List of practice Questions

The cost price 15 articles is equal to the selling price of 20 articles. Find the loss percentage.

If point \(B(0, 1)\) is equidistant from points\( A(5, -3) \)and \(C(x, 6)\), then find the values of \( x\)

The heights of two right circular cones are in the ratio \(1 : 2\) and the circumferences of their bases are in the ratio \(3: 4.\) Find the ratio of their volumes.

The area of the region bounded by the line 2y = 5x +7, x-axis and the lines x - 1 and x -3 is :

If y = Asinx + Bcosx, Where A and B are constants, then \(\frac{d^2y}{dx^2}\) is equal to :

If xy = e^(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :

If f(x) is a function which is derivable in an interval 1 containing a point c, then match List I with List II.

List I		List II
A.	f(x) has second order derivate at x = c such that f'(c) = 0 and f'(c) < 0; then	I.	point of inflexion of f(x)
B.	Necessary condition for point x = c to be extreme point of f(x) is	II.	‘c’ is point of local minima of f(x)
C.	If f'(x) does not change its sign as x crosses the point x = c then it is called a	III.	c is a critical point of f(x)
D.	f(x) has second order derivate at x = c such that f'(c) and f'(c) > 0; then	IV.	‘c’ is point of local maxima of f(x)

Choose the correct answer from the options given below :

Which one of the following is not an Arithmetic progression ?

The price relatives and weights of a set of commodities are given as:

Commodity	P	Q	R
Price Relative	100	130	180
Weight	x	2x	y

If the sum of weights is 54 and index for the set is 130, then the values of x and y are

The simple interest of Rs 6500 for \(1\frac{1}{2}\) years at 10% is

If CE||DB, what is the value of x:

A man spends 60% of his income and saves the remaining. His income increases by 28% and his expenditure also increases by 30%. Find the percentage increase in his savings.

Area lying in first quadrant and bounded by the circle \(x^2+ y^2 = 9\) and the lines x = 1 and x = 3 is:

If\(|\vec {a}+\vec {b}|=15, |\vec {a}-\vec{b}| =10,|\vec a|=\frac{11}{2}\) then the value of |\(\vec b\)| is/are:

The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:

The straight line \( \frac{x+2}{3} = \frac{z-3}{ -2}, y-2 \) is

If set A has 5 elements and set B has 7 elements than number of one-one and onto mapping from A to B is:

A vector \(\overrightarrow{r}\) is inclined at equal angles to the three axes. If the magnitude of \(\overrightarrow{r}\) is \(3\sqrt3\) units, then the value of \(\overrightarrow{r}\) is:

The value of \(\int_0^3 |2x-6|dx\) is:

In a partnership, A invests one-fourth of the capital for one-third of the time, B invests one-third of the capital for one-fourth of the time and C invests the rest of the capital for the whole time. Out of a profit of ₹3,500, A's share is:

Match List I with List II

Choose the correct answer from the options given below:

The point on the curve y²=16x for which the y-coordinate is changing 2 times as fast as the x-coordinate is:

If Paasche's index number is 160 and Laspeyre's index number is 250, then Fisher's index number is:

In an examination the marks of six boys are 48, 59, 57, 37, 78, and 57 respectively. The average marks of all the six boys are :

If f(x) - 27x³ and g(x) = \((x)^{\frac{1}{3}}\), then gof(x) is :