AP EAPCET 2022 - 4th July Evening Shift

A manager decides to distribute ₹ 20000 between two employees \(X\) and \(Y\). He knows \(X\) deserves more than \(Y\), but does not know how much more. So, he decides to arbitrarily break ₹ 20000 into two parts and give \(X\) the bigger pa...

If \(a=2, b=3, c=4\) in a \(\triangle A B C\), then \(\cos C=\)

In a \(\triangle A B C, \frac{a}{b}=2+\sqrt{3}\) and \(\angle C=60^{\circ}\). Then, the measure of \(\angle A\) is

In a \(\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=\)

In a \(\triangle A B C\)
\((b+c) \cos A+(c+a) \cos B+(a+b) \cos C=\)

In a \(\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq\)

Suppose \(\triangle A B C\) is an isosceles triangle with \(\angle C=90^{\circ}, A=(2,3)\) and \(B=(4,5)\). Then, the centroid of the triangle is

The sum of the real roots of the equation \(|x-2|^2+|x-2|-2=0\) is

If \(f(f(0))=0\), where \(f(x)=x^2+a x+b, b \neq 0\), then \(a+b=\)

If \(\frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6}\), then \(A^2+B^2=\)

If the difference between the roots of \(x^2+a x+b=0\) and that of the roots of \(x^2+b x+a=0\) is same and \(a \neq b\), then

For what values of \(a \in Z\), the quadratic expression \((x+a)(x+1991)+1\) can be factorised as \((x+b)(x+c)\), where \(b, c \in Z\) ?

If the mean of the data \(p, 6,6,7,8,11,15,16\), is 3 times \(p\), then the mean deviation of the data from its mean is

If the pair of straight lines \(9 x^2+a x y+4 y^2+6 x+b y-3=0\) represents two parallel lines, then

A line passing through \(P(2,3)\) and making an angle of \(30^{\circ}\) with the positive direction of \(X\)-axis meets \(x^2-2 x y-y^2=0\) at \(A\) and \(B\). Then the value of \(P A: P B\) is

Suppose, in \(\triangle A B C, x-y+5=0, x+2 y=0\) are respectively the equations of the perpendicular bisectors of the sides \(A B\) and \(A C\). If \(A\) is \((1,-2)\), the equation of the line joining \(B\) and \(C\) is

Suppose \(P\) and \(Q\) are the mid-points of the sides \(A B\) and \(B C\) of a triangle where \(A(1,3), B(3,7)\) and \(C(7,15)\) are vertices. Then, the locus of \(R\) satisfying \(A C^2+Q R^2=P R^2\) is

If the points of intersection of the coordinate axes and \(|x+y|=2\) form a rhombus, then its area is

If the equation of the plane which is at a distance of \(1 / 3\) units from the origin and perpendicular to a line whose directional ratios are \((1,2,2)\) is \(x+p y+q z+r=0\), then \(\sqrt{p^2+q^2+r^2}=\)

If the equation of the plane passing through the point \(A(-2,1,3)\) and perpendicular to the vector \(3 \hat{i}+\hat{j}+5 \hat{k}\) is \(a x+b y+c z+d=0\), then \(\frac{a+b}{c+d}=\)

If \(x\)-coordinate of a point \(P\) on the line joining the points \(Q(2,2,1)\) and \(R(5,2,-2)\) is 4, then the \(y\)-coordinate of \(P=\)

If \((2,3, c)\) are the direction ratios of a ray passing through the point \(C(5, q, 1)\) and also the mid-point of the line segment joining the points \(A(p,-4,2)\) and \(B(3,2,-4)\), then \(c \cdot(p+7 q)=\)

\(D, E, F\) are respectively the points on the sides \(B C, C A\) and \(A B\) of a \(\triangle A B C\) dividing them in the ratio \(2: 3,1: 2,3: 1\) internally. The lines \(\mathbf{B E}\) and \(\mathbf{C F}\) intersect on the line $$\mathbf...

If \(A+B+C=\pi, \cos B=\cos A \cos C\), then \(\tan A \tan C=\)

A true statement among the following identities is

The value of \(\tan \left(\frac{7 \pi}{8}\right)\) is

\(1+\sec ^2 x \sin ^2 x=\)

If \(P\) and \(Q\) are two points on the curve \(y=2^{x+2}\) in the rectangular cartesian coordinate system such that \(\mathbf{O P} \cdot \hat{i}=-1, \mathrm{OQ} \cdot \hat{i}=2\), then \(\mathrm{OQ}-4 \mathrm{OP}=\)

If \(\mathbf{a}+\mathbf{b}+\mathbf{c}=0\) and \(|\mathbf{a}|=7,|\mathbf{b}|=5,|\mathbf{c}|=3\) then the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is

\(O A B C\) is a tetrahedron. If \(D, E\) are the mid-points of \(O A\) and \(B C\) respectively, then \(\mathbf{D E}=\)