AP EAPCET 2022 - 5th July Morning Shift

In a Binomial distribution, if '\(n\)' is the number of trials and the mean and variance are 4 and 3 respectively, then \(2^{32} p\left(X=\frac{n}{2}\right)=\)

For a Poisson distribution, if mean \(=l\), variance \(=m\) and \(l+m=8\), then \(e^4[1-P(X>2)]=\)

In any \(\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\)

In a \(\triangle A B C\), if \(r_1=36, r_2=18\) and \(r_3=12\), then \(s=\)

In a \(\triangle A B C, a=6, b=5\) and \(c=4\), then \(\cos 2 A=\)

If \(S=\left\{m \in R: x^2-2(1+3 m) x+7(3+2 m)=0\right.\) has distinct roots}, then the number of elements in \(S\) is

The sum of the real roots of the equation \(x^4-2 x^3+x-380=0\) is

If one root of the cubic equation \(x^3+36=7 x^2\) is double of another, then the number of negative roots are

Suppose that the three points \(A, B\) and \(C\) in the plane are such that their \(x\)-coordinates as well as \(y\)-coordinates are in GP with the same common ratio. Then, the points \(A, B\) and \(C\)

205 students take an examination of whom 105 pass in English, 70 students pass in Mathematics and 30 students pass in both. How many students fail in both subjects?

If the mean deviation of the data \(1,1+d 1+2 d, \ldots, 1+100 d,(d>0)\) from their mean is 255, then '\(d\)' is equal to

Suppose the slopes \(m_1\) and \(m_2\) of the lines represented by \(a x^2+2 h x y+b y^2=0\) satisfy \(3\left(m_1-m_2\right)-7=0\) and \(m_1 m_2-2=0\). Then, which of the following is true?

Suppose that the sides passing through the vertex \((\alpha, \beta)\) of a triangle are bisected at right angles by the lines \(y^2-8 x y-9 x^2=0\). Then, the centroid of the triangle is

Suppose \(P\) and \(Q\) lie on \(3 x+4 y-4=0\) and \(5 x-y-4=0\) respectively. If the mid-point of \(P Q\) is \((1,5)\), then the slope of the line passing through \(P\) and \(Q\) is

The length of intercept of \(x+1=0\) between the lines \(3 x+2 y=5\) and \(3 x+2 y=3\) is

If P divides the line segment joining the points \(A(1,2,-1)\) and \(B(-1,0,1)\) externally in the ratio 1 : 2 and \(Q=(1,3,-1)\), then \(PQ=\)

If the direction cosines of a line are \(\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)\) and \(c-a=4\), then \(ca=\)

Let the plane \(\pi\) pass through the point (1, 0, 1) and perpendicular to the planes \(2x + 3y - z = 2\) and \(x - y + 2z = 1\). Let the equation of the plane passing through the point (11, 7, 5) and parallel to the plane \(\pi\) be $$ax ...

\(\text { If } \sin \theta+\operatorname{cosec} \theta=4, \text { then } \sin ^2 \theta+\operatorname{cosec}^2 \theta=\)

If \(2 \cosh 2 x+10 \sinh 2 x=5\), then \(x=\)

If \(\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta\), then the least \(n\) for which \(a_{2 n}=0\) is

If \(\sin \theta=-\frac{3}{4}\), then \(\sin 2 \theta=\)

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$$

Which of the following trigonometric values are negative?
I. \(\sin \left(-292^{\circ}\right)\)
II. \(\tan \left(-190^{\circ}\right)\)
III. \(\cos \left(-207^{\circ}\right)\)
IV. \(\cot \left(-222^{\circ}\right)\)

\(\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=\)

a, b, c are non-coplanar vectors. If
\(\mathbf{a}+3 \mathbf{b}+4 \mathbf{c}=x(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c})+y(\mathbf{a}+5 \mathbf{b}-2 \mathbf{c}) +z(6 \mathbf{a}+14 \mathbf{b}+4 \mathbf{c}) \text {, then } x+y+z=\)

Three vectors of magnitudes \(a, 2 a, 3 a\) are along the directions of the diagonals of 3 adjacent faces of a cube that meet in a point. Then, the magnitude of the sum of those diagonals is

If \(\mathbf{a}\) is collinear with \(\mathbf{b}=3 \hat{i}+6 \hat{j}+6 \hat{k}\) and \(\mathbf{a} \cdot \mathbf{b}=27\), then \(|\mathbf{a}|=\)

Let \(a, b\) and \(c\) be unit vectors such that \(a\) is perpendicular to the plane containing \(\mathbf{b}\) and \(\mathbf{c}\) and angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\). Then, $$|\mathbf{a}+\mathbf{b}+\math...

Let \(\mathbf{F}=2 \hat{i}+2 \hat{j}+5 \hat{k}, A=(1,2,5), B=(-1,-2,-3)\) and \(\mathbf{B A} \times \mathbf{F}=4 \hat{i}+6 \hat{j}+2 \lambda \hat{k}\), then \(\lambda=\)