Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?

  • (−3, −9)

  • (−3, −8)

  • (1/3, -8/3)

  • (1/3, -8/3)

536 Views

22.

The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on:

  • a circle

  • an ellipse which is not a circle

  • a hyperbola.

  • a hyperbola.

245 Views

23.

If one of the diameters of the circle, given by the equation, x2+y2−4x+6y−12=0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is:

  • 5√2

  • 5√3

  • 5

  • 10

786 Views

24.

Let P be the point on the parabola, y2=8x which is at a minimum distance from the centre C of the circle, x2+(y+6)2=1. Then the equation of the circle, passing through C and having its centre at P is:

  • x2+y2−4x+8y+12=0

  • x2+y2−x+4y−12=0

  • x2+y2− 4 x +2y−24=0

  • x2+y2− 4 x +2y−24=0

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25.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is:

  • 4/3

  • 4/√3

  • 2/√3

  • √3

264 Views

26.

The distance of the point (1, −5, 9) from the plane x−y+z=5 measured along the line x=y=z is:

  • 3√10

  • 10√3

  • 10/√3

  • 20/3

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27.

If the line   lies in the plane lx +my -z = 9, then l2 +m2 is equal to 

  • 26

  • 18

  • 5

  • 2

224 Views

28.

Let   be three unit vectors such that   then the angle between   is

  • 3π/4

  • π/2

  • 2π/3

  • 5π/6

185 Views

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29.

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

  • 3a2−26a+55=0

  • 3a2−32a+84=0

  • 3a2−34a+91=0

  • 3a2−34a+91=0


B.

3a2−32a+84=0

We know that, if x1, x2..... xn are n observations, then their standard deviation is given by


square root of 1 over straight n sum straight x subscript straight i superscript 2 space minus open parentheses fraction numerator space stack sum straight x subscript straight i with space below over denominator straight n end fraction close parentheses squared end root

we begin inline style space end style begin inline style have end style begin inline style comma end style begin inline style space end style begin inline style space end style begin inline style left parenthesis end style begin inline style 3 end style begin inline style. end style begin inline style 5 end style begin inline style right parenthesis squared end style begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator left parenthesis 2 squared space plus 3 squared space plus straight a squared plus 11 squared right parenthesis over denominator 4 end fraction begin inline style space end style begin inline style minus end style begin inline style space end style begin inline style open parentheses begin display style fraction numerator 2 plus 3 plus straight a plus 11 over denominator 4 end fraction end style close parentheses squared end style begin inline style space end style begin inline style space end style begin inline style space end style

space begin inline style rightwards double arrow end style begin inline style space end style 49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 4 space plus space 9 space plus straight a squared plus 121 over denominator 4 end fraction begin inline style minus end style begin inline style open parentheses begin display style fraction numerator 16 plus straight a over denominator 4 end fraction end style close parentheses squared end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style
begin inline style rightwards double arrow end style begin inline style space end style 49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 134 space plus straight a squared over denominator 4 end fraction begin inline style minus end style fraction numerator 256 space plus straight a squared plus 32 straight a over denominator 16 end fraction begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style

49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 4 straight a squared space plus 536 minus 256 minus straight a squared minus 32 straight a over denominator 16 end fraction

space begin inline style space end style begin inline style 49 end style begin inline style space end style begin inline style straight x end style begin inline style space end style begin inline style 4 end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style 3 end style begin inline style straight a squared end style begin inline style minus end style begin inline style 32 end style begin inline style straight a end style begin inline style plus end style begin inline style 280 end style begin inline style space end style begin inline style 3 end style begin inline style straight a squared end style begin inline style minus end style begin inline style 32 end style begin inline style straight a end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style 84 end style begin inline style space end style begin inline style equals end style begin inline style 0 end style

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30.

The Boolean Expression (p∧~q)∨q∨(~p∧q) is equivalent to:

  • ~p ∧ q

  • p ∧ q

  • p ∨ q

  • p ∨ q

246 Views

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