# NDA MATHEMATICS QUIZ 1

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## Question 1:

If area of a circle increases at a uniform rate then perimeter varies...........

## Question 2:

A spherical balloon is pumped at the rate of 10 cubic $\mathrm{cm}$. per minute. The rate of increase of its radius when its radius when its radius is $15 \mathrm{~cm}$ is given by $\frac{1}{k \pi} \mathrm{cm}$ per minute then $\mathrm{k}$ equals.

## Question 3:

A square plate of metal is expanding and each of its side is increasing at a rate of 2 $\mathrm{cm}$ per minute. At what rate is the area of the plate increasing when the side is 30 cm long ?

## Question 4:

A spherical ball of sugar is dissolved in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface area. Then which of the following is correct?

## Question 5:

A particle moves in such a way that the distance covered by it in $\mathrm{t}$ seconds measured from a fixed point on the line is given by $x=\frac{t^{3}}{3}-16 t .$ Acceleration when velocity is zero will be

## Question 6:

In which of the following interval the function $f(x)=\tan ^{-1} x-x$ decreases ?

## Question 7:

If the line $a x+b y+c=0$ is a normal to the hyperbola $x y=1$ then

## Question 8:

For what value of $\theta$; tangent to the curve $x=a \sqrt{\cos 2 \theta} . \cos \theta$ ;    $y=a \sqrt{\cos 2 \theta} \cdot \sin \theta$ is parallel to axis of $x$ ?

## Question 9:

Equation of the normal to the curve $y=2 x^{2}+3 \sin x$ at $x=0$ will be

## Question 10:

Equation of the normal to the curve $x^{3}+y^{3}=6 x y$ at the point $(3,3)$ will be