If f(x) = sinxx for x ≠ 00  

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Equation of tangent to the circle x2 + y2 - 2x - 2y + 1 = 0 perpendicular to y = x is given by

  • x + y ± 1 = 0

  • x + y = 2 ± 3

  • x + y ± 3 = 0

  • None of these


2.

If A and B are two such events that PA  B = PA  B, then which of the following is true?

  • P(a) + P(B) = 0

  • P(A) + P(B) = P(A)P(B/A)

  • P(A) + P(B) = 2P(A)P(B/A)

  • None of the above


3.

The y - coordinate of a point P on the line joining A(7, 2,1) and B(10, 5, 7) is 4. Then, x and z - coordinates of the point are

  • x = 9, z = 5

  • x = 3, z = 7

  • x = 2, z = 3

  • None of these


4.

If point D divides the base BC of a ABC in the ratio n : m, then the value of mBD2 + nCD2 + (m + n)AD2 is

  • mAC2 + nAB2

  • (m + n)(AC2 + AB2)

  • nAC2 + mAB2

  • None of these


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5.

A man is standing on the horizontal plane. The angle of elevation of top of the pole is α. If he walks a distance double the height of the pole, then the elevation of the pole is 2α. The value of α is

  • π12

  • π4

  • π3

  • π6


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6.

If f(x) = sinxx for x  00         for x = 0

where [x] denotes the greatest integer less than or eual to x, then limx0fx is equal to

  • 1

  • - 1

  • 0

  • Does not exist


D.

Does not exist

Given, fx = sinxx for x  00         for x = 0LHL = limx0-fx = limx0-sin1 + xx        = sin1 - 1- 1 = sin0- 1 = 0RHL = limx0+fx = limx0+sin1 + xx        = sin1 + 00 = 

Hence, limit does not exist.


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7.

The value of the angle between two straight lines y = 2 - 3x + 5 and y = 2 + 3x - 7 is

  • 30°

  • 60°

  • 45°

  • 90°


8.

Which of the following is a universal gate?

  • NAND

  • OR

  • AND

  • NOT


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9.

The value of sin(50°) cos (10°) + cos(50°) sin(10°) is

  • 12

  • 3

  • 32

  • 1


10.

Probability of getting a total of 7 or 9 in a single throw of two dice is

  • 518

  • 16

  • 19

  • None of these


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