W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7
6/35
10/21
21/10
35/6
Correct answer is A
\(W ∝ U\\
W = KU\\
K = \frac{W}{U}\\
K = \frac{5}{3}\\
W = \frac{5}{3}U\\
\frac{2}{7} = \frac{5}{3}U\\
U = \frac{2}{7} \times \frac{3}{5}\\
U = \frac{6}{35}\)
A polynomial in x whose roots are 4/3 and -3/5 is?
15x2 - 11x – 12
15x2 + 11x – 12
12x2 - x – 12
12x2 + 11x – 15
Correct answer is A
If 4/3 and -3/5 are roots of a polynomial
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t?
\(\frac{p^2 t}{s^3}\)
\(\frac{p^3 t}{s^3}\)
\(\frac{p^3 t}{s^2}\)
\(\frac{p^ t}{s^3}\)
Correct answer is A
\(p =\sqrt{\frac{rs^3}{t}}\\=
p^2 =\frac{rs^3}{t}\\
tp^2 = rs^3\\
r = \frac{p^2 t}{s^3}\)
I.S∩T∩W=S
II. S ∪ T ∪ W = W
III. T ∩ W = S
If S⊂T⊂W, which of the above statements are true?
I and II
I and III
II and III
I, II and III
Correct answer is A
If S \(\subset\) T \(\subset\) W,
S \(\cap\) T \(\cap\) W = S is true since S \(\cap\) T = S and S \(\cap\) W = S.
S \(\cup\) T \(\cup\) W = W is also true. S \(\cup\) T = T and T \(\cup\) W = W.
However, to say that T \(\cap\) W = S is not very true mathematically. Instead, it is safe to say S \(\subset\) (T \(\cap\) W).
{5,10}
{5, 10, 15}
{2, 5, 10}
{5, 10, 15, 20}
Correct answer is A
X = {n(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}
Implies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}
Put X = 1, 2, 3, 4, and 5
Y = {5, 10, 15, 20, 25}
X \(\cap\) Y = {2, 5, 10, 17, 26} \(\cap\) {5, 10, 15, 20, 25}
= {5, 10}