A polynomial is defined by f(x+1)=x3+px2−4x+2, find f(2)
-8
-2
2
8
Correct answer is C
Given: f(x+1)=x3+3x2−4x+2.
f(2)=f(x+1)⟹x+1=2;x=1
f(2)=13+3(1)2−4(1)+2=1+3−4+2=2
If (x + 1) is a factor of the polynomial x3+px2+x+6. Find the value of p.
-8
-4
4
8
Correct answer is B
If (x + 1) is a factor, then f(-1) = 0.
(−1)3+p(−1)2+(−1)+6=0
−1+p−1+6=0⟹p+4=0
p=−4
QRS is a triangle such that →QR=(3i+2j) and →SR=(−5i+3j), find →SQ.
8i + j
2i - j
-2i - 3j
-8i - j
Correct answer is A
→SQ=→SR+→RQ
→RQ=−→QR=−(3i+2j)=−3i−2j
→SQ=(−5i+3j)−3i−2j=−8i+j
Evaluate log10(13+14)+2log102+log10(37)
-3
0
56
1
Correct answer is B
log10(13+14)+2log102+log10(37)
13+14=712
= log10(712×22×37)
= log101=0
Given that sinx=−√32 and cosx>0, find x
300°
240°
120°
60°
Correct answer is A
In order to do this, simply find the option in the range where only the cos is +ve. This occurs in the range 270° \leq x \leq 360°.
Check: \sin 300 = - \sin 60 = \frac{-\sqrt{3}}{2}
\cos 300 = \cos 60 = \frac{1}{2}