MAT 2001

Instructions

For the following questions answer them individually

Question 51

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the two trees is

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Question 52

Rs 770 have been divided among A, B and C such that A receives 2/9th of what B and C together receive. Then A's share is

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Question 53

What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders are proportional ?

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Question 54

$$\frac{3\pi}{5}$$ radians is equal to

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Question 55

If $$\sin A : \cos A = 4 : 7$$, then the value of $$\frac{(7 \sin A - 3 \cos A)}{(7 \sin A+ 2 \cos A)}$$ is

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Question 56

A tree breaks due to storm and the broken part bends so that the top of the tree first touches the ground, making an angle of 30 with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is 10 m. The height of the tree is

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Question 57

If $$pqr = 1$$ then 

$$\left(\left(\frac{1}{(1 + p + q^{-1})}\right) + \left(\frac{1}{(1 + q + r^{-1})}\right) + \left(\frac{1}{(1 + r + p^{-1})}\right)\right)$$ is equal to

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Question 58

An edge of a cube measures 10 cm. If the largest possible cone is cut out of this cube, then the volume of the cone is

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Question 59

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is

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Question 60

If a and b are the roots of the equation $$x^2 - 6x + 6 = 0$$, then the value of $$a^2 + b^2$$ is

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