JEE MATHS UNIT 7
QUIZ NO 2
TOTAL QUESTIONS = 20
1. The value of lim (x → 0) (1 + x)^1/x is
A. 1
B. e
C. 0
D. infinity
2. The derivative of f(x) = x^2 + 2x is
A. 2x + 2
B. x^2 + 2
C. x + 1
D. 2x
3. The function f(x) = |x| is
A. continuous everywhere
B. not continuous at x = 0
C. differentiable everywhere
D. differentiable at x = 0
4. The limit of (1 - cos(x))/x^2 as x approaches 0 is
A. 1/2
B. 1
C. 0
D. infinity
5. The derivative of tan(x) is
A. sec^2(x)
B. cot(x)
C. sin^2(x)
D. -sec^2(x)
6. The value of lim (x → 0) x/sin(x) is
A. 0
B. 1
C. infinity
D. -1
7. The derivative of e^(2x) is
A. 2e^(2x)
B. e^(x)
C. 2e^(x)
D. e^(2x)
8. A function f(x) is said to be differentiable at x = a if
A. f'(a) exists
B. f(a) exists
C. left-hand limit equals right-hand limit
D. none of these
9. The limit of ln(1 + x)/x as x approaches 0 is
A. 0
B. 1
C. infinity
D. ln(x)
10. The derivative of sin(x)cos(x) is
A. cos^2(x)
B. sin^2(x)
C. cos(2x)
D. 0
11. The function f(x) = 1/x is
A. continuous everywhere except at x = 0
B. differentiable everywhere
C. not continuous
D. none of these
12. The value of lim (x → 0) (sin(2x)/x) is
A. 2
B. 1
C. 0
D. infinity
13. The derivative of ln(x^2) is
A. 1/x
B. 2/x
C. x/2
D. x
14. The limit of (x^3 - a^3)/(x - a) as x approaches a is
A. 3a^2
B. 3a
C. a^3
D. 0
15. The derivative of f(x) = x^2 + sin(x) is
A. 2x + cos(x)
B. x^2 + cos(x)
C. 2x - sin(x)
D. 2x + sin(x)
16. The limit of (tan(x) - sin(x))/x^3 as x approaches 0 is
A. 1/2
B. 1/3
C. 2/3
D. 0
17. If f(x) = e^x, then f'(x) is
A. e^x
B. ln(x)
C. 1/x
D. x
18. The derivative of cos^2(x) is
A. -2sin(x)cos(x)
B. 2sin(x)cos(x)
C. -sin^2(x)
D. cos^2(x)
19. The function f(x) = |x - 1| is
A. continuous but not differentiable at x = 1
B. differentiable at x = 1
C. not continuous at x = 1
D. none of these
20. The value of lim (x → 0) (1 - cos(2x))/x^2 is
A. 2
B. 1
C. 4
D. 0
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