CTET Solved Paper - UPTET Feburary 2014 Paper2
116. If (x - 2) is a factor of x3 + ax2 + bx + 16 and b = 4a, then respective values of a and b are
- Option : C
- Explanation : Let f (x) = x3 + ax2 + bx + 16
Since, (x - 2) is a factor of f (x)
∴ f (2) = 0
i.e. 8 + 4a + 2b + 16 = 0
⇒ 8 + 4a + 8a + 16 = 0 [as b = 4a]
∴ a = -2
and b = 4a-8
⇒ b=4(-2)=-8
⇒ a = -2, b = -8.
117. If the area of an equilateral triangle is 16√3 cm2, then the perimeter of the triangle is
- Option : B
- Explanation : Let side of equilateral triangle = a cm.
∴ √3/4 a2 = 16√3
⇒ a = 8cm.
∴ Perimeter = 3a = 24cm.
- Option : C
- Explanation : P (x) = (x + 1)· g (x) + 19,
where g(x) is the quotient
⇒ P (x) - 19 = (x+l)· g (x)
i.e. (x+l) divides P (x) - 19 completely.
i.e. P (-1) - 19 = 0
(-1)4 - 2(-1)3 + 3(-1)2 - a (-1) + 3a - 7 + 19 = 0
1 + 2 + 3 + a + 3a - 7 -19 = 0
⇒ 4a = 20
⇒ a = 5.
