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If $\alpha$ is a characteristic root of a non-singular matrix $A$, then characteristic root of $adjA$ is

$If\alpha ,\beta ,\gamma arerootsequation{x}^3+a{x}^2+bx+c=0,then{\alpha }^{-1}+{\beta }^{-1}+{\gamma }^{-1}=$

$Iff\left(x\right)=\{\begin{array}{ccc}\frac{sin(a+1)x+2sinx}{x}& ifx<0& \\ 2,& ifx=0& \\ \frac{\sqrt{1+bx}-1}{x},& ifx>0& \end{array}$ is continuous at x = 0, then find the values of a and b.

The value of $\left|\begin{array}{ccc}(a+1)(a+2)& a+2& 1\\ (a+2)(a+3)& a+3& 1\\ (a+3)(a+4)& a+4& 1\end{array}\right|$ is :

If A and B
are two events such that,
find P (not A and not B).

Pair the subtraction statements with their correct addition statements.

The asymptote of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ forms a triangle with any tangent to the hyperbola. The area of such triangle formed is $a^2\tan \lambda$ , where $\lambda \in (0,\frac{\pi }{2})$ then its eccentricity is

0.4 i^+ 0.8j^+ck^ is a unit vector when 'c' is equal to

Options:

A)-0.2

B)(0.2)^1/2

C)(0.8)^1/2

D) 0

The set of points in $C$ satisfying the inequality $\left|\arg \right(z)-\frac{\pi }{2}|<\frac{\pi }{2}$ is

A rod of length $3l$ units, slides with its ends $A$ and $B$ on the $x$ and $y$ axes respectively. Then the locus of the centroid of $△OAB$ is
(Here, $O$ is the origin.)

If
are
unit vectors such that
,
find the value of
.

The value of $\frac{{}^n{C}_0}{1\cdot 2}-\frac{{}^n{C}_1}{2\cdot 3}+\frac{{}^n{C}_2}{3\cdot 4}+\cdots +(-1{)}^n\frac{{}^n{C}_n}{(n+1)\cdot (n+2)}$ is

Prove
that the functionis
continuous at

If the sum of first n terms of an Arithmetic progression is $c{n}^2$, then the sum of squares of these n terms is

Shape of feasible region formed by following constraints is 4x + y ≥ 20, 2x + 3y ≥ 30, x, y, ≥ 0.

An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

If in a railway carriage $5$ persons can sit each side then number of ways in which a party of $4$ girls and $6$ boys can seat themselves so that the girls will always occupy the corner seats is

Let$f\left(x\right)={\log }_e\left(\sin x\right),(0<x<\pi )$ and $g\left(x\right)={\sin }^{-1}\left(e^x\right),(x\ge 0).$If $\alpha$ is a positive real number such that $a=\left(fog{)}^{\prime }\right(\alpha )$ and $b=\left(fog\right)\left(\alpha \right),$ then :

If $a\le 0$ then the real roots of the equation $x^2-2a|x-a|-3a^2=0$ is/are

Let $\underset{0}{\overset{2[x+14]}{\int }}\left\{\frac{x}{2}\right\}dx=\underset{0}{\overset{\left\{x\right\}}{\int }}[x+14]dx$, where $[\cdot ]$ and $\{\cdot \}$ denotes the greatest integer and fractional part of $x$ respectively. Then $\frac{\left[x\right]+14}{14}$ is equal to

Check the injectivity and surjectivity of the following functions:

(i) f: N → N given by f(x)
= x²

(ii) f: Z → Z given by f(x)
= x²

(iii) f: R → R given by f(x)
= x²

(iv) f: N → N given by f(x)
= x³

(v) f: Z → Z given by f(x)
= x³

Let ${\alpha }_1,{\alpha }_2$ and ${\beta }_1,{\beta }_2$ be the roots of $a{x}^2+bx+c=0$ and $p{x}^2+qx+r=0$ respectively. If the system of equations ${\alpha }_{1}y+{\alpha }_{2}z=0$ and ${\beta }_{1}y+{\beta }_{2}z=0$ has a non-trivial solution, then which of the following option is CORRECT ?

Let $g\left(x\right)=\underset{0}{\overset{x}{\int }}f\left(t\right)dt$, where $f$ is such that $\frac{1}{2}\le f\left(x\right)\le 1$ for $t\in [0,1]$ and $0\le f\left(t\right)\le \frac{1}{2}$ for $t\in [1,2]$ Then, $g\left(2\right)$ satisfies the inequality

If $f\left(x\right)=\frac{2x-{\sin }^{-1}x}{2x+{\tan }^{-1}x}$ is continuous at every point in its domain, then the value of $f\left(0\right)$ is

The area of the region bounded by $y-x=2$ and $x^2=y$ is equal to

Find
the degree measure of the angle subtended at the centre of a circle
of radius 100 cm by an arc of length 22 cm.

If the difference between mean and mode is $63$, then the difference between mean and median can be

If $-3\le |x|<7,$ then $x$ can be represented on the number line by

If $\alpha$ and $\beta$ are the roots of $x^2+2x+2=0,$ then the value of ${\left(\frac{1}{\alpha +2}\right)}^3+{\left(\frac{1}{\beta +2}\right)}^3$ is

Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …

If $M=\underset{0}{\overset{\pi /2}{\int }}\frac{\cos x}{x+2}dx,N=\underset{0}{\overset{\pi /4}{\int }}\frac{\sin x\cos x}{(x+1{)}^2}dx,$ then the value of $M–N$ is