List of top Mathematics Questions

If a=cos2α+isin2α and b=cos2β+isin2β then _______

If each observation of a Row data whose variance is σ² is multiplied by h, then the variance of the new set is

Match List-I and List-II

LIST I		LIST II
A.	Addition Theorem on probability	I.	\(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\)
B.	Binomial distribution	II.	\(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\)
C.	Baye's rule	III.	\(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\)
D.	Multiplication theorem on prob	IV.	\(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\)

Choose the correct answer from the options given below:

Consider the adjoining diagram: What is the minimum number of different colours required to paint the figure such that no two adjacent regions have same colour?

The integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}\)is

Given below are two statements
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below

If \(\overrightarrow F=y^2\hat{i}+xy\hat{j}+xz\hat{k}\) and C is the bounding curve of the hemisphere x²+y²+z²=9,z>0, oriented in the positive direction, then value of \(\int\limits_C \overrightarrow F\cdot d\hat{r}\) is

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

Given below are two statements
Statement I: Let G a finite group and H a subgroup of G. Then, the order of H is a divisor of the order of G. That is, |H| divides |G|
Statement II: Let a be an element in a finite group G. Then, O(a) divides |G|
In the light of the above statements, choose the most appropriate answer from the options given below

The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

Which of the following is incorrect?

The area of the region bounded by the curve x²=4y and the straight line x = 4y - 2 is

If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]²+[g(x)]² and h(5)=11, then h(10) =

The order of 16 in \((\mathbb{Z}_{24}, +_{24})\) is:

Function f(x)=(x+1)^cotx is continuous at x = 0, then the value of f(0) is

If \(u=cos^{-1}\frac{x+y}{\sqrt{x}+\sqrt{y}}\), then the value of \(x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}\) is

If income of A is 20% more than that of B, then income of B is how much percent less than that of A?

The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is

The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) is:

Which one of the following is not correct?

Let \(F: R^4 → R^3\) be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is

Which one of the following is wrong?

With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:

The sequence is