Mathematics (Solved Paper 2024 – II) (51 to 100)

Total Questions: 50

21. Letz z = [y] and y = [x] - x where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?

Correct Answer: (a) -1
Solution:

22. If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?

Correct Answer: (a) 7
Solution:Given, f(x) = 4x + 1, g(x) = kx + 2

fog(x) = 4(kx+2) + 1 = 4kx + 9

gof(x) = k(4x + 1) + 2 = 4kx + k + 2

fog(x) = g of (x) ⇒ g = k + 2 ⇒ k = 7

23. What is the minimum value of the function

f(x) = log₁₀(x² + 2x + 11)?

Correct Answer: (b) 1
Solution:

24. Which one of the following is correct regarding

Correct Answer: (d) Limit does not exist
Solution:

25. What is the maximum value of the a cos x + b sin x + c?

Correct Answer: (b)
Solution:

26. If f(2x) = 4x²+ 1 then for how many real values of x will f (2x) be the GM of f (x) and f (4x) ?

Correct Answer: (c) One
Solution:

27. If f(x) = [x]² - 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions?

Correct Answer: (d) 30
Solution:

28. If f(x) = 9x - 8√x such that g(x) = f(x) - 1 then which one of the following is correct?

Correct Answer: (b) g(x) = 0 has only one real root which is an integer
Solution:

29. Find ?

Correct Answer: (b) 0
Solution:

30. Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of of f(1/2) ?

Correct Answer: (a) 1/4
Solution: