Correct Answer: C. 8y - 14x - 13 = 0

Correct Answer: C. 4

Correct Answer: D. 0

Explanation

\(\frac{1}{x^2 - 4} = \frac{P}{(x + 2)} + \frac{Q}{(x - 2)}\)

I = p(x - 2) + Q(x + 2)

Let x = 2

I = P(2 - 2) + Q(2+ 2)

I = -4Q

Q = \(\frac{1}{4}\)

Let x = -2

I = P(-2 - 2) + Q(-2 + 2)

I = -4p

P = \(\frac{1}{-4}\)

PQQ = - \(\frac{1}{4} + \frac{1}{4}\)

= 0

Correct Answer: D. \(\frac{1}{2}\)

Explanation

\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)

from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)

= \(\frac{15}{8} \times \frac{12}{5}\)

= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)

from denominator \(6\frac{3}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \times \frac{4}{3}\)

= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)

\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)

= \(\frac{1}{2}\)

Explanation

(a) \(\log_{10} (3x - 1) - \log_{10} 2 = 3\)

\(\log_{10} (\frac{3x - 1}{2}) = 3\)

\(\implies \frac{3x - 1}{2} = 10^{3} = 1000\)

\(\implies 3x - 1 = 2000\)

\(3x = 2000 + 1 = 2001\)

\(x = \frac{2001}{3} = 667\)

(b)

\(\therefore \sqrt{\frac{0.8972 \times 3.536}{0.00249}} = 35.70\)

Correct Answer: C. 50%

Correct Answer: B. 3/2, 3, 6,

Explanation

\(T_n = 3. 2^{n - 2} \\

T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \\

T_1 = \frac{3}{2} \)

\(T_2 = 3. 2^{2 - 2} \\

T_2 = 3. 2^0 = 3\)

\(T_3 = 3. 2^{3 - 2} = 3. 2^1 \\

T_3 = 6\)

The first 3 terms of the sequence are \(\frac{3}{2}\), 3 and 6.

Correct Answer: B. y - x

Explanation

What must be added to 2x - 3y = Difference between x - 2y and 2x - 3y

x - 2y - 2y - (2x - 3y); x - 2y - 2x + 3y

= x - 2x + 3y - 2y

= y - x

Correct Answer: D. 6434

Correct Answer: D. 28000

Explanation

No. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\)

= \(\frac{800 \times 700 \times 500}{10 \times 1000}\)

= \(\frac{28000 0000}{10000}\)

= 28000