If the tangent at (1, 7) to the curve x2 = y – 6 touches th

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

For each t ∈R, let [t] be the greatest integer less than or equal to t. Then

limx0+ x1x+2x+......+15x

  • does not exist (in R)

  • is equal to 0

  • is equal to 15

  • is equal to 120


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2.

If the tangent at (1, 7) to the curve x2 = y – 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is

  • 95

  • 195

  • 185

  • 85


A.

95

Equation of tangent at (1,7) to curve x2 = y -6 is

x - 1 =12(y +7) -6

2x - y +5 = 0 ... (i)

Centre of circle  = (-8,-6)

Radius of circle = 64 + 36-c = 100-c

 Line (i) touches the circle 2(-8) -(-6) +54 + 1 = 100-C5 = 100-c c = 95


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3.

If α, β ∈ C are the distinct roots, of the equation x2 -x + 1 = 0, then α101 + β107 is equal to

  • 2

  • -1

  • 0

  • 1


4.

PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45o, 30o and 30o, then the height of the tower (in m) is

  • 50√2

  • 100

  • 50

  • 100√3


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5.

The sum of the coefficients of all odd degree terms in the expansion of x + x3 -15 + x - x3-15, (x>1) is

  • 2

  • -1

  • 0

  • 1


6.

Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of △PTQ is

  • 36√5

  • 45√5

  • 54√3

  • 60√3


7.

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is

  • At least 750 but less than 1000

  • At least 1000

  • Less then 500

  • At least 500 but less than 750


8.

Two sets A and B are as under:

A = {(a-b)∈ RxR:|a-5|<1 and |b-5|<1}

B = {(a,b)∈ Rx R: 4(a-6)2 + 9 (b-5)2 ≤ 36},then

  • Neither A ⊂ B nor B ⊂ A

  • B ⊂ A

  • A ⊂ B

  • A ∩ B = ∅


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9.

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the
parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and,∠CPB = θ then a value of tan θ is

  • 4/3

  • 1/2

  • 2

  • 3


10.

The Boolean expression ~ (p v q )v (-p ∧q ) is equivalent to

  • ~q

  • ~ p

  • p

  • q


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