Keam Maths Mocktest part 1

KEAM Math Mock Test

Question 1:

Let \( A = \{1, 2, 3\} \). How many subsets does \( A \) have?

• A. 6
• B. 7
• C. 8
• D. 9
• E. 10

Question 2:

Let \( f(x) = x^2 \) be a function from \( \mathbb{R} \) to \( \mathbb{R} \). What is the value of \( f(3) \)?

• A. 3
• B. 6
• C. 9
• D. 12
• E. 15

Question 3:

What is the value of \( \binom{5}{2} \)?

• A. 5
• B. 10
• C. 15
• D. 20
• E. 25

Question 4:

If \( A = \{1, 2, 3\} \) and \( B = \{2, 3, 4\} \), what is \( A \cup B \)?

• A. \(\{1, 2\}\)
• B. \(\{1, 2, 3\}\)
• C. \(\{1, 2, 3, 4\}\)
• D. \(\{2, 3\}\)
• E. \(\{2, 3, 4\}\)

Question 5:

Let \( f(x) = x^2 \) and \( g(x) = 2x \). Find \( (f \circ g)(x) \).

• A. \( 2x^2 \)
• B. \( 4x^2 \)
• C. \( x^2 + 2x \)
• D. \( x^4 \)
• E. \( 4x \)

Question 6:

Which of the following is a binary operation on the set of real numbers \( \mathbb{R} \)?

• A. Addition
• B. Subtraction
• C. Multiplication
• D. Division
• E. All of the above

Question 7:

If \( f: A \rightarrow B \) and \( g: B \rightarrow C \), what is the domain of \( g \circ f \)?

• A. A
• B. B
• C. C
• D. A U B
• E. B U C

Question 8:

What is the value of \( \log_2(8) \)?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Question 9:

Let \( A = \{1, 2, 3, 4\} \). Find the number of reflexive relations on \( A \).

• A. 16
• B. 64
• C. 256
• D. 1024
• E. 2048

Question 10:

If \( A = \{1, 2, 3\} \) and \( B = \{4, 5, 6\} \), what is \( A \cap B \)?

• A. \(\{1, 4\}\)
• B. \(\{2, 5\}\)
• C. \(\{3, 6\}\)
• D. \(\{1, 2, 3, 4, 5, 6\}\)
• E. \(\emptyset\)

Question 11:

Find the inverse of the function \( f(x) = 2x + 3 \).

• A. \( f^{-1}(x) = \frac{x - 3}{2} \)
• B. \( f^{-1}(x) = 2x - 3 \)
• C. \( f^{-1}(x) = \frac{x + 3}{2} \)
• D. \( f^{-1}(x) = \frac{2x + 3}{2} \)
• E. \( f^{-1}(x) = \frac{3x + 2}{2} \)

Question 12:

What is the range of the function \( f(x) = x^2 \)?

• A. \( \mathbb{R} \)
• B. \( \mathbb{R}^+ \)
• C. \( [0, \infty) \)
• D. \( (-\infty, 0] \)
• E. \( [0, 1] \)

Question 13:

If \( f(x) = x + 1 \) and \( g(x) = 2x \), find \( f(g(2)) \).

• A. 3
• B. 5
• C. 7
• D. 9
• E. 11

Question 14:

What is the power set of \( \{1, 2\} \)?

• A. \( \{ \{1\}, \{2\} \} \)
• B. \( \{ \{\}, \{1\}, \{2\} \} \)
• C. \( \{ \{\}, \{1\}, \{2\}, \{1, 2\} \} \)
• D. \( \{ \{1\}, \{2\}, \{1, 2\}, \{1, 2, 3\} \} \)
• E. None of these

Question 15:

If \( A = \{1, 2, 3\} \), find the number of elements in \( P(A) \) (power set of A).

• A. 3
• B. 6
• C. 8
• D. 9
• E. 10

Question 16:

Determine whether the function \( f(x) = x^2 + 2x + 1 \) is one-to-one.

• A. Yes
• B. No
• C. Cannot be determined
• D. Only for positive x
• E. None of the above

Question 17:

Let \( A = \{a, b\} \). Find the number of equivalence relations on \( A \).

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Question 18:

If \( A = \{1, 2, 3\} \) and \( B = \{4, 5, 6\} \), what is the Cartesian product \( A \times B \)?

• A. \(\{(1,4), (2,5), (3,6)\}\)
• B. \(\{(1,4), (1,5), (1,6), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6)\}\)
• C. \(\{(1,4), (2,4), (3,4), (1,5), (2,5), (3,5), (1,6), (2,6), (3,6)\}\)
• D. \(\{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}\)
• E. None of the above

Question 19:

Find the domain of the function \( f(x) = \frac{1}{x-2} \).

• A. \( \mathbb{R} \setminus \{2\} \)
• B. \( \mathbb{R}^+ \)
• C. \( \mathbb{R} \)
• D. \( (2, \infty) \)
• E. \( (-\infty, 2) \cup (2, \infty) \)

Question 20:

What is the image of 3 under the function \( f(x) = 2x + 1 \)?

• A. 5
• B. 6
• C. 7
• D. 8
• E. 9

Results

q1: "C", q2: "C", q3: "B", q4: "C", q5: "B", q6: "E", q7: "A", q8: "C", q9: "C", q10: "E", q11: "A", q12: "C", q13: "C", q14: "C", q15: "C", q16: "B", q17: "C", q18: "B", q19: "A", q20: "C"

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