Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Short Answer Type

401.

Find the equation of tangents to the curve y= x³+2x-4, which are perpendicular to line x+14y+3 =0.

2336 Views

Long Answer Type

402.

Prove space that space straight y equals fraction numerator 4 space sin space straight theta over denominator 2 space plus cos space straight theta end fraction space minus straight theta space is space an space increasing space function space of space straight theta space on space open square brackets 0 comma straight pi over 2 close square brackets

1368 Views

403.

Show that semi-vertical angle of a cone of maximum volume and given slant height is cos^-1 $fraction numerator 1 over denominator square root of 3 end fraction$ .

1713 Views

404.

Find the absolute maximum and absolute minimum values of the function f given by
$straight f left parenthesis straight x right parenthesis space equals sin squared straight x minus cosx comma space straight x space element of space left parenthesis 0 comma space straight pi right parenthesis$

619 Views

Short Answer Type

405.

Find the value(s) of x for which y = $open square brackets straight x left parenthesis straight x minus 2 right parenthesis close square brackets squared$ is an increasing function.

237 Views

406.

Find the equations of the tangent and normal to the curve $straight x squared over straight a squared minus straight y squared over straight b squared equals 1 space at space the space point space open parentheses square root of 2 straight a comma space straight b close parentheses.$

162 Views

Long Answer Type

407.

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum when the angle between them is $60 degree.$

162 Views

408.
Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is Also find the maximum volume.

Given, radius of the sphere is R.
Let r and h be the radius and the height of the inscribed cylinder respectively.
We have:

Let Volume of cylinder = V

Differentiating the above function w.r.t r, we have,

For maxima or minima,

Now, when

When

Hence, the volume of the cylinder is the maximum when the height of the cylinder is

490 Views

409.

Find the equation of the normal at a point on the curve x² = 4y which passes through the point (1, 2). Also, find the equation of the corresponding tangent.

336 Views

Short Answer Type

410.

The volume of a sphere is increasing at the rate of 3 cubic centimetres per second. Find the rate of increase of its surface area, when the radius is 2 cm.

3950 Views