List of top Mathematics Questions asked in TS EAMCET

Consider all functions given in List-I in the interval [1,3]. The List-2 has the values of 'c' obtained by applying Lagrange's mean value theorem on the functions of List-1. Match the functions and values of 'c'.

The set of all values of x for which $f(x) = ||x|-1|$ is differentiable is

If $y^3=x$ then the value of $\frac{dy}{dx}$ at $x=1$ is

If $x=t-\sin t, y=1-\cos t$ and $\frac{d^2y}{dx^2}=-1$ at $t=K, K>0$, then $\lim_{t \to K} \frac{y}{x} =$

If $y=(1-x^2)\text{Tanh}^{-1}x$ then $\frac{d^2y}{dx^2}=$

If $y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}$, $|x|<1$, then $\frac{dy}{dx} =$

If $x = \sqrt{1-\tan y}$, then $\frac{dy}{dx} =$

If $y = \text{Sec}^{-1}x$, then $\frac{d^2y}{dx^2} =$

If \( f(x) = \begin{cases} x^2 \cos\left(\frac{\pi}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then at \( x = 0 \), \( f(x) \) is

Let A($\alpha$,4,7) and B(3,$\beta$,8) be two points in space. If YZ plane and ZX plane respectively divide the line segment joining the points A and B in the ratio 2:3 and 4:5, then the point C which divides AB in the ratio $\alpha:\beta$ externally is

If the foot of the perpendicular drawn from the point (2,0,-3) to the plane $\pi$ is (1,-2,0) and the equation of the plane is $ax+by-3z+d=0$ then $a+b+d=$

If m:n is the ratio in which the point $\left(\frac{8}{5}, \frac{1}{5}, \frac{8}{5}\right)$ divides the line segment joining the points (2,p,2) and (p,-2,p) where p is an integer then $\frac{3m+n}{3n}=$

If $(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and $(1,1,-2)$, then $\alpha+\beta+\gamma=$

If A(2,1,-1), B(6,-3,2), C(-3,12,4) are the vertices of a triangle ABC and the equation of the plane containing the triangle ABC is $53x+by+cz+d=0$, then $\frac{d}{b+c}=$

The number of values of 'k' for which the points (-4,9,k), (-1,6,k), (0,7,10) form a right-angled isosceles triangle is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is

The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is

If the differential equation having $y = Ae^x + B\sin x$ as its general solution is $f(x)\frac{d^2y}{dx^2}+g(x)\frac{dy}{dx}+h(x)y=0$, then $f(x)+g(x)+h(x) =$

The differential equation of the family of all circles of radius 'a' is

If the general solution of $(1+y^2)dx = (\tan^{-1}y - x)dy$ is $x = f(y)+ce^{-\tan^{-1}y}$, then $f(y)=$

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three times by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is

A and B are two events of a random experiment such that $P(B)=0.4$, $P(A \cap \bar{B}) = 0.5$, $P(A \cup B) + P(A|B) = 1.15$, then $P(A)=$

Three companies C1, C2, C3 produce car tyres. A car manufacturing company buys 40% of its requirement from C1, 35% from C2 and 25% from C3. The company knows that 2% of the tyres supplied by C1, 3% by C2 and 4% by C3 are defective. If a tyre chosen at random from the consignment received is found defective then the probability that it was supplied by C2 is

In a Poisson distribution, if $\frac{P(X=5)}{P(X=2)} = \frac{1}{7500}$ and $\frac{P(X=5)}{P(X=3)} = \frac{1}{500}$, then the mean of the distribution is