List of top Mathematics Questions

For any differentiable function y of x, (d²x)/(dy²)((dy)/(dx))³+(d²y)/(dx²)=

Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ y+alpha₂ z=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then

Evaluate (x+\frac1x)²+(x²+\frac1x²)²+(x³+\frac1x³)² up to n terms is

If the matrix beginbmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endbmatrix is singular, then λ=

If [x] denotes the greatest integer ≤ x and -1≤ x<0, 0≤ y<1, 1≤ z<2, then the value of the determinant beginvmatrix [x]+1 & [y] & [z]
[x] & [y]+1 & [z]
[x] & [y] & [z]+1 endvmatrix is

If z₁=\sqrt3+i\sqrt3 and z₂=\sqrt3+i, then the complex number ((z₁)/(z₂))⁵0 lies in the

The sum to n terms of the series \frac12+\frac34+\frac78+(15)/(16)+⋯ is

The arithmetic mean of numbers a,b,c,d,e is M. What is the value of (a-M)+(b-M)+(c-M)+(d-M)+(e-M)?

If sin⁻1((2a)/(1+a²)) -cos⁻1((1-b²)/(1+b²)) =tan⁻1((2x)/(1-x²)), then what is the value of x?

In a △ ABC, if (cos A)/(a)=(cos B)/(b)=(cos C)/(c), and the side a=2, then area of the triangle is:

If A and B are positive acute angles satisfying 3cos²A+2cos²B=4 and (3sin A)/(sin B)=(2cos B)/(cos A), then the value of A+2B is equal to:

The general solution of the equation sin 2x + 2sin x + 2cos x +1 =0 is:

Let f(x)=dfracax+bcx+d, then f∘ f(x)=x, provided that:

The general solutions of $\sin^2x\cdot\sec x=\tan x-\sin x+1$ are

Given $X\sim B(n,p)$, if $E(X)=4$ and $\text{Var}(X)=2.4$, then $n=$

The eccentricity of a rectangular hyperbola is

If the p.m.f. of a random variable $X$ is given by
\[ \begin{array}{c|ccc} x & 0 & 1 & 2 \\ P(X=x) & q^2 & 2pq & p^2 \end{array} \] then, the standard deviation of $X$ is (given $p+q=1$)

The c.d.f. $F(x)$ of a discrete random variable $X$ is given by
\[ \begin{array}{c|cccccccc} X & -3 & -1 & 0 & 1 & 3 & 5 & 7 & 9 \\ F(X) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \end{array} \] Then $P(X=3)=$

The direction ratios of the line perpendicular to the lines having direction ratios $2,3,1$ and $1,2,1$ are

If $a,b,c$ are distinct positive numbers and the vectors $a\hat i+a\hat j+c\hat k,\ \hat i+\hat k$ and $c\hat i+c\hat j+b\hat k$ lie in a plane, then