#### Differential Calculus - Differentiability and Methods of Differentiation Model Question Paper

11th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:30:00 Hrs
Total Marks : 50
10 x 1 = 10
1. If $y={1\over a-z}$ ,then ${dz\over dy}$ is

(a)

$(a-z)^2$

(b)

-(z-a)2

(c)

(z+a)2

(d)

-(z+a)2

2. If y = mx + c and f(0) =$f '(0)=1$,then f(2) is

(a)

1

(b)

2

(c)

3

(d)

-3

3. ${d\over dx}(e^{x+5log \ x})$ is

(a)

exx4(x+5)

(b)

exx(x+5)

(c)

ex$+{5\over x}$

(d)

ex$-{5\over x}$

4. $x={1-t^2\over 1+t^2},y={2t\over 1+t^2}$ then ${dy\over dx}$is

(a)

$-{y\over x}$

(b)

${y\over x}$

(c)

$-{x\over y}$

(d)

${x\over y}$

5. The differential coefficient of log10 x with respect to logx10 is

(a)

1

(b)

-(log10 x)2

(c)

(logx 10)2

(d)

$x^2\over100$

6. If $y={(1-x)^2\over x^2}$ ,then ${dy \over dx}$ is

(a)

8

(b)

1

(c)

4

(d)

5

7. If pv=81,then ${dp\over dv}$ at v=9 is

(a)

1

(b)

-1

(c)

2

(d)

-2

8. If g(x)=(x2+2x+3) f(x) and f(0)=5 and $lim_{x \rightarrow 0}{f(x)-5\over x}=4$,then g'(0) is

(a)

20

(b)

14

(c)

18

(d)

12

9. The derivative of f(x)=x|x| at x =−3 is

(a)

6

(b)

-6

(c)

does not exist

(d)

0

10. If is differentiable at x = 1, then

(a)

$a={1\over2},b={-3\over 2}$

(b)

$a={-1\over2},b={3\over 2}$

(c)

$a=-{1\over2},b=-{3\over 2}$

(d)

$a={1\over2},b={3\over 2}$

11. 5 x 2 = 10
12. Show that the greatest integer function $f(x)=\left\lfloor x \right\rfloor$ is not differentiable at any integer?

13. Find the derivative of the function using first principle. f(x)=-x2+2

14. Differentiate the following with respect to x: y=ex+sin x+2

15. Find the derivative of the function with respect to corresponding independent variable: g(t) = t3cos t

16. Differentiate the following: F(x)=(x3+4x)7

17. 5 x 3 = 15
18. Determine whether the following function is differentiable at the indicated values.f(x) = x | x | at x = 0

19. Determine whether the following function is differentiable at the indicated values. f(x)=sin|x|at x=0

20. Find the derivative of the function with respect to corresponding independent variable: $y={tan \ x-1\over sec \ x}$

21. Find F'(x) if F(x)=$\sqrt{x^2+1}$

22. Differentiate the following: y=e−mx

23. 3 x 5 = 15
24. Find the slope of tangent line to the graph of f(x) = - 5x2 + 7x at (5, f(5)).

25. Find the derivative of the function with respect to corresponding independent variable: y = e-x. log x

26. Differentiate the following: $y=\sqrt{1+2 \ tan \ x}$