Question: 01
If 5 is a root of x2-(K-1)x+10=0 , then the value of “K” is
Option
1) –8 2) 7
3) 8 4) 12
Solution
Question: 02
Which of the following is/are not quadratic equations?
Option
1) (x2+1)(x2-1)=0
2) (x-2)2+1=x2+8
3) x(x+1)+8=(x+2)(x-2)
4) x2-55x+75=0
Solution
Question: 03
If α,β are the roots of x2+2x+5=0 then
Option
1) α+β=-2
2) αβ=5
3) (α/β)+ (β/α)=(-6/5)
4) α+β=2
Solution
Question: 04
If 5x²-4x+3=1, then x=
Option
1) 1 2) 3 3) 8 4) 7
Solution
Question: 05
If the roots of x2+kx+12=0 are in the ratio 1:3, then the value of ‘k’ is
Option
1) 8 2) –7 3) 7 4) –8
Solution
Question: 06
If α and β are the roots of the equation ax2+bx+c=0 (a ≠ 0) then [math]\frac{1}{\alpha}+\frac{1}{\beta}=[/math]
Option
1) [math]\frac{b}{c}[/math]
2) [math]\frac{-b}{c}[/math]
3) [math]\frac{b}{a}[/math]
4) [math]\frac{-b}{a}[/math]
Solution
Question: 07
If α and β are the roots of the equation ax2+bx+c=0 (a ≠ 0) then α2+β2=
Option
1) [math]\frac{b^2-4ac}{a^2}[/math]
2) [math]\frac{b^2+4ac}{a^2}[/math]
3) [math]\frac{b^2-2ac}{a^2}[/math]
4) [math]\frac{b^2+2ac}{a^2}[/math]
Solution
Question: 08
If α and β are the roots of the equation ax2+bx+c=0 (a ≠ 0) then |α-β|=
Option
1) [math]\frac{-\sqrt{{4ac-b}^2}}{a}[/math]
2) [math]\frac{\sqrt{{4ac-b}^2}}{\left|a\right|}[/math]
3) [math]\frac{\sqrt{b^2+4ac}}{\left|a\right|}[/math]
4) [math]\frac{\sqrt{b^2-4ac}}{\left|a\right|}[/math]
Solution
Question: 09
If sinα and cosα are the roots of px2+qx+r=0, (p ≠ 0) , then the relationship among p,q and r is
Option
1) q2-p2=2pr 2) p2-q2=2pr
3) p2-r2=2qr 4) p2+q2=2qr
Solution
Question: 10
If p and q are the roots of x2+px+q=0 then
Option
1) p=1 2) p = 1or 0
3) p=-2 4) p=-2 or 0
Solution
Question: 11
The roots of the equation [math]x^{\sqrt x}=\left(\sqrt x\right)^x[/math] are
Option
1) 0 and 1
2) 0 and 4
3) 1 and 4
4) 0, 1 and 4
Solution
Question: 12
If [math]\left(7+4\sqrt3\right)^{x^2-8}+\left(7-4\sqrt3\right)^{x^2-8}=14[/math] then the value of x is
Option
1) [math]\sqrt7[/math]
2) 3
3) [math]-\sqrt7[/math]
4) –3
Solution
Question: 13
If α,β are the roots of x2+5x+k=0 and α2β+αβ2=-30 , then k= _____
Option
1) 8 2) -6 3) 12 4) 6
Solution
Question: 14
The altitude of a right angled triangle is 7cm less than its base. If the hypotenuse is 13cm , then the lengths of the other two sides are
Option
1) 7cm, 12 cm
2) 5cm, 12cm
3) 5cm, 7cm
4) 13cm, 7cm
Solution
Question: 15
If there are two numbers whose sum is 27 and product is 182, then the larger number is
Option
1) 15 2) 14 3) 12 4) 6