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For real $x$, the maximum value of $\frac{e^{sinx}}{e^{cosx}}$ is

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by x is greater than y. The range of R is

1. 23.6

A bag contains 9 balls marked with the digits 1,2,3.....9. If two balls are drawn from the bag then find the number of ways of getting the sum of digits on the balls as odd?

Between any two real roots of $e^{-x}-\cos x=0$, there exists atleast $k$ root(s) of $\sin x-e^{-x}=0.$ Then $k$ is

If the
terms
of a G.P. are a, b and c, respectively. Prove that

A point P moves so that its distance from the point (a, 0) is always equal to its distance from the line x + a = 0. The

locus of the point is

The area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is (in sq. units)

The minimum value of $9ta{n}^2\theta +4co{t}^2\theta$ is

Prove that the function
f given by

is notdifferentiable at x = 1.

Out of a pack of 52 cards one is lost, from the remainder of the pack , two cards are drawn and are found to be spades .Find the chance that the missing card is a spade ?

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is _____.

In triangle $ABC$, let $\angle C=\frac{\pi }{2}$. If $r$ is the inradius and $R$ is circumradius of the triangle, then $2(r+R)$ is equal to:

The inverse of the real function f(x) = $\frac{4x}{3x+4}$ , $x\ne \frac{-4}{3}$,is f ^-1(x) =

Henko is renting a car. The rental charge is $17.50perdayplus$0.16 per mile. Henko can spend at most $33 for the cost of the car rental. If Henko rents the car for one day, which of the following is one possible number of miles Henko can drive the rental car?

The number of different positive integer triplets (x,y,z) satisfying the equations x² + y - z = 100 and x + y² - z = 124 is

Let $AB$ be a line segment of length 2. Construct a semicircle $S$ with $AB$ as diameter. Let $C$ be the midpoint of the arc $AB$. Construct another semicircle $T$ external to the triangle $ABC$ with chord $AC$ as diameter. The area of the region inside the semicircle $T$ but outside $S$ is

The speaker of this poem is most likely

The differential equation of the family of curves represented by the equation $x^{2}y=a$, is

Find the number of 5 letter words, with or without meaning, which can be formed out of the letters of the word MARIO , where the repetition of the letters is not allowed.

${lim}_{x\to 0}\frac{5x+4sin3x}{4sin2x+7x}$

Using
properties of determinants, prove that:

A die is thrown three times. Let X be the 'number of twos seen', find the expectation of X.

Consider a causal LTI system whose input x[n] and output y[n] are related by the difference equation



$y\left[n\right]=0.25y[n-1]+x\left[n\right]$ and



$x\left[n\right]=\delta [n-1],$ then the value of y[4]

Prove that $\frac{1}{2}tan\left(\frac{x}{2}\right)+\frac{1}{4}tan\left(\frac{x}{4}\right)+...+\frac{1}{2^n}tan\left(\frac{x}{2^n}\right)=\frac{1}{2^n}cot+\left(\frac{x}{2^n}\right)-cotx$ for all $nϵN$ and $0<x<\frac{x}{2}$.

For the matrix $A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& -3\\ 2& -1& 3\end{array}\right]$. Show that $A^3-6A^2+5A+11I=0$. Hence, find $A^{-1}$

The number of ways of choosing triplet $(x,y,z)$ such that $z>max\text{of}(x,y)$ and $x,y,z\in \{1,2,...,n,n+1\}$ is