The number of solutions of the equation12log3x + 1x&nbs

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

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

71.

Let α, β be the roots of x2 - x - 1 = 0 and Sn = αn + βn, for all integers n  1. Then, for every integer n  2

  • Sn + Sn - 1 = Sn +1

  • Sn - Sn - 1 = Sn +1

  • Sn - 1 = Sn +1

  • Sn + Sn - 1 = 2Sn +1


72.

If α, β are the roots of the quadratic equation x2 + px + q = 0, then the values of α3 + β3 and α4 + α2β2 + β4 are respectively

  • 3pq - p3 and p4 - 3p2q + 3q2

  • - p(3q - p2) and (p2 - q)(p2 + 3q)

  • pq - 4 and p4 - q4

  • 3pq - p3 and (p2 - q)(p2 - 3q)


73.

Let α, β denote the cube roots of unity other than 1 and α  β. Let S = n = 0302- 1nαβn. Then, the value of S is

  • either - 2w or - 2w2

  • either - 2w or 2w2

  • either 2w or - 2w2

  • either 2w or 2w2


74.

Let p (x) be a quadratic polynomial with constant term 1. Suppose p(x), when divided by x - 1 leaves remainder 2 and when divided by x + 1 leaves remainder 4. Then, the sum of the roots of p(x) = 0 is

  • - 1

  • 1

  • - 12

  • 12


Advertisement
75.

If z1 = 2 + 3i and z2 = 3 + 4i  be two points on the complex plane. Then, the set of complex number z satisfying z - z12 + z - z22 = z1 - z22 represnts

  • a straight line

  • a point

  • a circle

  • a pair of straight line


76.

If α and β are roots of x2 - x + 1 = 0, then the value of α2013 + β2013 is

  • 2

  • - 2

  • - 1

  • 1


77.

If α and β  B are the roots of the quadratic equation is, x2 + ax + b = 0, (b 0), then the quadratic equation whose roots are α - 1β, β - 1α, is

  • ax2 + a(b - 1)x + (a - 1)2 = 0

  • bx2 + a(b - 1)x + (b - 1)2 = 0

  • x2 + ax + b = 0

  • abx2 + bx + a = 0


78.

If α and β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac, then

  • α = 4β or β = 4α

  • α = - 4β or β = - 4α

  • α = 3β or β = 3α

  • α = - 3β or β = - 3α


Advertisement
Advertisement

79.

The number of solutions of the equation

12log3x + 1x +5 + logex + 52 = 1

  • 0

  • 1

  • 2

  • infinite


C.

2

Given equation is,

                   12log3x + 1x +5 + log3x + 52 = 1 12 . 112log3x + 1x +5 + 12log3x + 52 = 1                 loganb = 1nlogab         22log3x + 1x +5 + 12 . 2log3x + 5 = log33                          log3x + 1x +5 . x + 5 = log33                  logm + logn = logmn and lognn = 1 (x + 1)= 3          x = 2

So, only one soiution is possible.


Advertisement
80.

If sinα, cosα  be the roots of the equation x2 - bx + c = 0, Then, which of the following statements is/are correct?

  • c 12

  • b  2

  • c > 12

  • > 2


Advertisement