If α and β are the roots

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let L denote the line in the xy-plane with x and y intercepts as 3 respectively. Then the image of the point (– 1, – 4) in the line is :

  • 85, 295

  • 115, 285

  • 295, 85

  • 295, 115


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2.

If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to :

  • 2αα - 1

  • 2αα + 1

  • 2α2

  •  - 2αα + 1


D.

 - 2αα + 1

Given equation is

2x (2x + 1) = 1  4x2 + 2x  1 = 0 ...(i)roots of equation i are α and β α + β = - 12 β = - 12 - α     ... iiand 4α2 + 2α - 1 = 0 α2 = 14 - α2      ...iiinow - 2αα + 1 = - 2α2 - 2α= - 214 - α2 - 2α= - 12 - α = β


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3.

If the tangent tothe curve, y = f(x) = xlogex, (x > 0) at a point (c, f(c)) is parallel to the line-segment joining the points (1, 0) and (e, e), then c is equal to :

  • e  - 1e

  • 1e - 1

  • e1e - 1

  • e11 - e


4.

If the constant term in the binomial expansion of x - kx210 is 405, then k = ?

  • 3

  • 2

  • 1

  • 9


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5.

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, the eccentricity e of the ellipse satisfies : 

  • e4 + 2e2 - 1 = 0

  • e2 +  e - 1

  • e2 + 2e - 1 = 0

  • e4 + e2 - 1 = 0


6.

The set of all real values for which the function

fx = 1 - cos2x . λ + sinx, x   - π2, π2,

has exactly one maxima and exactly one minima, is

  • - 12, 12 - 0

  • - 32, 32

  • - 12, 12

  • - 32, 32 - 0


7.

Consider the statement: For an integer n, if n3  1 is even, then n is odd. The contrapositive statement of this statement is:

  • For an integer n, if n is even, then n3 – 1 is odd

  • For an integer n, if n is even, then n3 – 1 is even.

  • For an integer n, if n3 – 1 is not even, then n is not odd

  • For an integer n, if n is odd, then n3 – 1 is even.


8.

The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is:

  • 310, 165

  • - 5310, 165

  •  - 165, 5310

  • 65, 5310


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9.

The angle of elevation of the summit of a mountain from a point on the ground is 45º. After climbing up one km towards the summitat an inclination of 30º from the ground, the angle of elevation of the summit is found to be 60º. Then the height (in km) of the summit from the ground is

  • 3 + 13 - 1

  • 13 + 1

  • 13 - 1

  • 3 - 13 + 1


10.

Let θ = θ5 and A = cosθsinθ - sinθcosθ. If B = A + A4, Then detB : 

  • 0

  • 1

  • lies in (2, 3)

  • lies in (1, 2)


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