Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

  •  1/14

  • 1/7

  • 5/14

  • 5/14

168 Views

12.

Statement 1: ~ (p ↔ ~ q) is equivalent to p ↔ q
Statement 2 : ~ (p ↔ ~ q) is a tautology

  • Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

  • Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

  • Statement–1 is true, statement–2 is false.

  • Statement–1 is true, statement–2 is false.

135 Views

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13.

Statement 1: The variance of first n even natural numbers is fraction numerator straight n squared minus 1 over denominator 4 end fraction
Statement 2: The sum of first n natural numbers is fraction numerator straight n space left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction and the sum of squares of first n natural numbers is fraction numerator straight n left parenthesis straight n plus 1 right parenthesis left parenthesis 2 straight n plus 2 right parenthesis over denominator 6 end fraction

  • Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

  • Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

  • Statement–1 is true, statement–2 is false.

  • Statement–1 is true, statement–2 is false.


D.

Statement–1 is true, statement–2 is false.

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14.

Let a, b, c be such that 0 (a +c) ≠ . If open vertical bar table row cell space space space straight a end cell cell straight a plus 1 end cell cell space space straight a minus 1 end cell row cell negative straight b end cell cell straight b plus 1 end cell cell space space straight b minus 1 end cell row cell space space space straight c end cell cell space straight c minus 1 end cell cell space space straight c plus 1 end cell end table close vertical bar plus open vertical bar table row cell straight a plus 1 end cell cell straight b plus 1 end cell blank row cell straight a minus 1 end cell cell straight b minus 1 end cell cell straight c plus 1 end cell row cell left parenthesis negative 1 right parenthesis to the power of straight n plus 2 end exponent straight a end cell cell left parenthesis negative 1 right parenthesis to the power of straight n plus 1 end exponent straight b end cell cell left parenthesis negative 1 right parenthesis to the power of straight n space straight c end cell end table close vertical bar space equals space 0,then the value of 'n' is 

  • 0

  • any even integer

  • any odd integer

  • any odd integer

167 Views

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15. integral subscript 0 superscript straight pi[cot x]dx, where [.] denotes the greatest integer function, is equal to
  • π/2

  • 1

  • -1

  • -1

104 Views

16.

For real x, let f(x) = x3+ 5x + 1, then

  • f is one–one but not onto R

  • f is onto R but not one–one

  • f is one–one and onto R

  • f is one–one and onto R

102 Views

17.

Let y be an implicit function of x defined by x2x – 2xxcoty – 1 = 0. Then y′ (1) equals 

  • -1

  • 1

  • log 2

  • log 2

179 Views

18.

Given P(x) = x4+ ax3 + cx + d such that x = 0 is the only real root of P′ (x) = 0. If P(–1) < P(1),then in the interval [–1, 1].

  • P(–1) is the minimum and P(1) is the maximum of P

  • P(–1) is not minimum but P(1) is the maximum of P

  • P(–1) is the minimum but P(1) is not the maximum of P

  • P(–1) is the minimum but P(1) is not the maximum of P

141 Views

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19.

Let f(x) = (x + 1)2– 1, x ≥ – 1
Statement – 1: The set {x : f(x) = f–1(x)} = {0, –1}.
Statement – 2: f is a bijection.

  • Statement–1 is true, Statement–2 is true,Statement–2 is a correct explanation for statement–1 

  • Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

  • Statement–1 is true, statement–2 is false.

  • Statement–1 is true, statement–2 is false.

116 Views

20.

Let f(x) = x|x| and g(x) = sinx

Statement 1 : gof is differentiable at x = 0 and its derivative is continuous atthat point
Statement 2: gof is twice differentiable at x = 0

  • Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

  • Statement–1 is true, Statement–2 is true;Statement–2 is not a correct explanation for statement–1.

  • Statement–1 is true, statement–2 is false.

  • Statement–1 is true, statement–2 is false.

106 Views

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