List of top Mathematics Questions

A die is thrown 10 times, the probability that an odd number will come up atleast one time is

Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let z = px + qy, where p, q > 0. Condition on p and q so that the minimum of z occurs at (3, 0) and (1, 1) is

The feasible region of an LPP is shown in the figure. If Z = 11x + 7y then the maximum value of Z occurs at

The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}\) and the plane 2x - 2y + z = 5 is

The distance of the point (1, 2, -4) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) is

If a line makes an angle of \(\frac{\pi}{3}\) with each of x and y-axis, then the acute angle made by z-axis is

The point (1, -3, 4) lies in the octant

If \(|\vec{a}\times\vec{b}|+|\vec{a}.\vec{b}|^2\)=144 and \(|\vec{a}|\) = 6, then \(|\vec{b}|\) is equal to

If the vectors \(2\hat{i}-3\hat{j}+4\hat{k},2\hat{i}+\hat{j}-\hat{k}\) and \(\lambda\hat{i}-\hat{j}+2\hat{k}\) are coplanar, then the value of λ is

If \(\vec{a}\) and \(\vec{b}\) are unit vectors and θ is the angle between \(\vec{a}\) and \(\vec{b}\), then sin\(\frac{θ}{2}\) is

The two vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}+3\hat{j}+5\hat{k}\) represent the two sides \(\vec{AB}\) and \(\vec{AC}\) respectively of a ΔABC. The length of the median through A is

The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is \(\frac{2x}{y}\) represents

The general solution of the differential equation x²dy - 2xydx = x⁴cosx dx is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c₁y = (c₂ + c₃)e^x+c₄ is

The area of the region bounded by the line y = 2x + 1, x-axis and the ordinates x = -1 and x = 1 is

The area of the region bounded by the curve y²=8x and the line y = 2x is

The value of \(\int\limits_0^1\frac{\log(1+x)}{1+x^2}\ dx\) is

The value of \(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos x}{1+e^x}\ dx\) is

The value of \(\int\limits^{\frac{1}{2}}_{-\frac{1}{2}}\cos^{-1}x\ dx\) is

The value of \(\int\frac{1+x^4}{1+x^6}dx\) is

If the side of a cube is increased by 5%, then the surface area of a cube is increased by

The maximum value of \(\frac{\log_ex}{x}\), if x > 0 is

If the curves 2x = y² and 2xy = K intersect perpendicularly, then the value of K² is

If y = 2xⁿ⁺¹ + \(\frac{3}{x^n}\) then x²\(\frac{d^2y}{dx^2}\) is