Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

If, for a positive integer n, the quadratic equation,
x(x + 1) + (x + 1) (x + 2) + .....
+ (x + n -1 ) (x + n) = 10n
has two consecutive integral solutions, then n is equal to :

  • 11

  • 12

  • 9

  • 9


A.

11

nx squared space plus space straight x left parenthesis 1 space plus space 3 plus 5 plus..... space plus space left parenthesis 2 straight n minus 1 right parenthesis right parenthesis space plus
space left parenthesis 1.2 space plus space 2.3 space plus space..... space plus space left parenthesis straight n minus 1 right parenthesis. straight n right parenthesis minus 10 straight n space equals space 0
rightwards double arrow space nx squared space plus space straight x space left parenthesis straight n squared right parenthesis space plus space fraction numerator straight n left parenthesis straight n squared minus 1 right parenthesis over denominator 3 end fraction space minus space 10 straight n space equals space 0
rightwards double arrow space straight x squared space plus space straight x space left parenthesis straight n right parenthesis space plus space fraction numerator left parenthesis straight n squared minus 1 right parenthesis over denominator 3 end fraction minus 10 space equals space 0 space less than subscript straight beta superscript straight alpha
left parenthesis straight alpha space minus space straight beta right parenthesis squared space equals space 1
rightwards double arrow space left parenthesis straight alpha space plus space straight beta right parenthesis squared space minus space 4 αβ space equals space 1
rightwards double arrow space straight n squared space minus space 4 space open parentheses fraction numerator straight n squared minus 1 over denominator 3 end fraction minus 10 close parentheses space equals space 1
rightwards double arrow space straight n space equals space 11
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2.

The function straight f colon space straight R space rightwards arrow with space on top space open square brackets negative 1 half comma 1 half close square brackets space defined space as space straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x over denominator 1 plus space straight x squared end fraction comma space is

  • neither injective nor surjective.

  • invertible

  • injective but not surjective.

  • injective but not surjective.

371 Views

3.

The following statement
(p → q ) → [(~p → q) → q] is

  • a fallacy

  • a tautology

  • equivalent to ~ p → q

  • equivalent to ~ p → q

397 Views

4.

For any three positive real numbers a, b and c, (25a2 + b2) + 25(c2 – 3ac) = 15b(3a + c), Then

  • b , c and a are in G.P

  • b, c and a are in A.P

  • a, b and c are in A.P

  • a, b and c are in A.P

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5.

hyperbola passes through the point P(√2, √3) and has foci at (± 2, 0). Then the tangent to this hyperbola at P also passes through the point

  • left parenthesis negative square root of 2 comma space minus square root of 3 right parenthesis
  • left parenthesis 3 square root of 2 space comma space 2 square root of 3 right parenthesis
  • left parenthesis 2 square root of 2 space comma 3 space square root of 3 right parenthesis
  • left parenthesis 2 square root of 2 space comma 3 space square root of 3 right parenthesis
1078 Views

6.

Let a, b, c ∈ R. If f(x) = ax2 + bx + c is such
that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, ∀x,y ∈ R,then sum from straight n space equals 1 to 10 of space straight f space left parenthesis straight n right parenthesis is equal to

  • 225

  • 330

  • 165

  • 165

330 Views

7.

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector.Then the maximum area (in sq. m) of the flower-bed, is

  • 30

  • 12.5

  • 10

  • 10

332 Views

8.

The value of
(21C110C1) + (21C210C2) + (21C310C3) + (21C410C4) + .... +
(21C1010C10) is

  • 220 – 210

  • 221 – 211

  • 221 – 210

  • 221 – 210

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9. stack lim space with straight x space rightwards arrow straight pi over 2 below space fraction numerator cot space straight x space minus cos space straight x over denominator left parenthesis straight pi minus 2 straight x right parenthesis cubed end fraction space equals
  • 1/4

  • 1/24

  • 1/16

  • 1/16

396 Views

10.

If 5(tan2x – cos2x) = 2cos 2x + 9, then the value of cos4x is

  • -7/9

  • -3/5

  • 1/3

  • 1/3

542 Views

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