AP EAPCET 2022 - 4th July Morning Shift

A box contains 100 balls, numbered from 1 to 100 . If 3 balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd numb...

If 6 is the mean of a Poisson distribution, then \(P(X \geq 3)=\)

In a lottery, containing 35 tickets, exactly 10 tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

A bag contains 7 green and 5 black balls. 3 balls are drawn at random one after the other. If the balls are not replaced, then the probability of all three balls being green is

In a \(\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=\)

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

In a \(\triangle A B C\), if \(a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=\)

If the angles of a \(\triangle A B C\) are in the ratio \(1: 2: 3\), then the corresponding sides are in the ratio

The number of positive real roots of the equation \(3^{x+1}+3^{-x+1}=10\) is

If \(f(x)=a x^2+b x+c\) for some \(a, b, c \in R\) with \(a+b+c=3\) and \(f(x+y)=f(x)+f(y)+x y, \forall x, y \in R\). Then, \(\sum_\limits{n=1}^{10} f(n)=\)

The number of real roots of the equation \(\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}\) is

The mean deviation about the mean for the following data.
\(5,6,7,8,6,9,13,12,15 \text { is }\)

If the lines represented by \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) intersect on the \(X\)-axis, which of the following is in general incorrect?

For \(\alpha \in\left[0, \frac{\pi}{2}\right]\), the angle between the lines represented by \([x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \theta \tan \alpha) y]=0\) is

The least distance from origin to a point on the line \(y=x+3\) which lies at a distance of 2 units from \((0,3)\) is

Suppose a triangle is formed by \(x+y=10\) and the coordinate axes. Then, the number of points \((x, y)\) where \(x\) and \(y\) are natural numbers, lying inside the triangle is

Starting from the point \(A(-3,4)\), a moving object touches \(2 x+y-7=0\) at \(B\) and reaches the point \(C(0,1)\). If the object travels along the shortest path, the distance between \(A\) and \(B\) is

The point of intersection of the lines \(\mathbf{r}=2 \mathbf{b}+t(6 \mathbf{c}-\mathbf{a})\) and \(\mathbf{r}=\mathbf{a}+s(\mathbf{b}-3 \mathbf{c})\) is

If \((a, b, c)\) are the direction ratios of a line joining the points \((4,3,-5)\) and \((-2,1,-8)\), then the point \(P(a, 3 b, 2 c)\) lies on the plane

If the point \((a, 8,-2)\) divides the line segment joining the points \((1,4,6)\) and \((5,2,10)\) in the ratio \(m: n\), then \(\frac{2 m}{n}-\frac{a}{3}=\)

The \(x\)-intercept of a plane \(\pi\) passing through the point \((1,1,1)\) is \(\frac{5}{2}\) and the perpendicular distance from the origin to the plane \(\pi\) is \(\frac{5}{7}\). If the \(y\)-intercept of the plane \(\pi\) is negative ...

If \((1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,\) then \(n=\)

If the identity \(\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c\) holds for some \(a, b, c \in Q\) then \((a, b, c)=\)

The value of \(\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}\) is

\(\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=\)

If \(\operatorname{cosech} x=\frac{4}{5}\), then \(\sinh x=\)

The vectors \(3 \mathbf{a}-5 \mathbf{b}\) and \(2 \mathbf{a}+\mathbf{b}\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular, then the acute angle between \(\mathbf{a}\) and $...

Let \(\mathbf{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(x=2 y\). If \(|\mathbf{a}|=5 \sqrt{2}\) and a makes an angle of \(135^{\circ}\) with the Z-axis, then \(\mathbf{a}=\)

In quadrilateral \(A B C D, \mathbf{A B}=\mathbf{a}, \mathbf{B C}=\mathbf{b}\). \(\mathbf{D A}=\mathbf{a}-\mathbf{b}, M\) is the mid-point of \(B C\) and \(X\) is a point on DM such that, \(\mathbf{D X}=\frac{4}{5}\) DM.
Then, the points $$...

Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be the position vectors of the vertices of a \(\triangle A B C\). Through the vertices, lines are drawn parallel to the sides to form the \(\Delta A^{\prime} B^{\prime} C^{\prime}\). Then, the cent...