Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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11.

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

  • 3x + 2y = 6xy

  • 3x + 2y = 6

  • 2x + 3y = xy

  • 3x + 2y = xy


D.

3x + 2y = xy

 Let the equation of line be 

 (i)
(a) passes through the fixed point (2,3)

 .... (ii)

P(a, 0), Q(0, b), O(0, 0), Let R(h, k),

Midpoint of OR is (h/2, k/2)
Midpoint of PQ is (a/2, b/2)

⇒h =a, k = b... (iii)

From (ii) & (iii)


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12.

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + .....
If B – 2A = 100λ, then λis equal to

  • 496

  • 232

  • 248

  • 464


13.

Let a1, a2, a3, ...., a49 be in A.P. such that k = 012ak-1 = 416 and  a9 + a43 = 66. if a12 + a22 + ....... + a172 = 140m then m is equal to

  • 33

  • 66

  • 68

  • 34


14.

Let f(x) = x2 + 1x2 and g (x)  = x - 1x, x Ε R - {-1,0,1}.
if h(x) = f(x)g(x), then the local minimum value of h(x) is:

  • 22

  • 3

  • -3

  • -22


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15.

If i=19 (xi -5) = 9 and i = 19(xi - 5)2 = 45 then the
standard deviation of the 9 items x1, x2, ...., x9 is

  • 3

  • 9

  • 4

  • 2


16.

If the system of linear equations
x + ky + 3z = 0
3x + ky – 2z = 0
2x + 4y – 3z = 0

has a non-zero solution (x,y,z), then xz/y2 is equal to

  • 30

  • -10

  • 10

  • -30


17.

If x-42x2x2xx-42x2x2xx-4 = (A +Bx)(x-A)2, then the ordered pair (A,B) is equal to

  • (4,5)

  • (-4,-5)

  • (-4,3)

  • (-4,5)


18.

Let S = {t ∈ R: f(x) = |x-π|.(e|x| - 1) sin |x| is not differentiable at t}. Then the set S is equal to

  • {0,π}

  • ϕ (an empty set)

  • {0}

  • {π}


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19.

let y = y(x) be the solution of the differential equation sin x dydx + y cos x = 4x, x (0, π). If y = π2 = 0, then yπ6 is equal to:

  • -49π2

  • 493π2

  • -893π2

  • -89π2


20.

Let S = { x ∈ R : x ≥ 0 and 2|x-3| + x(x-6) + 6 = 0} Then S:

  • Contains exactly four elements

  • Is an empty set

  • Contains exactly one element

  • Contains exactly two elements


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