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MATHMAA

SECTION - A

1) c. 150

Explanation:-

LCM(a,b) = $$\large \frac{a*b}{HCF(a,b)}$$

= $$\large \frac{1800}{12}$$

= 150

Therefore the LCM(a,b) = 150

Hence the correct option is 'c'.

2) b. Two decimal places

Explanation:-

$$\large \frac{33}{20}$$ = $$\large \frac{33}{2² 5}$$

= $$\large \frac{33*5}{2^{2}5^{2}}$$

= $$\large \frac{33*5}{(2*5)^{2}}$$

= $$\large \frac{33*5}{10^{2}}$$

Therefore the given fraction will terminate after two decimal places.

3) d. 16:81

Explanation:-

ratio of areas of similar triangles = square of ratios of its corresponding sides

= $$\large \frac{4^{2}}{9^{2}}$$

= $$\large \frac{16}{81}$$

Therefore the ratio of area of given similar triangles is 16:81

Hence the correct option is 'd'.

4) c. 1

Explanation:-

tan10° tan75° tan15° tan80° = tan10° tan(90-15)° tan15° tan(90-10)°

= tan10° cot10° tan15° cot15°

= 1*1

= 1

Therefore tan10° tan75° tan15° tan80° = 1.

Hence the correct option is 'c'.

5) a.3

Explanation:-

148x + 231y = 527    ---------(1)

231x + 148y = 610    ---------(2)

(1)+(2)

379(x+y) = 1137

x+y = $$\large \frac{1137}{379}$$

= 3

Therefore x+y = 3.

Hence the correct option is 'a'.

6) b. x² - 3x + 2

Explation:-

If the sum of the roots of a quadratic equation be 'a' and product of the roots is 'b' then the equation formed by them is

x² - ax + b = 0

Here, a = 3 and b = 2

Therefore the equation formed is

x² - 3x + 2

Hence the correct option is 'b'.

7) b. cos60°

Explanation:-

2cos²30° - 1 = 2($$\large (\frac{√3}{2})^{2}$$ - 1

= 2($$\large \frac{3}{4}$$) - 1

= $$\large \frac{3}{2}$$ - 1

= $$\large \frac{3-2}{2}$$

= $$\large \frac{1}{2}$$

= cos60°

Therefore 2cos²30° - 1 = cos60°

Hence the correct option is 'b'.

8) c. 22

Explanation:-

3median = mode + 2mean

Here, mode = 18 and mean = 24

3median = 18 + 2(24)

median = $$\large \frac{66}{3}$$

= 22

Therfore median = 22.

Hence the correct option is 'c'.