Calculus MCQ Questions for IAT_NEST

Practice Questions

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Q1SingleMarks: 4.00Negative: -1.00

For the displayed piecewise function with exponential branch for x>0 and (1-cos2x)/x² for x<0, find f(0)=a for continuity.

A. 1B. 2C. 0D. 3

Q2SingleMarks: 4.00Negative: -1.00

For f(x)=sinx+1/sinx on (0,π), which statement is true?

A. Local minimum at π/2B. Local maximum at π/3C. Local minimum at π/6D. Local maximum at π/4

Q3SingleMarks: 4.00Negative: -1.00

If real polynomial p satisfies integral from 0 to 1 of p(t)dt=0, what is always true?

A. No roots in [0,1]B. All roots lie in [0,1]C. Exactly one root in [0,1]D. At least one root in [0,1]

Q4SingleMarks: 4.00Negative: -1.00

g=1 on [-1,1] and 0 otherwise; f(x)=lim(h→0)[1/(2h)]∫(x-h to x+h)g(y)dy. Find f(1).

A. 2-JanB. -1C. 1D. 0