If the quadratic equation ax2+bx+c=0 if a and c are of opposite signs and b is real,then roots of the equation are
Real and distinct
Real and equal
imaginary
Both roots positive
The number having two digits such that it is 4 times the sum and three times the product of its two digits are
8
16
24
32
The least integral value of x for which 33-x(2+3x)>0 is
-11
-3
-2
-1
If the roots of x2+bx+c=0 are two consecutive integers then b2-4c=
0
1
2
3
3x-5x2+12 has maximum at x=
2/5
-2/5
3/10
-3/10
I:If α,β are the roots of the equation ax2+bx+c=0 then the quadratic equation whose roots are α+β,αβ is a2x2+a(b-c)x-bc=0 II:If α,β are the roots of 9x2+6x+1=0 then the equations with the roots 1/α,1/β is x2+6x+9=0
only I is true
only II is true
both I and II are true
neither I nor II true
I: The equation of the line parallel to 2x+3y-5=0 and passing through the point (3, -4) is 2x+3y-13=0 II: The equation of the line perpendicular to 2x+3y-5=0 and passing through the point (3, -4) is 3x-2y- 17=0
Only I is true
Only II is true
Both I and II are true
Neither I nor II are true
If the two equations x2-cx+d=0 and x2-ax+b=0 have a common root and the second equation has equal roots,then
b+d=ac
2(b+d)=ac
b+d=2ac
(b+d)2=a+c
The solution set of x2>4x-5 is
(-∞,1-√2][1+√2,∞)
R
(-1,1/2)
[-1,1/2]
The extreme value of x2-5x+6 is
1/4
-1/4
1/2
-1/2
If x4 then the value of x2-7x+12 is
Zero
positive
negative
not determined
If x2+4y2-8x+12=0 is satisfied by real values of x and y then y must lies between
2,6
2,5
-1,1
-2.-1
x2-2x+10 has minimum at x=
If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=
-8/9
8/9
4/9
-4/9
If the roots of x2-2(5+2k)x+3(7+10k)=0 are equal then k=
1/2,1
-1/2,1
2,1/2
2,-1/2
A number consists of two digits whose product is 30.If the digits are interchanged the resulting numbers will exceed the previously by 9.The number is
56
54
38
28
If α,β are the roots of ax2+bx+c=0 then (α/β – β/α)2=
b2(b2-4ac)/c2a2
b2(b2-4ac)/ca3
b2(b2-4ac)/a4
b2(b2-4ac)/c4
The cost of a cloth piece is Rs.35/-.If the length of the cloth piece is 4 metres more and each metre costs Rs.1/- less,the cost would remain unchanged.The length of the cloth piece is
10 metres
12 metres
15 metres
20 metres
If α, β are different values of θ satisfying the equations 5 cos θ+12 sin θ=11 then the value of sin (α+β)=
119/120
5/12
120/169
12/5
If x≠3/2 then the value of 4x2-12x+9 is
If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=
13/17
17/13
-17/13
-13/11
If xy+2x-3y-k is resolvable into two linear factors then k=
4
6
-5
The maximum value of a2-abx-b2x2 is
5a2/4
a2/2
a
-a
If A,B,C are the minimum value of x2-8x+17,2x2+4x-5,3x2-7x+1 then the ascending order of A,B,C is
A,B,C
B,C,A
C,A,B
B,A,C
If 4 < x < 8 then the value of 12x-x2-32 is
If x2+ky2+x-y is resolvable into two linear factors then k=
If ax2+bx+c=0 and bx2+cx+a=0 have a common root and a≠0 then a3+b3+c3/abc=
9
If the system of equations x + y + z =6, x + 2y + 3z=10 has no solution then λ=
5
If b2-4ac>0,then the graph of y= ax2+bx+c
Cuts x-axis in two real points
Real and Equal
Lies entirely above the x-axis
Cannot be determined
The quadratic equations x2 – 6xa = 0 and x2 – cx + 6 = 0 and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is