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Assume X, Y, Z, W and P are
matrices of order,
and
respectively.
The restriction on n, k and p so that
will
be defined are:

A. k = 3, p = n

B. k is arbitrary, p = 2

C. p is arbitrary, k = 3

D. k = 2, p = 3

If $|x-7{|}^2-3|x-7|-10=0$, then value(s) of $x$ can be equal to

Q. If $x>y$, and $y>z$, and all $x,y,$ and $z$ are positive, then which of the following is necessarily correct?



Q. यदि $x>y$, और $y>z$, और $x,y,$ और $z$ सभी धनात्मक हैं, तो निम्नलिखित में से कौन सा विकल्प आवश्यक रूप से सही है?

If $a_1,a_2,a_3,...,a_n$ are in A.P. with common difference $d$ where $a_r>0,\forall r=1,2,3,...,n,$ then $\tan [{\tan }^{-1}\left(\frac{d}{1+a_1{a}_2}\right)+{\tan }^{-1}\left(\frac{d}{1+a_2{a}_3}\right)+\cdots +{\tan }^{-1}\left(\frac{d}{1+a_{n-1}{a}_n}\right)]=$

Consider a circle with its centre lying on the focus of the parabola $y^2=2px$ such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is

Write the derivative of $f\left(x\right)=3|2+x|\text{at}x=-3$.

The solution of the differential equation $\left[\right(x+1)\frac{y}{x}+\sin y]dx+[x+\ln x+x\cos y]dy=0$is

(where $c$ is integration constant)

Solution of the equation $xdy=(y+x\frac{f\left(\frac{y}{x}\right)}{f^{\prime }\left(\frac{y}{x}\right)})dx$

Consider two families $A$ and $B.$ Suppose there are $4$ men, $4$ women and $4$ children in family $A$ and $2$ men, $2$ women and $2$ children in family $B.$ The recommended daily amount of calories is $2400$ for a man, $1900$ for a woman, $1800$ for a child and $45$ grams of proteins for a man, $55$ grams for a woman and $33$ grams for a child.

The requirement of calories and proteins for each person is given by matrix $R$ and the number of family members in each family is given by matrix $F.$



Matrix $R$ is

The number of points where function $f\left(x\right)=max\{|\tan x|,\cos |x|\}$ is non-differentiable in the interval $(-\pi ,\pi ),$ is

Which of the following curves best represents the Moseley law?

The projection of the line $\frac{x+1}{-1}=\frac{y}{2}=\frac{z-1}{3}$ on the plane $x-2y+z=6$ is the line of intersection of this plane with the plane

${}^n{C}_r+2{}^n{C}_{r-1}+{}^n{C}_{r-2}$ =

How is functional structure different from a divisional structure?

If Neena says, "Anita's father Raman is the only son of my father-in-law Mahipal", then how is Bindu, who is the sister of Anita, related to Mahipal ?

If $\frac{{\log }_{10}a}{12}=\frac{{\log }_{10}b}{21}=\frac{{\log }_{10}c}{15},$ then $bc$ is equal to

Two persons each makes a single throw with a pair of dice. Then the probability that the sum on both dice are unequal, is:

Evaluate the definite integrals.
${\int }_0^1\frac{1}{\sqrt{1-x^2}}dx.$

The equation of common tangent to the curves $y^2=16x$ and $xy=–4$, is :

If $\left[x\right]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\underset{0}{\overset{2}{\int }}{x}^2\left[x\right]dx$ equals

Find the equation of the circle with
Centre (1,1) and radius $\sqrt{2}$

If a matrix $A=[a_{ij}{]}_{3\times 2}$ is given by $a_{ij}=\frac{i^2+j^2}{2},$ then the matrix is

Prove that:
$\left|\begin{array}{ccc}{a}^2+2a& 2a+1& 1\\ 2a+1& a+2& 1\\ 3& 3& 1\end{array}\right|=(a-1{)}^3$

Let $\overrightarrow{a}=2\hat{i}-3\hat{j}+4\hat{k}$ and $\overrightarrow{b}=7\hat{i}+\hat{j}-6\hat{k}$ If $\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{r}\times \overrightarrow{b},\overrightarrow{r}\cdot (\hat{i}+2\hat{j}+\hat{k})=-3,$ then $\overrightarrow{r}\cdot (2\hat{i}-3\hat{j}+\hat{k})$ is equal to:

The complete set of values of $a$ for which the inequality $(a-1)x^2-(a+1)x+(a-1)\ge 0$ is true for all $x\ge 2$ is

P, Q and R are equal partners in a firm. R retires and the goodwill of the firm is valued at Rs 3,60,000. No goodwill account appears as yet in the books of the firm. P and Q agree to share future profits in the ratio of 3:2. Pass necessary journal entry for goodwill.