List of practice Questions

Amit can do a task in 10 days and Bhanu can do the same task in 40 days. In how many days will the task be completed if they work together ?

If \(f(x)=\begin{cases} \frac{1-\cos4x}{x^2} & x\ne0 \\ k & x=0 \end{cases}\) is continuous at x = 0, then the value of k is :

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then

If \(\vec{a}\) and \(\vec{b}\) are two non zero vectors such that \(|\vec{a}|\)=10, \(|\vec{b}|=2\) and \(\vec{a}.\vec{b}=12\), then value of \(|\vec{a}\times\vec{b}|\) is :

A shopkeeper bought an item for ₹600 and marked on it 50% higher than its cost price. He allowed 20% discount on it. Find his profit percentage.

Three partners A, B and C shared the profit in a business in the ratio 6:9:10 respectively. If A,B and C invested the money for 12 months, 7 months and 5 months respectively, then the ratio of their investment is:

A bike costing ₹120000 has a scrap value of ₹30000. If the book value of the bike at the end of third year is ₹90000, then the useful life of the bike is,

The perimeter of one face of a cube is 24cm, its volume must be :

The perimeter of a square and a regular hexagon are equal. The ratio of the area of the hexagon the area of the square is :

Work done by A in one day is half of the work by B in one day. Work done by B is half on the work done by C in one day. If C alone can do the work in 7 days, then in how many days can A, B and C together complete the work ?

Mean, Median and Mode of a data are related by the relation

If \(\frac{x}{(b + c)(b + c - 2a)} = \frac{y}{(c - a)(c + a - 2b)} = \frac{z}{(a - b)(a + b - 2c)}\), then the value of \(x + y + z\) is:

The volume of a sphere of radius r is obtained by multiplying its surface area with :

If the present value of a perpetuity of ₹600 payable at the end of every six months is ₹18000, then the rate of interest is:

The effective rate equivalent to a nominal rate of 8% per annum compounded semi-annually is:

The region represented by the system of inequalities x, y≥0, y≤8, x + y≤4 is:

The interval on which the function \(f(x)=2x^3 +12x^2 +18x-7\) is decreasing, is:

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2 \lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:

Which index number is used to compare cost of living at two different cities?

The set of value of \(x\) for which the angle between the \(\overrightarrow a = 2x²\hat i + 4x \hat j + \hat k\) and \(\overrightarrow b =7\hat i-2\hat j + x\hat k\) is obtuse is :

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is:

Match List I with List II

Choose the correct answer from the options given below:

A person buys a flat for which he makes down payment of ₹7,50,000 and the balance is to be paid in 10 years by monthly instalments of ₹22,000 each. If the bank charges interest at the rate of 12% per annum, then the actual price of the flat using flat rate system is:

If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:

Two bags of iron ore weight 180 kg 250 gm and 270 kg 50 gm respectively. How much iron ore (in gm) must be taken out from the first bag and added to the second bag so that weight of the first bag may then be two-third of the second bag?