MATHS TEST PAPER
1) IF the quadratic equations ax2 +2cx +b =0 and ax2 +2bx +c=0 have a common root , then a+4b + 4c =
1) -2 2) -1 3) 0 4) 1
2) if A , G , H represents arithmetic mean , geometric mean , harmonic mean between two unequal positive no.s. then equation Ax2 - |G| x ? H= 0 has
1) both roots r fractions 2) at least one root which is negative fraction
3) exactly one positive root 4) at least one root integer.
3) if 0<a<b<c, and the roots c , d of the equation ax2 +bx +c =0 are non real complex no.s, then
1) |c| = |d| 2) |c|>1 3) |d| <1 4) none
4) If x2 - 11x + a and x2 - 14x + 2a have a common factor , then a = to ...
1)0,8 2)5,24 3)0,24 4)1,2
5) )The no. of values of k for wich the EQUATION x2 - 3x + k = 0 has 2 distinct roots lying in the interval (0,1)are...
1)3 2)2 3)infinite 4)no value of k
6) for any real x , the erxpression 2(k-x)[x + sqrt(x2 + k2)] can not exceed??
1 ) k2 2) 2k2 3) 3k2 4) 4k2
7) the quadratic equation whose root are the AM and HM between the roots of the equation ax2 +bx +c = 0 is
1) abx2+(b2+ac)x +bc=0 2) 2abx2 + (b2+ 4ac)x+ 2bc =0
3) 2abx2 + (b2 +ac)x +bc =0 4) none.
8) If the ratio of the roots of the =qn x2 + px + q = 0 be = to the ratio of roots of x2 + tx + m = 0 , then
1)p2 m = q2 t 2)p m2 = q2 t 3)p2 t = q2 m 4)p2 m = t2 q
9) Two students while solving a quadratic equation in x with leading coeff. ' I ' , one copied the const. term incorrectly and got the roots 3 , 2 . the other copied the correct term (-6) , the correct roots are....
1) -2 , 3 2)-3 , 2 3)-6 , -1 4)-1 , 6
10) If 3 + i is a root of x2 + ax + b = 0 , where a,b belongs to R , then a equals to ....
1)3 2)-3 3)6 4 ) -6
FILL IN THE BLANKS :
11)IF THE ROOTS OF ax2 +bx +c =0 (a,b,c means real) are imaginary and a+c< b, then
4a+ c < ____________.
12) if (x2 -3x+2) is a factor of ( x4 ?px2 +q) , then p and q r respectively _____________.
13) if the roots of the equation x2 ? 2ax + a2 +a-3 =0 are real less than 3 , then a<_________.
14) the difference between the corresponding roots of the equations x2 +ax +b =0 and x2+bx +a=0 are same , then a+b = ______________.
15) the no. of quadratic equations which r unchanged by squaring their roots is_____________.