# Recent questions and answers in Mathematics

### The minimum area of triangle formed by the tangent to the ellipse $\large\frac{x^2}{a^2} +\frac{y^2}{b^2} $$=1 and coordinating axes is : ### If \sin x + \cos y = \large \frac{1}{3} and \cos x + \sin y = \frac{1}{2}, then \tan \frac{(x-y)}{2} ### The number of distinct roots of \begin{bmatrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & cos x & \sin x \end{bmatrix} is a ### The inverse of the following statement If x=3, then x^2=9 is ### The number of five digit number formed with out repetition , divisible by 6 with digits 0,1,2,3,4,5 is ### Equation of a line passing through (-1,2,-3) and perpendicular to the place 2x+3y+z+5=0 is ### The side of a parallelogram are 2 \hat i +4 \hat j -5 \hat k and \hat i +2 \hat j +3 \hat k, then the unit vector parallel to one of the diagonals is : ### The length of the normals drawn from the point on the axis of the parabola y^2 =8x whose distance from the focus is ### The solution of the differential equation \large\frac{dy}{dx} =\frac{xy}{x^2+y^2} is ### If \cos \alpha+\cos \beta + \cos \gamma=0= \sin \alpha +\sin \beta + \sin \gamma then \sin^2 \alpha +\sin ^2 \beta +\sin ^2 \gamma ### If A=\begin{bmatrix} i & -i \\ -i & i \end{bmatrix} and B=\begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} then A^8 equals ### If a,b,c be the sides of a triangle ABC and if roots of the equation . a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal , then \sin ^2 \bigg(\large\frac{A}{2} \bigg) ,$$ \sin ^2 \bigg(\large\frac{B}{c} \bigg),$$\sin ^2 \bigg(\large\frac{c}{2} \bigg)$are in

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