Mathematics | Study Mode

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Question 2
A
zero 
B
C
D
Explanation.
Share Answer \(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)

\(\frac{6x}{5} - \frac{3}{5} = \frac{5x}{4} - \frac{3}{4}\)

\(\frac{6x}{5} - \frac{5x}{4} = \frac{3}{5} - \frac{3}{4}\)

\(\frac{24x - 25x}{20} = \frac{12 - 15}{20}\)

\(\frac{-x}{20} = \frac{-3}{20}\)

-20x = -60

x = \(\frac{-60}{-20}\)

x = 3

Correct Option:
D
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Question 3
A
\(\frac{1}{\sqrt{r}}\) 
B
\(\sqrt{r}\) 
C
\(\sqrt{r^2 + 1}\) 
D
\(\sqrt{r^2 - 1}\) 
Explanation.
Share Answer cos xo = \(\frac{1}{r}\); \(\sqrt{r^2 - 1}\)

By Pythagoras r2 = 12 + x2 - 1

x = \(\sqrt{r^2 - 1}\)

tan xo = \(\sqrt{r^2 - 1}\)

= \(\sqrt{r^2 - 1}\)

Correct Option:
D
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Question 4
A
x = 1, y = -2 
B
x = 1, y = 3 
C
x = -2, y = -1 
D
x = 4, y = -3 
Explanation.
Share Answer 3x - 2y = 7; Solve by elimination method

x + 2y = -3

3x - 2y = 7.....(i)

-3x + 6y = -9.....(ii)

-8y = 16

y = \(\frac{16}{-8} = -2\)

Put y = -2 into equation (i); 3x - 2y = 7

3x - 2(-2) = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

x = \(\frac{3}{3}\) = 1

Correct Option:
A
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Question 5
A
\(\frac{1}{12}\) 
B
\(\frac{5}{12}\) 
C
\(\frac{7}{2}\) 
D
\(\frac{11}{12}\) 
Explanation.
Share Answer set = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

multiple of 3 = 6, 9, 12, 15

multiple of 4 = 4, 8, 12

Prob(multiple of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4)

= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{2}\)

Correct Option:
C
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Question 7
A
11 
B
14 
C
16 
D
18 
Explanation.
Share Answer Volume of cylinder = \(\pi r^2 h\)

= \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18

= 11088cm3

1000cm3 = \(\frac{1}{1000}\) x 11088cm3

= 11.088

= 11

Correct Option:
A
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Question 8
A
B
C
12 
D
15 
Explanation.
Share Answer Each interior angle = \(\frac{360^o}{n}\)

45o = \(\frac{360^o}{n}\)

45on = 360o

n = \(\frac{360^o}{45}\)

= 8

Correct Option:
B
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Question 10
A
142cm2 
B
132cm2 
C
122cm2 
D
112cm2 
Explanation.
Share Answer A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120

Area of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\)

where s = \(\frac{a + b + c}{2}\)

= \(\frac{3 + 4 + 5}{2}\)

= \(\frac{12}{2}\)

= 6

Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\)

= \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6

Area of triangle faces = 2 x 6 = 12cm2

Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12

= 132cm2

Correct Option:
B
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