Instructions

For the following questions answer them individually

Question 21

In a figure, $$\triangle ABC$$ is a right angled triangle at $$C$$, semicircles are drawn on $$AC$$, $$BC$$ and $$AB$$'s diameter. Find the area of the shaded region.

Note: Figure not as per scale

Question 22

If both the roots of the equation $$x^{2}-4ax+3-3a+4a^{2}=0$$ exceed 2, then the value of a:

Question 23

Shankar Fertilizer Limited and Shah Fertilizer Limited purchased one packet of Phosphorus each at the same price. Later on GreenP Company purchased both the packets at equal price from Shankar Fertilizer Limited and Shah Fertilizer Limited. But the profit percentage of Shankar Fertilizer Limited was $$X$$ while that of Shah Fertilizer Limited was $$Y$$. Shah Fertilizer Limited calculated his profit on the selling price. Thus $$Y=45\frac{9}{20}\%$$. If the GreenP 20 Company sells one of the packets to Mehrauli Nursery at $$X\%$$ profit, then what is the cost price for Mehrauli Nursery. while GreenP Company purchased each of the Phosphorus packets at Rs. 330?

Question 24

ABCD is a rectangle in the clockwise direction. The coordinates of A are (1,3) and the coordinates of C are (5,1), the coordinates of vertices B and D satisfy the line $$y=2x+c$$, then what will be the coordinates of the mid-point of BC.

Question 25

$$ABC$$ is a triangle, $$\angle B=60^\circ, \angle C=45^\circ$$, BC is produced to / extended till D so that $$\angle ADB=30^\circ$$, then given $$\sqrt{3}=\frac{19}{11}$$ and $$BC \times CD=3^{4}\times 2^{3}\times\frac{11}{19}$$, what will be the square of the altitude from A to BC?

Question 27

The mean of the 29 observations is 337. If the first term is increased by 1, second term by 2 and so on. The new mean will be:

Question 29

The goods train between Bhilai to Lucknow without rakes can go upto the speed of 72km/hour, and the speed gets diminished by the quantity that varies as the square root of the number of wagons attached. If it is known that with 4 wagons the speed is 56 km/hour, the greatest number of wagons with which the engine can just move is:

Question 30

Mr. Shyam invested a sum of Rs. 2000 through Kitocoin trading app available on his mobile. The invested amount appreciated after 3 years by 10% at the compound rate of appreciation. This appreciated amount is equal to the amount that is the result of 3 years depreciation by a certain compound rate of depreciation from Rs.3917. Find the difference between the compound rate of appreciation and depreciation:

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