If y = 4x + 3 is parallel to a tangent to the parabola y2 = 12x,

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The number of solution(s) of the equation x + 1 - x - 1 = 4x - 1 is/are

  • 2

  • 0

  • 3

  • 1


2.

The value of z2 + z - 32 + z - i2 is minimum when z equals

  • 2 - 23i

  • 45 + 3i

  • 1 + i3

  • 1 - i3


3.

If limx02asinx - sin2xtan3x exists and is equal to 1, then the value of α is

  • 2

  • 1

  • 0

  • - 1


4.

The solution of the equation log101log7x + 7 + x = 0 is

  • 3

  • 7

  • 9

  • 49


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5.

The number of digits in 20301 given, log102 = 0.3010 is

  • 602

  • 301

  • 392

  • 391


6.

If R be the set of all real numbers and f : R ➔ R is given by f(x) = 3x2 + 1. Then, the set f-1([1, 6]) is

  • - 53, 0, 53

  • - 53,  53

  • - 13, 13

  •  - 53, 53


7.

The value of tanπ2 + 2tan2π5 + 4cot4π5 is

  • cotπ5

  • cot2π5

  • cot4π5

  • cot3π5


8.

Let the number of elements of the sets A and B be p and q, respectively. Then, the number of relations from the set A to the set B is

  • 2p + q

  • 2pq

  • p + q

  • pq


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9.

In a ABCtanA and tanB are the roots of pq(x2 + 1) = r2x. Then, ABC is

  • a right angled triangle

  • an acute angled triangle

  • an obtuse angled triangle

  • an equilateral triangle


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10.

If y = 4x + 3 is parallel to a tangent to the parabola y2 = 12x, then its distance from the normal parallel to the given line is

  • 21317

  • 21917

  • 21117

  • 21017


B.

21917

Given equation of parabola is

y2 = 12x      ...(i)

On differentiating both sides w.r.t. x, we get

2ydydx = 12 dydx = 6y

Since, the normal to the curve is parallel to the line y = 4x + 3

 Slope of normal curve = Slope of line - y6 = 4       y = - 24

From Eq. (i), we get

- 242 = 12x 24 × 24 = 12x            x = 48

 Normal point on a curve is (48, - 24). 

 Distance from (48,- 24) to the line 4x - y + 3 = 0 is,

4 × 48 + 24 + 342 + 12 = 21917


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