List of top Mathematics Questions asked in TS EAMCET

If \( \alpha, \beta \in \mathbb{R} \) and \( \alpha \leq \frac{x^2 - 3x + 4}{x^2 - 4x + 5} \leq \beta \) for all \( x \in \mathbb{R} \), then \( (2\alpha - 3)^2 + (2\beta - 3)^2 = \)

If all roots of \[ x^5-3x^4+2x^3-3x^2+5x-2=0 \] are increased by real value h so that term containing \(x^3\) vanishes in transformed equation and h is integer, then h=

If two roots of the equation \( x^5 - 9x^4 + 27x^3 - 23x^2 - 24x + 36 = 0 \) are repeated roots of multiplicity 2 and all the roots are integers then the sum of the squares of all different roots of the equation is:

If \( \alpha, \beta, \gamma, \delta \) are the roots of the equation \( x^4 - 10x^3 + 35x^2 - 50x + 24 = 0 \) and \( \alpha^2, \beta^2, \gamma^2, \delta^2 \) are the roots of the equation \( x^4 + ax^3 + bx^2 + cx + d = 0 \), then \( a = \)

Two real roots of \[ 3x^4+ax^3+55x^2-52x+12=0 \] are positive and equal. Product of other two roots is 1. If roots belong to natural numbers then \[ a\beta-a+\frac{\gamma}{\delta}= \]

If \[ \vec a=\hat i+p\hat j-3\hat k,\qquad \vec b=2\hat i-3\hat j+q\hat k,\qquad \vec c=\hat i+2\hat j+2\hat k\;(p0) \] are three vectors such that the magnitude of projection of \(\vec a\) on \(\vec c\) is \(3\) and the magnitude of projection of \(\vec b\) on \(\vec c\) is \(2\), then the magnitude of projection of \(\vec a\) on \(\vec b\) is

If the vectors \[ \vec a=4\hat{i}+6\hat{j}+\lambda\hat{k},\qquad \vec b=\hat{i}-2\hat{j}-3\hat{k}, \qquad \vec c=4\lambda\hat{i}+\hat{j}-3\hat{k} \] are coplanar and \(\lambda\in\mathbb{Z}\), then \(\vec a\cdot\vec c=\)

If \(\vec a\) is a vector perpendicular to the plane containing the vectors \[ 2\hat i-\hat j+3\hat k \quad\text{and}\quad -\hat i+3\hat j+2\hat k, \] then the magnitude of the projection of the vector \[ 3\hat i+2\hat j-\hat k \] on \(\vec a\) is

The straight line given by the equation \[ \vec r=(4\hat{i}+5\hat{j}+\hat{k})+s(4\hat{i}+6\hat{j}+2\hat{k}) \] is coplanar with the straight line given below. Choose the correct option.

A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is

If 2 coins are tossed and 2 dice are thrown, probability of getting at least 1 head and sum at least 9 is

A dealer bought a fixed number of laptops from 3 different companies A, B and C. Among these laptops, \(28\%\) are bought from A, \(32\%\) are bought from B and \(40\%\) are bought from C. \(2.5\%\) of laptops bought from A, \(1.5\%\) bought from B and \(1\%\) bought from C are likely to be defective. If a customer found that the laptop bought by him is defective, then the probability that it was from B is

Three persons A, B and C planned to have a running race among themselves. If the probability that A wins the race is three times that of B and the probability that B wins the race is \(\dfrac32\) times that of C, then the difference in probabilities of A and C to win the race is

Two persons A and B are playing a game of rolling 2 dice alternately. The person who first gets the sum of the numbers appearing on the dice as a prime number will win the game. If A starts the game, then the probability of B winning the game is

If a 4-digit number is chosen from all possible 4-digit numbers, probability of getting exactly three odd digits and one even digit is

Let \[ S=\{2,3,5,7,11,13\} \] Consider all onto functions from \(S\) to \(S\). If function \(f\) is chosen randomly, probability that \[ f(3)>3f(2) \] is

In the interval \([-5,5]\), if \[ f(x)=(x+3)^2(x-2)^3 \] is increasing on \[ S=\{x\mid -5\le x<\alpha \text{ and } \beta<x\le5\}, \] then \(f(\alpha)-f(\beta)=\) ?

If the angle between the curves \[ y^2=4x \] and \[ y=ax^2-5 \] at the point \((1,2)\) is \(\alpha\), then \[ (a-2)|\tan\alpha| = ? \]

The edges of a cuboid are measured with a scale having an error of \(0.01\) cm per cm. If the dimensions of the cuboid are \[ (l,b,h)=(12,5,7), \] then the percentage error in the volume of the cuboid is

\(f(x)\) is a cubic polynomial and the curve represented by \(y=f(x)\) passes through the origin. The function \(y=f(x)\) is an increasing function in \[ (-\infty,0)\cup(1,\infty) \] and a decreasing function in \[ (0,1). \] If \[ f'(2)=6, \] then the \(c\) of Lagrange's Mean Value Theorem on the interval \([0,2]\) satisfies the equation

The function \[ f(x)=x|x-1|+|x+2| \] is

If the line \[ 2x+y=7 \] touches the curve \[ y=f(x) \] at \[ x=\frac12, \] then the sum of the lengths of the normal and subnormal is

If \[ f(x)=x^3-19x+30 \] is a real valued function with domain \([-4,1]\), then the value of \(c\) according to Lagrange's Mean Value Theorem for \(f(x)\) is