AP EAPCET 2021 - 20th August Morning Shift

In a \(\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}\), then the triangle is

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2+x+1=0\), then the equation whose roots are \(\alpha^{2021}, \beta^{2021}\) is given by

If \(2, 1\) and \(1\) are roots of the equation \(x^3-4 x^2+5 x-2=0\), then the roots of \(\left(x+\frac{1}{3}\right)^3-4\left(x+\frac{1}{3}\right)^2+5\left(x+\frac{1}{3}\right)-2=0\)

If \(f(x)=2x^3+mx^2-13x+n\) and 2, 3 are the roots of the equation \(f(x)=0\), then the values of m and n are

The mean deviation from the mean of the set
of observation \(-1,0,4\) is

Let an angle of a triangle is 60\(^\circ\). If the variance of the angles of the triangle is 1014\(^\circ\), then the other two angles are

For the random variable X with probability distribution is given by the table

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When the axes are rotated through an angle
45\(^\circ\), the new coordinates of a point P are
(1, \(-\)1). The coordinates of P in the original
system are

Find the equation of a straight line passing through \((-5,6)\) and cutting off equal intercepts on the coordinate axes.

Line has slope \(m\) and \(y\)-intercept 4 . The distance between the origin and the line is equal to

The equation of the base of an equilateral triangle is \(x+y=2\) and one vertex is \((2,-1)\), then the length of the side of the triangle is

The equation of a straight line which passes through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to \((x \sec \theta+y \operatorname{cosec} \theta)=a\) is

The acute angle between lines \(6 x^2+11 x y-10 y^2=0\) is

If the lines, joining the origin to the points of intersection of the curve \(2 x^2-2 x y+3 y^2+2 x-y-1=0\) and the line \(x+2 y=k\), are at right angles, then \(k^2\) equals

The equation of bisector of the angle between the lines represented by \(3 x^2-5 x y+4 y^2=0\) is

If the bisectors of the pair of lines \(x^2-2 m x y-y^2=0\) is represented by \(x^2-2 n x y-y^2=0\), then

If the lines, \(\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}\) and \(\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}\) are coplanar, then \(\sin ^{-1}(\sin \lambda)+\cos ^{-1}(\cos \lambda)\) is equal to

The line passing through \((1,1,-1)\) and parallel to the vector \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) meets the line \(\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}\) at \(A\) and the plane \(2 x-y+2 z+7=0\) at \(B\). Then...

If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthocentre, centroid, circumcentre and incentre, then H + G + S + I is equal to

A(2, 3, 4), B(4, 5, 7), C(2, \(-\)6, 3) and D(4, \(-\)4, k) are four points. If the line AB is parallel to CD, then k is equal to

If the direction cosines of two lines are \(\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)\) and \(\left( {{5 \over {13}},{{12} \over {13}},0} \right)\), then identify the direction ratios of a line which is bisecting one o the angle ...

If \(\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)\), then \(\theta\) is equal to

What is the value of \(\cos \left(22 \frac{1}{2}\right)^{\circ}\) ?

If \(\cos \theta=-\sqrt{\frac{3}{2}}\) and \(\sin \alpha=\frac{-3}{5}\), where '\(\theta\)' does not lie in the third quadrant, then the value of \(\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}\) is equal to

If \(\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}\), then \(\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}\) is equal to

The sides of a triangle inscribed in a given circle subtend angles \(\alpha, \beta, \gamma\) at the center. The minimum value of the AM of \(\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)\) and $$\cos \left(\g...

The position vectors of the points \(A\) and \(B\) with respect to \(O\) are \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). The length of the internal bisector of...

Let \(\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}\) and \(\mathbf{w}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). Then which of the following statement is t...

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

Let \(\mathbf{a}=\hat{\mathbf{i}}\) and \(\mathbf{b}=\hat{\mathbf{j}}\), the point of intersection of the lines \(\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}\) and \(\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}\) ...