If the line lx + my + n = 0 is tangent to the parabola y2 = 4ax,

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.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

171.

If x + y = k is normal to y2 = 12x, then k is

  • 3

  • 9

  • - 9

  • - 3


172.

A particle moves along a straight line according to the law s = 16 - 2t + 3t3, where s metres is the distance of the particle from a fixed point at the end of t second. The acceleration of the particle at the end of 2s is

  • 3.6 m/s2

  • 36 m/s2

  • 36 km/s2

  • 360 m/s2


173.

Divide 10 into two parts such that the sum of double of the first and the square of the second is minimum

  • (6, 4)

  • (7, 3)

  • (8, 2)

  • (9, 1)


174.

If 2x + y + λ = 0 is normal to the parabola y2 = 8x, then λ, is

  • - 24

  • 8

  • - 16

  • 24


Advertisement
Advertisement

175.

If the line lx + my + n = 0 is tangent to the parabola y2 = 4ax, then

  • mn = al2

  • lm = an2

  • ln = am2

  • None of the above


C.

ln = am2

Given parabola, 2ydydx = 4a dydx = 2ay                                ...iwhich is the slope of tangent.Given, Ix + my + n = 0is an equation of tangent of the parabola      y2 = 4ax.    Slope of tanent = - lm       ...iiFrom Eqs. (i) and (ii)   2ay = - lm  y = - 2aml y2 = 4ax 4a2m2l2 = 4ax         x = am2l2On putting the values of x and y in the following equationlx + my + n = 0lam2l2 + m- 2aml + n = 0             am2l - 2am2l + n = 0          am2l = n  am2 = nlwhich is the required relation.


Advertisement
176.

All the points on the curve y2 = 4ax + asinxa, where the tangent is parallel to the axis of x are lies on

  • circle

  • parabola

  • straight line

  • None of these


177.

The length of normal at any point to the curve y = c coshxc is

  • fixed

  • y2c2

  • y2c

  • yc2


178.

The height of right circular cylinder of maximum volume inscribed in a sphere of diameter 2a is

  • 23a

  • 3a

  • 2a3

  • a3


Advertisement
179.

The approximate value of f(x) = x3 + 5x2 - 7x + 9 at x = 1.1 is

  • 8.6

  • 8.5

  • 8.4

  • 8.3


180.

The point on the curve 6y = x3 + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is

  • (4, 11)

  • (4, - 11)

  • (- 4, 11)

  • (- 4, - 11)


Advertisement