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

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

1.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

  • 256

  • 220

  • 219

  • 219

286 Views

2.

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

3.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

  • 7 over 81 space left parenthesis 179 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 9 left parenthesis 99 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis
958 Views

4.

A ray of light along straight x space plus square root of 3 straight y end root space equals space square root of 3 get reflected upon reaching X -axis, the equation of the reflected ray is 

  • straight y equals space straight x plus square root of 3
  • square root of 3 straight y end root space equals space straight x minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
  • straight y space equals space square root of 3 straight x end root minus square root of 3
441 Views

Advertisement
5.

The number of values of k, for which the system of equations
(k+1) x + 8y = 4k
kx + (k+3)y = 3k -1
has no solution, is 

  • infinite 

  • 1

  • 2

  • 2

269 Views

Advertisement

6.

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

177 Views

Advertisement
7.

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

  • (-5,2)

  • (2,-5)

  • (5,-2)

  • (5,-2)

181 Views

8.

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

  • x= y= z

  • 2x =3y = 6z

  • 6x = 3y= 2z

  • 6x = 3y= 2z

207 Views

Advertisement
9.

Consider :
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.

  • Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I 

  • Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

  • Statement -I is True; Statement -II is False.

  • Statement -I is True; Statement -II is False.

289 Views

10. limit as straight x space rightwards arrow 0 of fraction numerator left parenthesis 1 minus cos space 2 straight x right parenthesis left parenthesis 3 plus cos space straight x right parenthesis over denominator straight x space tan space 4 straight x end fraction space is space equal space to space
  • -1/4

  • 1/2

  • 1

  • 1

188 Views

Advertisement