Instructions

For the following questions answer them individually

Question 61

Alloy A contains metals x and y in the ratio 5 : 2 and alloy B contains these metals in the ratio 3 : 4. Alloy C is prepared by mixing A and in theratio 4 : 5. The percentageofy in alloy C is:

Question 62

Keshav, Surjeet and Thomasstarted a business with investments in the ratio 2 : 3 : 4. The ratio of their period of investments is 5 : 6 : 9. Twenty percentof the profit was spent on rent and maintenanceof the office. Remaining profit was distributed among themselves.If the difference in the shares of profit of Keshav and Surjeet is â‚¹7264, then how muchis the total profit (in â‚¹)?

Question 63

If $$a + b + c = 0$$, then what is the value of $$\frac{(b + c)^2}{bc} + \frac{(c + a)^2}{ca} + \frac{(a + b)^2}{ab} ?$$

Question 64

If $$x - \frac{1}{x} = \sqrt{77}$$, then one of the values of $$x^3 + \frac{1}{x^3}$$ is:

Question 65

The average daily production of toys in a factory in the month of December is 512. If the average production during first 20 days is 515 and that of the last 13 days is 510, then what is the average of production on 19 and 20 December?

Question 66

A sum of money was lentin two parts in the ratio 4 : 5 for 4 years and 5 years respectively, both at the rate of 8% per annum simple interest. If the difference between the interests earned from the twoparts is â‚¹ 4680, then what was the total sum lent(in â‚¹)?

Question 67

A shopkeeper bought a machine for â‚¹4600 and spent â‚¹500 on its repairs and transport. He marked the machine at 8% above the over all cost price. If he sold the machine for â‚¹4681.80 after giving x% discount, then the value of x is:

Question 68

In a circle with centre O, AB and CD are parallel chords on the opposite sides of a diameter. If AB = 12 cm, CD = 18 cm and the distance between the chords AB and CD is 15 cm, then find the radius of the circle (in cm).

Question 69

If $$\sin(A + B) = 1$$ and $$\cos(A - B) = \frac{\sqrt{3}}{2}, A + B \leq 90^\circ$$ and $$A > B$$, then the value of $$\frac{5 \sin^2 B + 4 \tan^2 A}{2 \sin B \cos A}$$ is:

Question 70

If $$\sin^6 \theta + \cos^6 \theta = \frac{1}{3}, 0^\circ < \theta < 90^\circ$$, then what is the value of $$\sin \theta \cos \theta$$?

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