Mathematics Tes...

The equations of the sides AB,BC and CA of a triangle ABC are 2x+y=0,x+py=39 and x−y=3 respectively and P(2,3) is its circumcentre. Then which of the following is NOT true?

If \(A B^{T}\) is defined as a square matrix then what is the order of the matrix \(B\), where matrix \(A\) has order \(2 \times 3\)?

What is the area bounded by the curves \(|y|=1-x^{2}\)?

The number of solutions, of the equation \(\mathrm{e}^{\sin x}-2 \mathrm{e}^{-\sin x}=2\) is

If an angle \(A\) of a \(\triangle A B C\) satisfies \(5 \cos A+3=0\), then the roots of the quadratic equation, \(9 x^2+27 x+20=0\) are.

If \(z\) be a complex number satisfying \(|\operatorname{Re}(z)|+|\operatorname{Im}(Z)|=4\), then \(|Z|\) cannot be: 

What is the value of \(\lambda\) for which the vectors \(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(-\hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) are perpendicular?

If \(Z=1+i\), where \(i=\sqrt{-1}\), then what is the modulus of \(Z+\frac{2}{Z} ?\)

The equations x = a cos θ - b sin θ , and y = a sin θ + b cos θ, 0 ≤ θ ≤ 2π represent:

The equations of the sides \(\mathrm{AB}, \mathrm{BC}\) and \(\mathrm{CA}\) of a triangle \(\mathrm{ABC}\) are \(2 \mathrm{x}+\mathrm{y}=0, \mathrm{x}+\mathrm{py}=15 \mathrm{a}\) and \(\mathrm{x}-\mathrm{y}=3\) respectively. If its orthocentre is \((2, \mathrm{a}),-\frac{1}{2}<\mathrm{a}<2\), then \(\mathrm{p}\) is equal to.................