The distance s in metres covered by a particle in t seconds is s=32t2−3t. Find its acceleration.
1ms−2
2ms−2
3ms−2
4ms−2
Correct answer is C
The two time differentiation of distance with respect to time will give the acceleration.
s=32t2−3t
dsdt=v=3t−3
dvdt=a=3
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
40°
44°
45°
54°
Correct answer is C
2x+y=4≡y=4−2x⟹m1=−2
−3x+y+7=0≡y=−7+3x⟹m2=3
tanθ=m1−m21−m1m2=−2−31−(−2)(3)=−5−5=1
\tan \theta = 1 \implies \theta = 45°
Find the number of different arrangements of the word IKOTITINA.
30240
60840
120960
362880
Correct answer is A
IKOTITINA has 9 letters with 2Ts and 3Is. Therefore, the number of different arrangements
= \frac{9!}{2!3!} = \frac{9.8.7.6.5.4}{2} = 30240
2x + 3y + 6 = 0
3x - 2y - 6 = 0
-3x + 2y - 6 = 0
-2x + 3y - 6 =0
Correct answer is D
Equation of a straight line : y = mx + b
where m = the slope of the line
b = y- intercept
Given the two points (-3, 0) and (0, 2).
m = \frac{2 - 0}{0 - (-3)} = \frac{2}{3}
y = \frac{2}{3}x + 2 \implies 3y = 2x + 6
-2x + 3y - 6 = 0