Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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11.

The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

  • ellipse

  • parabola

  • circle

  • circle


D.

circle

Equation space of space normal space is space straight Y minus straight y space equals space minus space dx over dy left parenthesis straight X minus straight x right parenthesis
rightwards double arrow space straight G space identical to open parentheses straight x space plus space straight y dy over dx comma 0 close parentheses
open vertical bar straight x plus straight y dy over dx close vertical bar space equals space vertical line 2 straight x vertical line
rightwards double arrow straight y dy over dx space equals space straight x space or space straight y space dy over dx space equals space minus space 3 straight x
straight y space dy space equals space straight x space dx space or space ydy space equals space minus space 3 xdx
straight y squared over 2 space equals space straight x squared over 2 space plus space straight c space or space straight y squared over 2 space equals space minus fraction numerator 3 straight x squared over denominator 2 end fraction plus straight c
straight x squared minus straight y squared space equals space minus 2 straight c
3 straight x squared space plus space straight y squared space equals 2 straight c
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12.

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

  • 4

  • 10

  • 6

  • 6

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13.

For the Hyperbola fraction numerator straight x squared over denominator cos squared space straight alpha end fraction space minus space fraction numerator straight y squared over denominator begin display style sin squared end style begin display style space end style begin display style straight alpha end style end fraction space equals 1 which of the following remains constant when α varies?

  • Eccentricity

  • Directrix

  • Abscissae of vertices

  • Abscissae of vertices

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14.

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = logex on the interval [1, 3] is

  • 2log3e

  • loge3/2

  • log3e

  • log3e

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15.

The sum of the series fraction numerator 1 over denominator 2 space factorial space end fraction minus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space..... space upto space infinity

  • e-2

  • e–1

  • e-1/2

  • e-1/2

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16.

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

  • 40

  • 20

  • 80

  • 80

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17.

The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

  • (−1, 1)

  • (0, 2)

  • (2, 4)

  • (2, 4)

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18.

If the difference between the roots of the equation x2 + ax + 1 = 0 is less than 5 , then the set of possible values of a is

  •  (−3, 3)

  • (−3, ∞)

  • (3, ∞)

  • (3, ∞)

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19.

The largest interval lying in  open parentheses negative straight pi over 2 comma straight pi over 2 close parentheses spacefor which the function open square brackets straight f left parenthesis straight x right parenthesis space equals 4 to the power of negative straight x squared end exponent space plus space cos to the power of negative 1 end exponent space open parentheses straight x over 2 minus 1 close parentheses plus space log space left parenthesis cos space straight x right parenthesis close square brackets is defined, is

  • [0, π]

  • open parentheses negative straight pi over 2 comma straight pi over 2 close parentheses
  • [-π/4, π/2)

  • [-π/4, π/2)

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20.

If D = open vertical bar table row 1 1 1 row 1 cell 1 plus straight x end cell 1 row 1 1 cell 1 plus straight y end cell end table close vertical barfor x ≠ 0, y ≠ 0 then D is

  • divisible by neither x nor y

  • divisible by both x and y

  • divisible by x but not y

  • divisible by x but not y

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