List of top Mathematics Questions

The integrating factor of \(sinx \frac{dy}{dx}+2ycosx=4\) is:

The area of the region bounded by the curve \(y^2 = 4x\), y -axis and the line\(y = 2\)  is

From a well shuffled pack of 52 cards, three cards are drawn one by one. The probability that the three cards are Jack, Queen and King respectively?

The present value of a perpetual income of x paybale at the end of each 6 months is ₹ 1,80,000. If the money is worth 5% compounded semi-annually, then the value of x is ₹:

\(2\tan^{-1} \frac12+\tan^{-1}\frac 17=\tan^{-1}x\), then the value of \(x\) is:

Match List I with List II

List I	List II
A. The region represented by \(x \geq 0, y \geq 0\)	I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)	II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)	III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)	IV. bounded

Choose the correct answer from the options given below:

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :

A sum of\( 10,000\) becomes \( 14,400\) on compound interest in \(2\) years. What is the rate of interest per annum?

If A is a skew-symmetric matrix of order n. then

The effective rate which is equivalent to stated rate of \(6\%\) compounded semiannually is:

Match List - I with List - II.

List - I	List -II
(A) \(P(\overline{A} \cap B)\)	(I)\(P(A)+P(B)\)
(B)\(P(A\cap \overline B)\)	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) \(P[(A\cap \overline B) \cup (\overline A \cap B)]\)	(III)\(P(B)-P(A\cap B)\)
(D)\(P(A\cup B)+ P(A\cap B)]\)	(IV)\(P(B)-P(A\cap B)\)

Choose the correct answer from the options given below:

The region R on the set \(A=\{x \in Z:0\leq x\leq 12\}\) , given by \(R=\{(a,b):|a-b|\)  is a multiple of 4 \(\}\)  is :

The prices and the quantities of three commodities are given are :

The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of \(x\) is:

The symbols that we use to represent number names are called a numerals. Children see numerals such as “6” in their everyday lives constantly. However, numerals are ---------- than quantities.

There are two values of a for which the determinant, \(\Delta =\begin{bmatrix}1& -2& 5\\[0.3em]0& a& 1\\[0.3em] 0& 4& 2a\\[0.3em] \end{bmatrix} = 86\), then the sum of these values of a is:

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

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

If \(e^y(x+2)=10\), then \(\frac{d^2y}{dx^2}\) is equal to:

If \(f(x)=-3x^2\), then f(x) is:

The value of \(∫(5x-2)^3\) dx is:

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:

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 :

The ratio of areas under the curves \(y=sinx \) and \(y=sin2x\) ,from \(x=0\) to  \( x=\frac{\pi}{3}\) is

The solution of the differential equation \(\frac{dy}{dx}=-\frac{x}{y}\) is:

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: