If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω.The

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let α,  β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that

  • β ∈(0, 1)

  • β ∈(-1, 0)

  • |β| = 1

  • |β| = 1

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2.

The coefficient of x7 in the expansion of (1 - x - x2 +x3)6 is :

  • 144

  • -132

  • -144

  • -144

174 Views

3.

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

  • 18 Months

  • 19 Months

  • 20 Months

  • 20 Months

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4.

Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest. The negation of the statement ì Suman is brilliant and dishonest if and only if Suman is richî can be ex- pressed as

  •  ~ P ^ (Q ↔ ~ R)

  • ~ (Q ↔ (P ^ ~R)

  • ~ Q ↔ ~ P ^ R

  • ~ Q ↔ ~ P ^ R

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5.

If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω.Then (A, B) equals

  • (0,1)

  • (1,1)

  • (1,0)

  • (1,0)


B.

(1,1)

(1 + ω)7 = A + Bω
(-ω2)7 = A + Bω
- ω14 = A + Bω

2 = A + Bω
1 + ω = A + Bω
therefore,
(A, B) = (1, 1)

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6.

If the mean deviation about the median of the numbers a, 2a, ....., 50a is 50, then |a| equals 

  • 2

  • 3

  • 4

  • 4

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7.

Let R be the set of real numbers.
Statement-1 : A = {(x, y) ∈R × R : y - x is an integer} is an equivalence relation on R.
Statement-2 : B = {(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R.

  • Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

  • (2) 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. 

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8.

Consider 5 independent Bernoulliís trials each with a probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval

  • (1/2, 3/4]

  • (3/4, 11/12]

  • [0, 1/2]

  • [0, 1/2]

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9. fraction numerator straight d squared straight x over denominator dy squared end fraction equal to
  • open parentheses fraction numerator straight d squared straight x over denominator dy squared end fraction close parentheses to the power of negative 1 end exponent
  • negative open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses to the power of negative 1 end exponent open parentheses dy over dx close parentheses to the power of negative 3 end exponent
  • open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses open parentheses dy over dx close parentheses to the power of negative 2 end exponent
  • open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses open parentheses dy over dx close parentheses to the power of negative 2 end exponent
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10.

The value of p and q for which the function f(x) =open curly brackets table attributes columnalign left end attributes row cell table attributes columnalign left columnspacing 1.4ex end attributes row cell fraction numerator sin space left parenthesis straight p space plus 1 right parenthesis space straight x space plus space sin space straight x over denominator straight x end fraction comma end cell cell straight x less than 0 end cell row cell straight q comma end cell cell straight x space equals space 0 space is space continuous space for space all space straight x space in space straight R comma space are colon end cell end table
fraction numerator square root of straight x space plus straight x squared end root minus square root of straight x over denominator straight x to the power of 3 divided by 2 end exponent end fraction space comma space straight x greater than space 0 space end cell row space end table close

  • p = 1/2. q = -3/2

  • p = 5/2, q = 1/2

  • p = - 3/2, q = 1/2

  • p = - 3/2, q = 1/2

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