Mathematics Questions
Found 4 practice questions from various admission tests.
1. What is the derivative of sin(x²)?
BUET Engineering Mock TestA. cos(x²)
B. 2x cos(x²)✓ Correct
C. -2x cos(x²)
D. 2x sin(x²)
Explanation: Using chain rule: d/dx(sin(u)) = cos(u) * du/dx. Here u = x², so du/dx = 2x. Answer is 2x cos(x²).
2. Evaluate the integral of 1/x dx from x=1 to x=e.
BUET Engineering Mock TestA. 0
B. 1✓ Correct
C. e
D. ln(e) - 1
Explanation: Integral of 1/x is ln|x|. Evaluating from 1 to e gives ln(e) - ln(1) = 1 - 0 = 1.
3. What is the sum of the first 10 terms of an arithmetic progression with a=2 and d=3?
BUET Engineering Mock TestA. 155✓ Correct
B. 165
C. 175
D. 185
Explanation: S_n = n/2 * (2a + (n-1)d). S_10 = 10/2 * (2*2 + 9*3) = 5 * (4 + 27) = 5 * 31 = 155.
4. What is the value of lim(x→0) (sin x)/x?
DU A-Unit (Science) MockA. 0
B. 1✓ Correct
C. Infinity
D. Undefined
Explanation: It is a standard trigonometric limit.