, 6}. Let X denote the larger of the two numbers. The variance of X is:
Correct Answer: Option A (7/3)
Explanation: Detailed explanation will be updated shortly.
Q18. The area of the region bounded by the curve y = x|x|, the x-axis, and the lines x = -1 and x = 1 is:
Correct Answer: Option A (0)
Explanation: Detailed explanation will be updated shortly.
Q19. The equation of the plane passing through the point (1,1,1) and containing the line of intersection of the planes x+y+z-6=0 and 2x+3y+4z+5=0 is:
Correct Answer: Option A (20x + 23y + 26z - 69 = 0)
Explanation: Detailed explanation will be updated shortly.
Q20. If ∫ [ (x⁴ - 1) / (x² * √(x⁴+x²+1)) ] dx = f(x) + C, then f(x) is:
Correct Answer: Option A (√(x² + 1 + 1/x²))
Explanation: Detailed explanation will be updated shortly.