Mathematics (Solved Paper 2024 – II) (01 to 50)

Total Questions: 50

31. Consider the following numbers :

A. tan 22.5°

B. cot 22.5°

C. tan 22.5° - cot 22.5°

How many of the above are irrational numbers?

Correct Answer: (b) Only one
Solution:

32. what is x + y + z equal to?

Correct Answer: (b) 0
Solution:(b)

33. If p tan (θ - 30°) = q tan (θ + 120°) then what is (p + q)/(p - q) equal to?

Correct Answer: (d) 2cos 2θ
Solution:

34. Let P and Q be two non-void relations on a set A. Which of the following statements are correct?

A. P and Q are reflexive ⇒ P ∩ Q is reflexive.

B. P and Q are symmetric is symmetric. ⇒ P ∪ Q

C. P and Q are transitive ⇒ P ∩ Q is transitive.

Select the answer using the code given below.

Correct Answer: (d) A, B and C
Solution:(d)

35. If A and B are two non-empty sets having 10 elements in common, then how many elements do A × B and B × A have in common?

Correct Answer: (d) 100
Solution:

36. What is the remainder when 7ⁿ - 6n is divided by 36 for n = 100?

Correct Answer: (b) 1
Solution:

37. What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as circle and lines)?

Correct Answer: (c) 14
Solution:There are 4 lines, then the maximum number of intersection points are

4c₂= 6 And maximum number of intersection of circle with 4 lines are 4 × 2 = 8

Thus, the required intersection point = 6 + 8 = 14.

38. In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p² : q². Which one of the following is correct?

Correct Answer: (c) The common difference is equal to twice the first term
Solution:

39. What is the number of real roots of the equation (x-1)² + (x-3)² + (x-5)² = 0?

Correct Answer: (a) None
Solution:

40. In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?

Correct Answer: (a) 60
Solution:

Given, total student = 240

Since, 10 student failed in every subject.

Hence, Remaining total = 230

Now, According to question,

a + b + c + d + e + f + g = 230                    ...(i)

and b + c + d = 110                                       ...(ii)

and e + f + g = 60                                         ...(iii)

using equation (ii) and (iii) in equation (i), we get

⇒ a = 230 - (110 + 60) = 60