Continuity and Differentiability Test

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Continuity and Differentiability Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

If y = tan^-1 (2x/1 - x²) + cos^-1(1 - x²/ 1 + x²), then dy/dx =

A
1

B
0

C
2/(1 + x²)

D
4/(1 + x²)
Question 2
1 / -0

If y = ae^mx + be^-mx, then d²y/dx² =

A
m² y

B
- m² y

C
my

D
- my
Question 3
1 / -0

d / dx { cos^-1 (1 - x² / 1 + x²)} =

A
2 /(1 + x²)

B
- 2 /(1 + x²)

C
2 x / |x| (1 + x²) , x ≠ 0

D
none of these
Question 4
1 / -0

d/dx [sin^-1 {2x /(1 + x²)}] =

A
2 / 1 + x²

B
- 2 / 1 + x²

C
2 (1 - x²) / | 1 - x² | (1 + x² ) , x ≠ ± 1

D
none of these
Question 5
1 / -0

If y = sin^-1 (1 - √x / 1 + √x) + sec^-1 (1 + √x / 1 - √x) , then dy/dx (x ≠ 1) is

A
0

B
1

C
- 1

D
none of these
Question 6
1 / -0

The set of points where the function f (x) = |x -1|* e^x is differentiable is

A
R - {1}

B
R - {2}

C
R

D
none of these
Question 7
1 / -0

A function f(x) is differentiable at x = a if

A
only LHL exists

B
only RHL exists

C
both LHL and RHL exists

D
both LHL, RHL exists and equal
Question 8
1 / -0

Let f(x) be a polynomial function of secong degree. If f(1) = f(-1) and a₁ ,a₂ , a₃ are in AP then df(a₁ )/dx, df(a₂ )/dx, df(a₃ )/dx are in

A
AP

B
GP

C
HP

D
None of these
Question 9
1 / -0

Derivative of cos(x + y) is

A
-sin(x+y)

B
sin(x+y)

C
sin(x+y)/{1+ sin(x+y)}

D
-sin(x+y)/{1+ sin(x+y)}

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Re-Attempt Weekly Quiz Competition

Continuity and Differentiability Test - 2

Result

Continuity and Differentiability Test - 2

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Rank

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SHARING IS CARING

Question 1

1

0

2/(1 + x2)

4/(1 + x2)

Question 2

m2 y

- m2 y

my

- my

Question 3

2 /(1 + x2 )

- 2 /(1 + x2 )

2 x / |x| (1 + x2) , x ≠ 0

none of these

Question 4

2 / 1 + x2

- 2 / 1 + x2

2 (1 - x2) / | 1 - x2 | (1 + x2 ) , x ≠ ± 1

none of these

Question 5

0

1

- 1

none of these

Question 6

R - {1}

R - {2}

R

none of these

Question 7

only LHL exists

only RHL exists

both LHL and RHL exists

both LHL, RHL exists and equal

Question 8

AP

GP

HP

None of these

Question 9

-sin(x+y)

sin(x+y)

sin(x+y)/{1+ sin(x+y)}

-sin(x+y)/{1+ sin(x+y)}

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2/(1 + x²)

4/(1 + x²)

m² y

- m² y

2 /(1 + x²)

- 2 /(1 + x²)

2 x / |x| (1 + x²) , x ≠ 0

2 / 1 + x²

- 2 / 1 + x²

2 (1 - x²) / | 1 - x² | (1 + x² ) , x ≠ ± 1