21)Which of the following equation is not a linear equation
22)If x2+kx+1=0 has a root x=1 then k =
23)If the roots of the quadratic equation ax2 + bx+c=0 are sinα and cosα, then 
= …….
B)
Explanation:If the roots of (ax^2 + bx + c = 0) are (sin α) and (cos α), then (1 + 2 = ?)
Given roots: (sin α + cos α = –) and (sin α cos α = $\frac{c}{a}).
Using the identity:
sin2 α + cos2 α = 1 ⇒ (sin α + cos α)2 – 2 sin α cos α = 1
Substitute:
\[ \left(-\frac{b}{a}\right)^2 – 2\left(\frac{c}{a}\right) = 1 ⇒ \frac{b^2}{a^2} – \frac{2c}{a} = 1 \] Rearrange:
\[ 1 + 2\frac{c}{a} = \frac{b^2}{a^2} \]
= …….
A) 
B) 
C) a2
D) b2
View Answer
B)
Explanation:If the roots of (ax^2 + bx + c = 0) are (sin α) and (cos α), then (1 + 2
= ?)Given roots: (sin α + cos α = –
) and (sin α cos α = $\frac{c}{a}).Using the identity:
sin2 α + cos2 α = 1 ⇒ (sin α + cos α)2 – 2 sin α cos α = 1
Substitute:
\[ \left(-\frac{b}{a}\right)^2 – 2\left(\frac{c}{a}\right) = 1 ⇒ \frac{b^2}{a^2} – \frac{2c}{a} = 1 \] Rearrange:
\[ 1 + 2\frac{c}{a} = \frac{b^2}{a^2} \]
24)If the system of equation 3x-2y-7=0 and kx+2y+11=0 has unique solution then …….
25)If 7x-5y=2 and 3x+y=4, then x=
26)The distance between the points (0, 0) and (5,12) is
27)If the slope of the line through (x,5) and (5,2) is 3, then the value of x is
28)If △ABC~△PQR, ∠A=32°, ∠R=65° then ∠B=
29)The angle in the minor segment is
30)In the figure ∠BAO=30°, ∠BCO=40° then ∠AOC=
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