List of top Mathematics Questions

If a triangle \(ABC\) has vertices \(A(1,-6),B(2,-3)\) and \(C(3,-2)\), then the coordinates of its orthocenter are....
If \(cos(pθ)+cos(qθ) = 0\) and \(p\neq q\), then the general value of \(θ\) (where n is any integer) is...
If the line \(4x+3y = 7\) touches the hyperbola \(x^2-y^2 = 7\), then the sum of the co-ordinates of the point of contact is...
If \(θ\) is the acute angle between the lines represented by the equation \(x^2-3xy+2y^2 = 0\), then \(\frac{3sinθ+2cosθ}{3sinθ-2cosθ} =\)
If \(P = tan20^{\circ}\), then the value of \(\frac{tan160^{\circ}-tan110^{\circ}}{1+tan160^{\circ}tan110^{\circ}}\) in terms of \(P\), is...
If \(ω\) is a complex cube root of unity, then the value of the expression \(2(1+\frac{1}{ω})(1+\frac{1}{ω^2})+3(2+\frac{1}{ω})(2+\frac{1}{ω^2})+\ldots +(n+1)(n+\frac{1}{ω})(n+\frac{1}{ω^2})\) is...
In \(△ABC\), with the usual notations, \(\angle C = 90^{\circ}\), then \(sin(A-B)\) is equal to....
The number of five-digit numbers formed using the digits \(2,3,5,7,9\) without repetition and which are greater than \(24000\) are
A certain disease has a prevalence of \(1\%\) in the population. A diagnostic test for the disease has a sensitivity of \(98\%\) and a specificity of \(95\%\). If a person from this population tests positive, then the probability that they actually have the disease is...
It is known that a box of \(8\) batteries contains \(3\) defective pieces and a person randomly selects \(2\) batteries from this box. Then the probability distribution of the number of defective batteries is
The equation of a line passing through a point \((4,-2,3)\) and perpendicular to the XZ-plane is....
If a line makes angles \(α,β,γ\) with the coordinate axes, then the sum of values of \(sin^2α+sin^2β+sin^2γ\) and \(cos2α+cos2β+cos2γ\) is ...
In a multiple-choice examination, there are \(10\) questions with one correct option out of \(4\) options for each question. A student gets \(4\) marks for each correct answer and \(1\) mark is deducted for each incorrect answer. The probability that a student, guessing randomly on every question, scores \(30\) marks in this exam is...
The equation of the plane passing through the intersection of planes \(2x-y+z = 3\), \(4x-3y+5z = -9\) and parallel to the line \(\frac{x+1}{2} = \frac{y+3}{4} = \frac{z-3}{5}\) is...
The vector equation of the plane which is at a distance of \(5\) units from the origin and normal to the vector \(2\hat{i}+\hat{j}-2\hat{k}\) is
If \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) are three non zero and non-coplanar vectors such that \(\overset{̄}{a}\times (\overset{̄}{b}\times \overset{̄}{c}) = \frac{\overset{̄}{b}}{2}\), then the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is ...
If \(\overset{̄}{a} = \hat{i}+\hat{j}+\hat{k},\overset{̄}{b} = \hat{i},\overset{̄}{c} = c_1\hat{i}+c_2\hat{j}+c_3\hat{k}\) with \(c_1 = 1\), \(c_2 = 2\), then value of \(c_3\) such that \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) are coplanar is ____
The general solution of the differential equation \((x+y)\frac{dy}{dx} = 1\) is
If \(\overset{̄}{a}\) and \(\overset{̄}{b}\) have the same magnitude and angle between them is \(60^{\circ}\) and their scalar product is \(\frac{1}{2}\), then \(|\overset{̄}{a}|\) is ____
A body cools according to Newton's law of cooling from \(100^{\circ}\)C to \(60^{\circ}\)C in \(20\) minutes. The temperature of the surroundings being \(20^{\circ}\)C, then the total time required for the body to cool down to \(30^{\circ}\)C is
If \(\overset{̄}{a},\overset{̄}{b}\) and \(\overset{̄}{c}\) are non-coplanar unit vectors such that the angle between any two of them is \(60^{\circ}\), and the vector \(\overset{̄}{d} = x\overset{̄}{a}+y\overset{̄}{b}+z\overset{̄}{c}\) is perpendicular to both \(\overset{̄}{a}\) and \(\overset{̄}{b}\), then the value of \(\frac{(x+y)}{z}\) is
If \(\int _{π/6}^{π/3}\frac{1}{1+sinx+cosx}dx = log2\), then the value of \(\int _{π/6}^{π/3}\frac{cosx}{1+sinx+cosx}dx =\) ............
The area of the region bounded by the curve \(y = 2^{kx}\) and \(x = 0,x = 2\), in first quadrant is \(\frac{2}{log2}\), then the value of \(k\) is
The differential equation of \(3y = \sqrt[3]{x+c}\) is
The area of the region bounded by the curve \(y = x^3\) and the lines \(y = 8\) and \(x = 0\) is ... square units.