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This mock test of Test: Tangent And Normal (Competition Level) - 2 for JEE helps you for every JEE entrance exam.
This contains 9 Multiple Choice Questions for JEE Test: Tangent And Normal (Competition Level) - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The x–intercept of the tangent at any arbitrary point of the curve is proportional to

Solution:

QUESTION: 2

The line = 1 touches the curve y = be^{–x/a} at the point

Solution:

QUESTION: 3

If the subnormal at any point on y = a1 – n x^{n} is of constant length, then the value of n is

Solution:

QUESTION: 4

If the tangent at P of the curve y^{2} = x^{3} intersects the curve again at Q and the straight lines OP, OQ make angles a, b with the x–axis, where `O' is the origin, then tan a/tan b has the value equal to

Solution:

QUESTION: 5

The length of the normal to the curve x = a(q + sin q), y = a (1 – cos q), at q = is

Solution:

QUESTION: 6

The beds of two rivers (within a certain region) are a parabola y = x^{2} and a straight line y = x – 2. These rivers are to be connected by a straight canal. The co-ordinates of the ends of the shortest canal can be

Solution:

QUESTION: 7

If the area of the triangle included between the axes and any tangent to the curve x^{n} y = a^{n} is constant, then n is equal to

Solution:

QUESTION: 8

At (0, 0), the curve y^{2} = x^{3} + x^{2}

Solution:

QUESTION: 9

For the curve x = t^{2} – 1, y = t^{2} – t, the tangent line is perpendicular to x-axis where

Solution:

Given curve is x = t^{2 }− 1,y = t^{2 }− t

Derivating w.r.to t we get

d x/ dt =2t -------(1)

and dy / dt = 2t − 1 -------(2)

dividing (2) by (1) we get

dy / dx = (2t − 1) / 2t

Therefore, the slope of the tangent is (2t − 1) / 2t

Given that the tangent is perpendicular to x-axis. Therefore, tangent is parallel to y-axis.

We know that slope of y-axis is infinity and the slopes of the two parallel lines are equal.

Therefore, slope of the tangent is infinity.

Hence, (2t − 1) / 2t = 1/0

⟹ 2t = 0

⟹ t = 0

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