List of practice Questions

A train covers a certain distance at 60 km/h and returns at 40 km/h. The average speed for the entire journey is:
Pointing to a photograph, Ramesh says, ``She is the daughter of the only son of my grandfather.'' How is the woman related to Ramesh?
If all ZEBRAs are ANIMALs and some ANIMALs are PETs, which of the following is definitely true?
A sum of money becomes 4 times itself in 20 years at compound interest. In how many years will it become 16 times itself at the same rate?
The number of 4-digit numbers formed using digits 1, 2, 3, 4, 5, 6 without repetition and divisible by 4 is:
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.
Draw a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2). Also, find its area.
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin.Find vertices of the triangle.

Find the distance between P(x1,y1) and Q(x2,y2) when: (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Solve the given inequality for real\(x:\frac{ x}{3} > \frac{x}{2} +1\).

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the center. Find the height of the arch at a point 1.5 m from one end.

Solve the given inequality for real \(x: \frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}\).

Solve the given inequality for real\(x: \frac{1}{2}(\frac{3x}{5}+4) ≥ \frac{1}{3}(x-6)\).

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.
Solve the given inequality for real x: 2(2x + 3) - 10 < 6 (x - 2).
Solve the given inequality for real x: 37 – (3x + 5) ≥ 9x – 8(x – 3)
Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Solve the given inequality for real\(x: \frac{x}{4} < \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}\).