## Differentiation Quiz

Important topics for Maths has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with the day-to-day experiences.

Q1. If ax^2+2hxy+by^2=1, then (d^2y)/(dx^2) is
•  (h^2-ab)/(hx+by)^2
•  (ab-h^2)/(hx+by)^2
•  (h^2+ab)/(hx+by)^2
•  None of these
Solution

Q2.

•  x/(2y-1)
•  x/(2y+1)
•  1/(x(2y-1))
•  1/(x(1-2y))
Solution
(c) y=√(log⁡x+y) ⇒y^2=log⁡x+y ⇒2y dy/dx=1/x+dy/dx⇒dy/dx=1/(x(2y-1))

Q3.

•   x dy/dx-y
•  (x dy/dx-y)^2
•  y dy/dx-x
•  (y dy/dx-x)^2
Solution
(b) From the given relation y/x=log⁡x-log⁡(a+bx) Differentiating w.r.t. x, we get ((x dy/dx)-y)/x^2 =1/x-b/(a+bx)=a/(x(a+bx)) ∴x dy/dx-y=ax/(a+bx) (1)

Q4. If graph of y=f(x) is symmetrical about y-axis and that of y=g(x) is symmetrical about the origin. If h(x)=f(x)∙g(x), then (d^3 h(x))/(dx^3) at x=0 is
•  Cannot be determined
•  f(0)∙g(0)
•  0
•  None of these
Q5. If √(1-x^2)+√(1-y^2)=a(x-y), then dy/dx is equal to
•  √((1-x^2)/(1-y^2))
•  √((1-y^2)/(1-x^2))
•  √((x^2-1)/(1-y^2))
•  (y^2-1)/(1-x^2)
Solution

Q6. If y^2=ax^2+bx+c, then y^3(d^2 y)/(dx^2 ) is
•  a constant
•  a function of x only
• a function of y only
•  a function of x and y
Solution

Q7.If f'(x)=√(2x^2-1) and y=f(x^2), then dy/dx at x=1 is
•  2
•  1
•  -2
•  None of these
•  0
•  1
•  -1
•  None of these
Solution

Q9.If f"(x)=-f(x) and g(x)=f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and given that F(5)=5, then F(10) is
•  5
•  10
•  0
•  15
Solution
(a) F'(x)=[f(x/2).f'(x/2)+g(x/2)g'(x/2)] Here g(x)=f'(x) and g'(x)=f''(x)=-f(x) So F'(x)=f(x/2)g(x/2)-f(x/2)g(x/2)=0 ⇒F(x) is a constant function ⇒F(10)=5

Q10.

•  1
•  -1
•  1/√2
• None of these
Solution
(b) y=cos^(-1)⁡(cos⁡x)=cos^(-1)⁡{cos⁡[2Ï€-(2Ï€-x)]} =cos^(-1)⁡[cos⁡(2Ï€-x)] =2Ï€-x ∴dy/dx=-1 at x=5Ï€/4

#### Written by: AUTHORNAME

AUTHORDESCRIPTION

## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: Differentiation-Quiz-9
Differentiation-Quiz-9