Question: 01
[math]\sqrt x=\sqrt{2x-1}[/math] then x =
Option
1) 1 2) 4 3) 2 4) 3
Solution
Question: 02
The sum of roots of 6x2 – 2022 = 0
Option
1) 2022 2)1011/3
3) 6 4) 0
Solution
Question: 03
The discriminant of the equation 3x2-2x+(1/3)=0
Option
1) 0 2) -2
3) 3 4) -3
Solution
Question: 04
The quadratic equation with rational coefficients whose one of the roots is [math]\left(2-\sqrt3\right)[/math] is
Option
1) x2-4x+1=0 2) x2+4x-1=0
3) x2-4x-1=0 4) x2-2x-3=0
Solution
Question: 05
If the product of two consecutive positive integers is 306, then the numbers are
Option
1) 14, 15 2) 15, 16
3) 16, 17 4) 17, 18
Solution
Question: 06
If the roots of (b-c)x2+(c-a)x+(a-b)=0 are equal, then
Option
1) 2a=b+c 2) 2b=a+c
3) 2c=a+b b 4) a=b+c
Solution
Question: 07
[math]\left(1-\frac{1}{1+x}\right)\div\left(\frac{1}{1+x}\right)=[/math]
Option
1) 1 2) x2
3) 2x 4) x
Solution
Question: 08
If D = 0, then the roots of ax2+bx+c=0 are
Option
1) [math]\frac{b}{2a},\frac{b}{2a}[/math]
2) [math]\frac{-b}{2a},\frac{-b}{2a}[/math]
3) [math]\frac{c}{2a},\frac{c}{2a}[/math]
4) [math]\frac{-a}{2b},\frac{-a}{2b}[/math]
Solution
Question: 09
If px2+qx+r=0 has equal roots, then r =
Option
1) q2/2p 2) q/2p
3) -q2/4p 4) q2/4p
Solution
Question: 10
The sum of squares of the roots of x2+8x+15=0 is
Option
1) 30 2) 34
3) 40 4) 44
Solution
Question: 11
If α,β are the roots of 5x2+5x+6=0 then (1+α)(1+β)=
Option
1) 4/5 2) 3/5
3) 6/5 4) 6/5
Solution
Question: 12
If α,β are the roots of 5x2+5x+7=0 then
Option
1) α+β=-1
2) αβ=7/5
3) (1+α)(1+β)=7/5 4)
4) αβ=-7/5
Solution
Question: 13
If x2-2x+1=0 , then
Option
1) [math] x+\frac{1}{x}=2[/math]
2) [math] x-\frac{1}{x}=0[/math]
3) [math] x^2+\frac{1}{x^2}=2[/math]
4) [math] x^4+\frac{1}{x^4}=2[/math]
Solution
Question: 14
If [math]x=\sqrt{3+\sqrt{3+\sqrt{3+……\infty}}}, [/math]then
Option
1) x2-x+3=0
2) x2+x+3=0
3) x2-x-3=0
4) x2+x+3=0
Solution
Question: 15
If one root of the polynomial f(x)=5x2+3x+k is reciprocal of the other, then the value of “k” is
Option
1) 0 2) 5
3) 1/6 4) 6