21. If logₓ256 = 8/5, then x =
Answer: 16
22. The direction cosines of the vector 3i – 4j + 5k are
Answer: 3/5, -4/5, 1/5
23. lim(x→1) (1 + log x – x)/(1 – 2x + x²) =
Answer: 1
24. If A = {1, 2}, B = {0, 1} then A x B =
Answer: {(1, 0), (1, 1), (2, 0), (2, 1)}
25. The 7th and 13th terms of an arithmetic sequence are 34 and 64, respectively. The 18th term is
Answer: 88
26. The equation of the straight line passing through (2, 4) and making equal intercepts on the axes is
Answer: 2x + y – 8 = 0
27. The maximum value of the function f(x) = 3 cos x – 4 sin x is
Answer: 5
28. A stone is thrown vertically upwards, and it reaches a height of x feet in t seconds given by x = 80t – 16t². At what time (in seconds) does the stone reach its maximum height?
Answer: 2
29. If log x / (b-c) = log y / (c-a) = log z / (a-b), then x^b+c * y^c+a * z^a+b =
Answer: 1
30. If the determinant of the matrix [ 1 2 -1; 1 x-2 1; x 1 1 ] is zero, then x =
Answer: 2
31. If f(x) = {sin πx, x ≠ 0; k, x = 0}, for f(x) to be continuous at x = 0, then k =
Answer: 5/π
32. The 7th term of an arithmetic progression is 40, then the sum of the first 13 terms is
Answer: 2080
33. The number of words that can be formed from the letters of the word ARTICLE in which vowels appear at the same positions is
Answer: 36
34. The inverse of the matrix [ 1 -2; 3 4 ] is
Answer: 1/10 [ 4 2; -3 1 ]
35. If |a x b| = 4 and |a.b| = 2, then |a|²|b|² =
Answer: 20
36. The conjugate of (2+i)² / (3+i) in the form a + ib is
Answer: 13/10 + i(-15/2)
37. If x = a(θ – sinθ), y = a(1 – cosθ), then y’ =
Answer: tan θ/2
38. The determinant of | 41 42 43; 44 45 46; 47 48 49 | is
Answer: 0
39. The value of tan⁻¹(1/2) + tan⁻¹(1/3) is
Answer: π/4
40. A railway compartment has 6 seats. The number of ways to seat 6 passengers on these seats is
Answer: 120