List of top Mathematics Questions asked in TS EAMCET

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spade cards. The probability that the missing card is not a spade is

Let \(E\) and \(F\) be two events such that \[ P(\bar E)=\frac13,\qquad P(E\cap F)=\frac13,\qquad P(\overline{E\cup F})=\frac16. \] Which of the following is correct?

The transformed equation of \[ 4x^2-4xy+7y^2-24=0 \] in the new coordinate system when the axes are rotated through an angle \(\theta\) about the origin in the positive direction is \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. \] If \[ 0<\theta<\frac{\pi}{4}, \] then \[ 1+b^2\sin^2\theta= \]

Let \(A(a,0)\) be a point on the \(X\)-axis. The locus of the midpoints of the line segments joining \(A\) and any point \(P\) on the parabola \[ y=16-x^2 \] is

If \(P(x,y,z)\) is the intersection of the lines \[ \vec r=(2\hat i-2\hat j+3\hat k)+t(\hat i-3\hat j+\hat k) \] and \[ \vec r=(2\hat j-\hat k)+s(\hat i-\hat j+3\hat k), \] then \(x+y+z=\)

Mean and variance of an ungrouped data of 15 numbers are \(12\) and \(14\) respectively. For another ungrouped data of 15 numbers the mean and variance are \(14\) and \(10\) respectively. If the two data are combined, then the variance of the combined data of 30 numbers is

If \[ \vec r=\vec a+t\vec b \quad\text{and}\quad \vec r=\vec p+l\vec b \] are two lines, where \[ \vec a=\hat i+2\hat j,\qquad \vec b=\hat i+\hat j+\hat k,\qquad \vec p=2\hat i+\hat k. \] The position vector of a point \(A\) is \[ 5\hat i+\hat j-3\hat k. \] Let \(B,C\) be the feet of the perpendiculars drawn from \(A\) to the given two lines respectively, then \[ \overrightarrow{BA}+\overrightarrow{AC}= \]

If \(\alpha,\beta,\gamma\;(\alpha>\beta>\gamma)\) are roots of the equation \[ x^3-x^2-4x+4=0, \] the volume of the parallelepiped whose coterminous edges are \[ \alpha\hat i+\beta\hat j+\gamma\hat k,\; \beta\hat i+\gamma\hat j+\alpha\hat k,\; \gamma\hat i+\alpha\hat j+\beta\hat k \] is

Let \[ A=\{1,2,3,4,\ldots,20\}. \] If three distinct elements are drawn from the set \(A\) at random, then the probability that the three numbers drawn are in increasing G.P. with common ratio as a non integral rational value is

If \[ \vec r=2\hat i-\hat j+2\hat k,\qquad \vec s=3\hat i-3\hat j+3\hat k,\qquad \vec t=\hat i+2\hat j+\hat k \] are three vectors and \(\vec a\) is a vector such that \[ \vec s\times\vec a=\vec r\times\vec a \] and \[ \left|\vec t\times\vec a\right|=\sqrt{128}, \] then \(|\vec t-\vec a|=\)

In a \(\triangle ABC\), if \(r_1=12,\; r_2=18,\; r_3=36\), then \(\Delta=\)

If \[ \alpha=\tan\left(2\sin^{-1}\left(\frac23\right)\right) \quad\text{and}\quad \beta=\sin\left(2\tan^{-1}\left(\frac13\right)\right), \] then the maximum value of \[ \alpha\sin\theta+\beta\cos\theta \] is

\(\vec a,\vec b,\vec c\) are the position vectors of three points \(A,B,C\) respectively. If \[ \angle ABC=\frac{\pi}{2}, \] and \[ \overrightarrow{AB} =\hat{i}+4\hat{j}+(4-\lambda)\hat{k}, \qquad \overrightarrow{AC} =(\lambda-1)\hat{i}+6\hat{j}+(2-\lambda)\hat{k}, \] then \(\lambda=\)

Evaluate \[ \log\left(\sinh\theta+\sqrt{\sinh^2\theta+1}\right). \]

In a triangle \(ABC\), if \[ a=\sqrt3+1,\qquad b=\sqrt3-1 \] and \[ \angle C=60^\circ, \] then \(\cos(A-B)=\)

The term independent of \(x\) in the expansion of \[ \left(5x+\frac{6}{x}\right)^4\left(\frac{1}{1-2x}\right) \] is

\(a_1,a_2,a_3\) are in arithmetic progression in which common difference is \(2\) and the first term is \(2\). If \[ \cos a_1+\cos a_2+\cos a_3 = \frac{\sin\alpha}{\sin\beta}\cos\gamma, \] then \(\alpha+\beta=\)

If \[ \tan(60^\circ+\theta)\tan(60^\circ-\theta) = \frac{a\cos^2\theta-b}{a\cos^2\theta-c}, \] then \[ \frac{a+c}{b}= \]

If in \((0,2\pi)\), \(2\cos x+k=3\sec x\) and \(\cot x=-1\), then the sum of squares of all possible values of \(k\) is

If \[ \frac{x+3}{(1-x)^2(1+x^2)} = \frac{A}{(1-x)} + \frac{B}{(1-x)^2} + \frac{Cx+D}{2(1+x^2)}, \] then \(B^2+C^2+D^2=\)

If \((\alpha,\beta)\subseteq\left(0,\dfrac{\pi}{2}\right)\) is the smallest set containing all the possible solutions of the inequality \[ \sin x+\cos2x>1, \] then \(\alpha+\beta=\)

A quadratic equation \[ x^2-ax+b=0,\qquad a>0 \] has real roots. If the sum of the roots is less than the product of the roots, then \(b\) lies in the interval

When each root of the equation \[ x^3-ax^2+bx+1=0 \] is diminished by \(h\), if the transformed equation takes the form \[ 9x^3+\left(9+\frac{a^3}{3}\right)=0, \] then \(ah=\)

If \(\alpha,\beta,5\) are the roots of the equation \[ x^3-ax+a= \frac{\sin^2x+\cos^4x} {\cos^2x+\sin^4x}, \] then \(a(\alpha+\beta)=\)

The number of numbers between \(345\) and \(543\) such that the sum of the digits in each number is \(15\) is