If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c �

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of all real values of x satisfying the equation
left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent is:

  • 3

  • -4

  • 6

  • 6

654 Views

2.

A complex number z is said to be unimodular, if |z|= 1. suppose z1 and z2 are complex numbers such that fraction numerator straight z subscript 1 minus 2 straight z subscript 2 over denominator 2 minus straight z subscript 1 begin display style stack straight z subscript 2 with minus on top end style end fraction is unimodular and z2 is not unimodular. Then, the point z1 lies on a

  • straight line parallel to X -axis

  • straight line parallel to Y -axis

  • circle of radius 2

  • circle of radius 2

264 Views

3.
Let α and  β be the roots of equations x2-6x-2 = 0. If an =αn- βn, for n≥1, the value of a10-2a8/2a9 is equal to 
  • 6

  • -6

  • 3

  • 3

856 Views

4.

The normal to the curve x2 + 2xy-3y2 =0 at (1,1)

  • does not meet the curve again

  • meets the curve again in the second quadrant

  • meets the curve again in the third quadrant

  • meets the curve again in the third quadrant

247 Views

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5.

If z is a complex number such that |z|≥2, then the minimum value of open vertical bar straight z space plus space 1 half close vertical bar

  • is equal to 5/2

  • lies in the interval (1,2)

  • is strictly greater than 5/2

  • is strictly greater than 5/2

287 Views

6.

Let α and β be the roots of equation px2 +qx r =0 p ≠0. If p,q and r are in AP and 1 over straight alpha space plus space 1 over straight beta = 4, then the value of |α- β| is

  • fraction numerator square root of 61 over denominator 9 end fraction
  • fraction numerator 2 square root of 17 over denominator 9 end fraction
  • fraction numerator square root of 34 over denominator 9 end fraction
  • fraction numerator square root of 34 over denominator 9 end fraction
220 Views

7.

If the coefficients of x3 and x4 in the expansion of (1+ax+bx2)(1-2x)18 in powers of x are both zero, then (a,b) is equal to

  • open parentheses 16 comma 251 over 3 close parentheses
  • open parentheses 14 comma 251 over 3 close parentheses
  • open parentheses 14 comma 272 over 3 close parentheses
  • open parentheses 14 comma 272 over 3 close parentheses
246 Views

8.

If [a x b b x c c x a] = λ[a b c]2, then λ is equal to 

  • 0

  • 1

  • 2

  • 2

261 Views

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9.

The real number k for which the equation, 2x3 +3x +k = 0 has two distinct real roots in [0,1]

  • lies between 1 and 2

  • lies between 2 and 3

  • lies between -1 and 0

  • lies between -1 and 0

183 Views

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10.

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

  • 1:2:3

  • 3:2:1

  • 1:3:2

  • 1:3:2


A.

1:2:3

Given equations are 
x2 +2x+3 =0  ... (i)
ax2 +bx +c =0 .. (ii)
 since, Eq(i) has imaginary roots, So eq (ii) will also have both roots same as eq (i)
thus,

straight a over 1 space equals space straight b over 2 space equals space straight c over 3
Hence, a:b:c  is 1:2:3

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