Eamcet - Maths - Theory Of Equations Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
Start Test

   Time Left : 00 : 30    : 00

If m,n,k are rational and m=k+(n/k),then the roots of x2+mx+n=0 are

  

  

  

  

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

  

  

  

  

If α,β are the roots of 3x2-5x+7=0 then α3+β3=

  

  

  

  

The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is

  

  

  

  

The equation ax2+bx+c=0 (a,bR) and x3-2x2+2x-1=0 have two roots common.Then a+b must equal to

  

  

  

  

If 1,-1,3 are the roots of x3+Ax2+Bx+C=0 then the ascending order of A,B,C is

  

  

  

  

The equations whose roots are squares of the roots of x4+x3+2x2+x+1=0 is

  

  

  

  

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

  

  

  

  

If α,β,γ are the roots of 4x3-6x2+7x+3=0 then αβ+βγ+αγ=

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0,then Σα2(β+γ)=

  

  

  

  

If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=

  

  

  

  

The equation whose roots are 2√3-5 and -2√3-5 is

  

  

  

  

If cos 2x = (√2 + 1)(cos x - 1/√2) , cos x ≠ 1/2 then x belongs to

  

  

  

  

The multiple roots of x4-2x3+11x2-12x+36=0 are

  

  

  

  

If two roots of x3-4x2+x+6=0 are in the ratio 2:3 then the roots are

  

  

  

  

If the roots of ax3+bx2+cx+d=0 are in G.P then the roots of dx3-cx2+bx-a=0 are in

  

  

  

  

The equation of the lowest degree with rational coefficients having a root √2+√3+i is

  

  

  

  

If α,β,γ are the roots of x3+qx+r=0 then the equation whose roots βγ+1/α,γα+1/β,αβ+1/γ is

  

  

  

  

The equations whose roots are exceed by 2 than those of x4+x3-10x2+4x+24=0 is

  

  

  

  

The roots of the equation (b-c)x2+(c-a)x+(a-b)=0 are

  

  

  

  

If x4+4x3-2x2-12x+9=0 has a pair of equal roots then the roots are

  

  

  

  

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

  

  

  

  

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ1/α β=

  

  

  

  

If both the roots of the equation x2-6ax+2-2a+9a2=0 exceed 3,then

  

  

  

  

If ax2+2bx+c=0,a1x2+2b1x+c1=0 have a common root,then the roots of the equation (b2-ac)x2+(2bb1-ac1-a1c)x+(b12-a1c1)=0 are

  

  

  

  

If α+β+γ=1,α2+β2+γ2=2 and α3+β3+γ3=3,then α5+β5+γ5=

  

  

  

  

If α,β,γ are the roots of the equation x3-px2+qx-r=0,then α3β3γ3=

  

  

  

  

The value of a for which each one of the roots of x2-4ax+2a2-3a+5=0 is greater tan 2,are

  

  

  

  

If 12x2-10xy+2y2+11x-5y+k is resolvable into two linear factors then k=

  

  

  

  

If x2-3x+2 is a factor of x4-px2+q=0,then(p,q)=

  

  

  

  

Note:
  • Click the 'Submit Test' button given in the bottom of this page to Submit your answers.
  • Test will be submitted automatically if the time expired.
  • Don't refresh the page.