Important Questions of Relations and Functions Mathematics | Zigya

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131.

If the sum of two of the roots of x3 + px2 - qx + r = 0 is zero, then pq is equal to

  • - r

  • r

  • 2r

  • - 2r


132.

The angle between the tangents drawn from the point (1, 2) to the ellipse 3x2 + 2y2 = 5 is

  • tan-11255

  • tan-112513

  • π4

  • π2


133.

The equation of the circle whose diameter is the common chord of the circles x2 + y+ 2x + 2y + 1 = 0 and x2 + y+ 4x + 6 y + 4 = 0 is

  • 10x2 + 10y2 + 14x + 8y +1 = 0

  • 3x2 + 3y2 - 3x + 6y - 8 = 0

  • 2x2 +2y2 - 2x + 4y +1 = 0

  • 2x2 + 2y2 - 2x + 4y + 1 = 0


134.

Area (in sq. units) of the region outside x2 + y3 = 1 and inside the ellipse x24 + y29 = 1

  • 3π - 2

  • 34 - π

  • 6π - 2

  • 64 - π


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135.

If 
straight f left parenthesis straight x right parenthesis space plus space 2 straight f open parentheses 1 over straight x close parentheses space equals space 3 straight x comma
straight x space not equal to space 0 space and space straight S space equals space open curly brackets straight x space straight epsilon space straight R colon space straight f space left parenthesis straight x right parenthesis space equals space straight f left parenthesis negative straight x right parenthesis close curly brackets semicolon space then space straight S

  • is an empty set

  • contains exactly one element.

  • contains exactly two elements.

  • contains exactly two elements.

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136.

For x ε R, f (x)=|log2−sinx| and g(x)=f(f(x)), then :

  • g is not differentiable at x=0

  • g'(0)=cos(log2)

  • g'(0)=-cos(log2)

  • g'(0)=-cos(log2)

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137.

Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

  • E1 and E2 are independent

  • E2 and E3 are independent.

  • E1 and E3 are independent.

  • E1 and E3 are independent.

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138.

If g is the inverse of a function f and f'(x) = fraction numerator 1 over denominator 1 plus straight x to the power of 5 end fraction comma then g'(x) is equal to 

  • 1+ x6

  • 5x4

  • fraction numerator 1 over denominator 1 plus space left curly bracket straight g left parenthesis straight x right parenthesis right square bracket to the power of 5 end fraction
  • fraction numerator 1 over denominator 1 plus space left curly bracket straight g left parenthesis straight x right parenthesis right square bracket to the power of 5 end fraction
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139.

If fk(x) = 1/k (sink x + cosk x), where x ε R and k ≥1, then f4 (x)-fo (x) equal to 

  • 1/6

  • 1/3

  • 1/4

  • 1/4

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140.

Let A and B be two events such that straight P left parenthesis space stack straight A space union straight B right parenthesis with bar on top space equals space 1 over 6 comma space straight P space left parenthesis straight A space intersection straight B right parenthesis space equals space 1 fourth space and space space straight P space left parenthesis straight A with bar on top right parenthesis space equals space 1 fourth where straight A with bar on top. Then, the events A and B are

  • independent but not equally likely

  • independent and equally likely

  • mutually exclusive and independent

  • mutually exclusive and independent

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