Mathematics (2017) | Study Mode

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Question 41
A

9

B

-9

C

6

D

-6

Explanation

x * y is an operation on 3x + 2y - 1

Find 3A - 1

x = 3, y = -1

3 * - 1 on 3x + 2y - 1

3(3) + 2(-1) -1

= 9 - 2 - 1

= 6


Correct option: C
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Question 42
A

3-Feb

B

2-Jan

C

-1

D

3-Feb

Explanation

Gradient of line joining points (3, 2), (1, 4)

Gradient = \(\frac{\text{Change in Y}}{\text{Change in X}}\)

= \(\frac{y_2 - Y_1}{x_2 - x_1}\)

(X1, Y1) = (3, 2)

(X2, Y2) = (1, 4)

Gradient = \(\frac{4 - 2}{1 + 3}\)

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

= -1


Correct option: C
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Question 43
A

4a

B

\(\frac{1}{8a}\)

C

8a

D

\(\frac{1}{4a}\)

Explanation

(3-64a3)\(^{-1}\)

\(\frac{1}{(3-64a^3)}\)

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


Correct option: D
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Question 44
A

1.03

B

0.07

C

0.03

D

1

Explanation

0.4, -0.4, 0.3, 0.47, -0.53, 0.2, -0.2

Range is the difference between the highest and lowest value

i.e Highest - Lowest

- 0.53, -0.4, -0.2, 0.2, 0.3, 0.4, 0.47

0.47 is the highest

- 0.53 is the lowest

- = 0.47 - (- 0.53)

-0.47 + 0.53

= 1.0


Correct option: D
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Question 45
A

4

B

3

C

2\(\frac{2}{3}\)

D

3 \(\frac{2}{3}\)

Explanation

1 - (\(\frac{1}{5}\) + 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))

1 - (\(\frac{1}{5}\) \(\times\) \(\frac{5}{3}\)) + (5 + \(\frac{5}{3}\))

1 - \(\frac{1}{3}\) + \(\frac{20}{3}\)

= \(\frac{22}{3}\)


Correct option: D
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Question 46
A

4x3 - 8x2 + 5x + 3

B

-4x3 + 8x2 - 5x + 3

C

-4x3 - 8x2 + 5x + 3

D

4x3 + 8x2 - 5x + 3

Explanation

(2x2 - x + 1) \(\times\) (3 - 2x);

3(2x2 - x + 1) - 2x (2x2 - x + 1)

6x2 - 3x + 3 - 4x3 + 2x2 - 2x

-4x3 + 8x2 -5x + 3


Correct option: B
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Question 47
A

1, - 2

B

- 2, n = 1

C

\(\frac{-2}{5}\), 1

D

\(\frac{2}{3}\)

Explanation

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n-6

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)


\(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\)

\(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\)

= \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\)

= \(\frac{0 - 4 \sqrt{6} - 6}{5}\)

= \(\frac{10 - 5 \sqrt{6}}{5}\)

= - 2 + -6

- m + n\(\sqrt{6}\) = - 2 + -6

m = - 2, n = 1


Correct option: B
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Question 48
A

\(\frac{-5}{3}\)

B

\(\frac{-2}{3}\)

C

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

D

\(\frac{5}{2}\)

Explanation

\(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) = \(\frac{\beta -\alpha}{\alpha \beta}\)

3x2 + 5x + 5x - 2 = 0.

Sum of root = +

Product of root =

x2 + \(\frac{5x}{3}\) - \(\frac{2}{3}\) = 0

= - \(\frac{-2}{3}\)

+ = \(\frac{5}{3}\)

- \(\frac{\alpha + \beta}{\alpha \beta}\) = - \(\frac{\frac{5}{3}}{\frac{2}{3}}\)


= - \(\frac{2}{3}\) \(\times\) \(\frac{3}{3}\)

= \(\frac{5}{2}\)


Correct option: D

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