The equivalent of (10110.011)2 in base 10 is?
26.325
24.372
42.443
22.375
Correct answer is D
Using the expansion method on (10110.011)2
(1 * 24) + (0 * 23) + (1 * 22) + (1 * 21) (0 * 20) + (0 * 2−1) + (1 * 2−2) + (1 * 2−3)
(1*16) + 0 (1*4) + (1*2) + 0 + 0 + (1*14) + (1*18)
16 + 4 + 2 + (0.25 + 0.125)
22 + 0.375
(10110.011)2 = 22.37510
Calculate the median of 14, 17, 10, 13, 18 and 10.
12.5
13.5
13.2
14.5
Correct answer is B
When rearranged: 10, 10, 13, 14, 17, 18
median = 13+142
= 272 or 13.5
Find the equation of a straight line parallel to the line 2x - y = 5 and having intercept of 5
2x + y = 5
2x + y = -5
2x - y = -5
2x - y = 5
Correct answer is C
Condition for Parallelism means that their gradient value is same
line 2x - y = 5 is rearranged
As y = 2x - 5 from y = mx + c
: line 2x - y = 5 has the gradient of 2
A parallel line with gradient of 2 and intercept of 5
→ 2x - y = -5
Rearranged as y = 2x + 5
Find the limit of y = x3+6x−7x−1 as x tends to 1
9
8
0
7
Correct answer is A
x3+6x−7x−1:
When numerator is differentiated → 3x2 + 6
When denominator is differentiated → 1
: 3x2+61
substitute x for 1
3∗12+61 = 3+61
= 91
= 9
If sec2θ + tan2θ = 3, then the angle θ is equal to?
90º
30º
45º
60º
Correct answer is C
Given that sec2θ + tan2θ = 3
Where sec2θ = 1 + tan2θ
: 1 + tan2θ + tan2θ = 3
2tan2θ = 3 - 1
2tan2θ = 2
divide both sides by 2
tan2θ = 1
tanθ = √1
tanθ = 1
θ = tan−1 (1)
θ = 45º