List of practice Questions

What is the value of \(x\)?
(1) \(x^2 − 5x + 4 = 0\)
(2) \(x\) is not prime.

If both \(ABDC\) and \(CPDFE\) are parallelograms, what is \(q + r\)?
(1) r = 70◦
(2) p = 110◦

If the yield per hectare of sugar is 3.86 tons, what is the ratio of area employed to produce sugar in Bihar to Gujarat?
If these five states constitute 77% of the country’s wheat production and 23% of the country’s wheat consumption is imported, what is the amount of wheat imported in 1998?
If sugar costs Rs. 700 per ton and wheat costs Rs. 400 per ton, what was the total worth of sugar and wheat production in India (for the five states)?

If Tamil Nadu registers an annual increase of 22% in rice production, what was the rice production in Tamil Nadu in 1998?

The year in which the expenses of XPL Electronics are highest is:
What is the ratio of total wheat production in the five states to total sugar production?
By how much percentage has the net profit dropped in 1996?
If XPL sold 20,000 units in both 1998 and 1999, by what percentage has the price per unit changed?
Which year showed the maximum percentage increase in sales?

What is the net profit percentage of XPL in 1998?

In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo. Find the total number of animals.

If \( \log (0.57) = -0.244 \), then the value of\(\log 57 + \log (0.57) + \log \sqrt{0.57}\) is:

A and B throw with one die for a stake of Rs. 11 which is to be won by the player who first throws a 6. If A has the first throw, what are their respective expectations?
A train crosses a platform 100 metres long in 60 seconds at a speed of 45 km/hr. The time taken by the train to cross an electric pole is:
If \( x = 1 + 2a + 3a^2 + 4a^3 + \ldots \) (\(|a| < 1\)) and \( y = 1 + 3b + 6b^2 + \ldots\) (\(|b| < 1\)), then find \( 1 + ab + (ab)^2 + (ab)^3 + \ldots \) in terms of \(x\) and \(y\).

\(M\) is the centre of the circle. \(l(QS) = 10\sqrt{2}\), \(\ell(PR) = \ell(RS)\) and \(PR \perp QS\). Find the area of the shaded region. (\(\pi = 3\))}

There are three coplanar parallel lines; if any \(p\) points are taken on each of the lines, then find the maximum number of triangles with the vertices of these points.
Two vertical lamp-posts of equal height stand on either side of a road 50 m wide. At a point \(P\) on the road between them, the elevation of the tops of the lamp-posts are \(60^\circ\) and \(30^\circ\). Find the distance of \(P\) from the lamp-post which makes angle of \(60^\circ\).
A 20 litre vessel is filled with alcohol. Some of the alcohol is poured out into another vessel of equal capacity, which is then completely filled by adding water. The mixture thus obtained is then poured into the first vessel to capacity. Then \(6\frac{2}{3}\) litres is poured from the first vessel into the second. Both vessels now contain an equal amount of alcohol. How much alcohol was originally poured from the first vessel into the second?
A person closes his account in an investment scheme by withdrawing Rs. 10,000. One year ago he had withdrawn Rs. 6000. Two years ago he had withdrawn Rs. 5000. Three years ago he had not withdrawn any money. How much had he deposited approximately at the time of opening the account 4 years ago, if the annual simple interest rate is 10%?
A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 min; 80 tonnes would sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing so that she may just reach the shore as she begins to sink.
If \( f\left(x + \frac{y}{8}, y - \frac{x}{8}\right) = xy \), then \( f(m,n) + f(n,m) = 0 \) is true:
In a 400 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slowest runner reach the same point at the end of the 5th minute for the first time after the start of the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?