Let L1 be a tangent to the parabola y2 = 4(x + 1) and L2 be a tan

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

Let L1 be a tangent to the parabola y2 = 4(x + 1) and L2 be a tangent to the parabola y2 = 8(x + 2) such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line :

  • x + 3 = 0

  • 2x + 1 = 0

  • x + 2y = 0

  • x + 2 = 0


A.

x + 3 = 0

Let tangent of y24x + 1 beL1 : t1y = x + 1 + t12      ...iand tangent of y2 = 8x + 2 beL2 : t2y = x + 2 + 2t22  ... iiL1 ⥿ L21t1 . 1t2 = - 1t2 × i - t1 × ii x + 3 = 0


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2.

If i = 1nxi - a = n and i = 1nxi - a2 = na, n, a1 > 1 then the standard deviation of nobservations  x1, x2,  ... xn is : 

  • a - 1

  • na - 1

  • na - 1

  • a - 1


3.

A limx10x - 12tcost2dtx - 1sinx - 1 = ?

  • 1

  • does not exist

  • 12

  •  - 12


4.

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse,  x24 + y22 = 1 from any of its foci?

  •  - 2, 3

  •  - 1, 2

  • (1, 2)

  •  - 1, 3


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5.

Out of 11 consecutive natural number if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference is :

  • 1099

  • 15101

  • 533

  • 5101


6.

Let a , b, c, d and ay non zero distinct real numbers such that (a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :

  • a, b, c, d are in A.P.

  • a, c, p are in G.P.

  • a, b, c, d are in G.P.

  • a, c, p, are in A.P.


7.

If p denotes the fractional part pf the number p, then 32008 = ?

  • 18

  • 38

  • 78

  • 58


8.

The region represented by z = x + iy  C : z - Rez  1 is also given by the inequality

  • y2  2x + 1

  • y2  x + 12

  • y2    2x +1

  • y2  x + 1


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9.

The negation of the Boolean expression p v (~ p  q) is equivalent to :

  • p  ~ q

  • ~ p  q

  • ~ p  ~ q

  • ~ p  ~ q


10.

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?

  • 2! 3! 4!

  • 3!(4!)3

  • 3! . 2 . (4!)

  • (3!)3 . (4!)


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