AP EAPCET 2021 - 19th August Morning Shift

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 successes is

In a \(\Delta ABC\), if a = 3, b = 4 and \(\sin A=\frac{3}{4}\), then \(\angle CBA\) is equal to

In \(\Delta ABC,A=75\Upsilon\) and \(B=45\Upsilon\), then the value of \(b+c\sqrt2\) is equal to

In \(\triangle A B C\), suppose the radius of the circle opposite to an \(\angle A\) is denoted by \(r_1\), similarly \(r_2 \leftrightarrow \angle B\) and \(r_3 \leftrightarrow \angle C\). If \(r\) is the radius of inscribed circle, then, w...

If D, E and F are respectively mid-points of AB, AC and BC in \(\Delta ABC\), then BE + AF is equal to

The sum of the roots of the equation \(e^{4 t}-10 e^{3 t}+29 e^{2 t}-22 e^t+4=0\) is

Let \(f(x)=x^3+a x^2+b x+c\) be polynomial with integer coefficients. If the roots of \(f(x)\) are integer and are in Arithmetic Progression, then \(a\) cannot take the value

The variance of the variates 112, 116, 120, 125 and 132 about their AM is

Which of the following set of data has least standard deviation?

If the axes are rotated through an angle \(45 \Upsilon\), the coordinates of the point \((2 \sqrt{2},-3 \sqrt{2})\) in the new system are

the sum of the squares of the intercepts made the line \(5x-2y=10\) on the coordinate axes equals

For three consecutive odd integers \(a \cdot b\) and \(c\), if the variable line \(a x+b y+c=0\) always passes through the point \((\alpha, \beta)\), the value of \(\alpha^2+\beta^2\) equals

If \(2x+3y+4=0\) is the perpendicular bisector of the line segment joining the points A(1, 2) and B(\(\alpha,\beta\)), then the value of \(13\alpha+13\beta\) equals

The equation of the pair of straight lines perpendicular to the pair \(2 x^2+3 x y+2 y^2+10 x+5 y=0\) and passing though the origin is

If the centroid of the triangle formed by the lines \(2 y^2+5 x y-3 x^2=0\) and \(x+y=k\) is \(\left(\frac{1}{18}, \frac{11}{18}\right)\), then the value of \(k\) equals

If \(m_1\) and \(m_2,\left(m_1>m_2\right)\) are the slopes of the lines represented by \(5 x^2-8 x y+3 y^2=0\), then \(m_1: m_2\) equals

If the slope of one of the lines represented by \(a x^2+2 h x y+b y^2=0\) is the square of the other then, \(\left|\frac{a+b}{h}+\frac{8 h^2}{a b}\right|\) is equal to

The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, \(-\)4) is

The direction cosines of a line which makes
equal angles with the coordinate axes are

Let \(O\) be the origin and \(P\) be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{O P}\) are \((1,-2,-2)\), then the coordinates of \(P\) are

The value of \(x\) satisfying the equation \(3 \operatorname{cosec} x=4 \sin x\) are

\(\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)\) is equal to

If \(\sin \alpha - \cos \alpha = m\) and \(\sin 2\alpha = n - {m^2}\), where \(- \sqrt 2 \le m \le \sqrt 2\), then n is equal to

If \(\sinh u=\tan \theta\), then \(\cosh u\) is equal to

A vector makes equal angles \(\alpha\) with \(X\) and \(Y\)-axis, and \(90 \Upsilon\) with \(Z\)-axis. Then, \(\alpha\) is equal to
(c) 45Yand 135Y
(d) $90 \mathrm{Y}$

Angle made by the position vector of the point (5, \(-\)4, \(-\)3) with the positive direction of X-axis is

If the volume of the parallelopiped formed by the vectors \(\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+a \hat{\mathbf{k}}\) and \(a \hat{\mathbf{i}}+\hat{\mathbf{k}}\) becomes minimum, then \(a\) is equal to

If \(\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}\) and \(\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}}{2}\), then angle between \(\mathbf{a}+\mathbf{b}\) and \(\mathbf{a}-\mathbf{b}\) is

Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(\mathbf{c}=7 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}\), then the area of parallel...

If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(|\mathbf{a}|=2, |\mathbf{b}|=3\) and \(\mathbf{a}+t \mathbf{b}\) and \(\mathbf{a}-t \mathbf{b}\) are perpendicular, where \(t\) is a positive scalar, then