The number of points on the line x + y = 4 which are unit distanc

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

In triangle ABC, a = 2, b = 3 and sin(A) = 23, then B is equal to

  • 30°

  • 60°

  • 90°

  • 120°


2.

The coefficient of xn, where n is any positive integer, in the expansion of 1 + 2x + 3x2 + ... 12

  • 1

  • n + 12

  • 2n + 1

  • n + 1


3.

The circles x2 + y2 - 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points, if

  • a < 2

  • 2 < a < 8

  • a > 8

  • a = 2


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4.

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

  • 0

  • 1

  • 2


D.

Given lines are x + y = 4 and 2x + 2y = 5 or x + y = 52

The distance between two parallel lines

d = 4 - 5212 + 12 = 322 = 324 > 1

Hence, no point lies in it.


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5.

Simplest form of 22 + 2 + 2 + 2cos4x is

  • secx2

  • secx

  • cscx

  • 1


6.

If y = tan-11 - sinx1 + sinx, then the value of dydx at x = π6 is

  • 12

  • 12

  • 1

  • - 1


7.

The sum of the infinite series

1 + 12! + 1 . 34! + 1 . 3. 56! + ...

  • e

  • e2

  • e

  • 1e


8.

If three positive real numbers a, b, c are in AP and abc = 4, then the minimum possible value of b is 2

  • 232

  • 223

  • 213

  • 252


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9.

If 5cos2θ + 2cos2θ2 + 1 = 0, when 0 < θ < π, then the values of θ are

  • π3 ± π

  • π3, cos-135

  • cos-135 ± π

  • π3, π - cos-135


10.

For any complex number z, the minimum value of z + z - 1 is

  • 0

  • 1

  • 2

  • - 1


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