Which of the following quadratic curves will not intersect with the x- axis?
y=2−4x−x2
y=x2−5x−1
y=2x2−x−1
y=3x2−2x+4
Correct answer is D
The criterion for the quadratic curve to intersect the x- axis is b2>4ac.
If 2log42=x+1, find the value of x.
-2
-1
0
1
Correct answer is C
2log42=x+1
log422=log44=1
x+1=1⟹x=0
8
6
-6
-8
Correct answer is B
Remainder for f(2) = 20.
f(2)=2(23)+22−3(2)+p=20
16+4−6+p=20
14+p=20
p=6
If f(x)=2x2−3x−1, find the value of x for which f(x) is minimum.
32
43
34
23
Correct answer is C
y=2x2−3x−1
dydx=4x−3=0 (At turning point)
4x=3⟹x=34
n + 1
2n + 1
3n + 1
4n + 1
Correct answer is B
Sn=n2(2a+(n−1)d=n2+2n
n(2a+(n−1)d=2n2+4n
2an+n2d−nd=2n2+4n
n2d=2n2
d=2
(2a−d)n=4n
2a−d=4⟹2a=4+d=4+2=6
a=3
Tn=a+(n−1)d
= 3+(n−1)2=3+2n−2=2n+1