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