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How do we proove when a number is divided by 0 then the answer is infinite or not defined

If x = cy + bz, y = az + cx, z = bx + ay where x, y, z are not all zeros, then the value of $a^2+b^2+c^2+2abc$ is

If $y^x-x^y=1$ then $\frac{dy}{dx}$ at $x=1$ is

The equation of the circle which touches x the axes of coordinates and the line $\frac{x}{3}+\frac{y}{4}=1$ and whose centres lie in the first quadrant is $x^2+y^2-2cx-2cy+c^2=0$ where c is equal to

tan⁴x

Solve the inequalities and represent the solution graphically on number line: 5x + 1 > –24, 5x – 1 < 24

If $x^3-x^2+5x-1=0$ has roots $\alpha ,\beta ,\gamma$ and $x^3+a{x}^2+bx+c=0$ has roots $\alpha \beta ,\beta \gamma ,\gamma \alpha$, then the value of $(a+b+c)$ is

Match the following by appropriately matching the lists based on the information given in Column I and Column II.

A bag contains some white and some black balls, all combinations being equally likely. The total number of balls in the bag is 12. Four balls are drawn at random from the bag at random without replacement.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ a.\text{Probability that all the four balls are black is equal to}& p.\frac{14}{33}\\ b.\text{If the bag contains 10 black and 2 white balls, then}& \\ \text{the probability that all four balls are black is equal to}& q.\frac{1}{5}\\ c.\text{If all the four balls are black, then the probability}& \\ \text{that the bag contains 10 black balls is equal to}& r.\frac{70}{429}\end{array}$

Are parallel vectors are also be equal and negative?

The general solution of the inequality $-2\le \frac{1-x}{4}<3$ is

The value of $\underset{n\to \infty }{lim}\sum _{r=n+1}^{2n}\frac{n}{n^2+r^2}$ is

The domain of $f\left(x\right)$ is $[0,1]$, then the domain of $y=f\left(e^x\right)+f\left(|\right[x\left]|\right)$ is

(where [.] denotes greatest integer function)

$f\left(x\right)=\frac{e^x}{1+e^x},I_1=\underset{f(-a)}{\overset{f\left(a\right)}{\int }}xg\left(x\right(1-x\left)\right)dx,I_2=\underset{f(-a)}{\overset{f\left(a\right)}{\int }}g\left(x\right(1-x\left)\right)dx,then\frac{I_2}{I_1}=$

If a variable tangent to the curve $x^{2}y=c^3$ makes intercepts $a,b$ on $x$ and $y-$axis respectively, then the value of $a^{2}b$ is

Find the local maxima of the function $f\left(x\right)=-x^2+7x-12$

Show that the function f: R_*
→ R_* defined byis
one-one and onto, where R_* is the set of all
non-zero real numbers. Is the result true, if the domain R_*
is replaced by N with co-domain being same as R_*?

Find the
derivative of

(i) (ii) (5x³
+ 3x – 1) (x – 1)

(iii) x^–3
(5 + 3x) (iv) x⁵ (3 – 6x^–9)

(v) x^–4
(3 – 4x^–5) (vi)

Let $A=\{1,2,3\},B=\{4,5,6,7,8\},$ $C=\{4,6,8,10,12\},$ then $n\left[\right(A\times B)-(A\times C\left)\right]=$

Find $\frac{dy}{dx}$of the functions given in question.

$x^y+y^x=1$

The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is $87\frac{1}{2}$. Find them.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$, if it exists.

If sin (sin^-1 x) = x, the interval in which x lies is__

Find the interval of c for which f(x) =(x²+2x+c)/(x²+4x+c) attains any real value

An ellipse having co-ordinate axes as its axes having lengths $2a$ and $2b$ units respectively, Where $a$ and $b$ are middle terms of a series $a_1,a_2,a_3\cdots a_{10},$ $a_i{a}_{11-i}=5\sqrt{3}\forall i\in N,i<11.$ If $B,F,F^{\prime }$ are one end of minor axis and foci of the ellipse respectively,such that triangle $FB{F}^{\prime }$ is an equilateral triangle, then equation of ellipse is

The values of $a$ and $b$ for which the system $\left[\begin{array}{ccc}3& -2& 1\\ 5& -8& 9\\ 2& 1& a\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}b\\ 3\\ -1\end{array}\right]$

has infinitely many solutions

If X = { $8^n-7n-1:nϵN$ } and Y = {$49(n-1):nϵN$}, then prove that $X\subseteq Y$.

Let x > 0 be a fixed real number. Then the integral ${\int }_0^{\infty }{e}^{-t}|x-t|dt$ is equal to.