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What is $\Delta G$ mixing for an ideal solution?

Which of
the following differential equations hasas
the general solution?

A.

B.

C.

D.

A merchant plans to sell two types of personal computers a desktop model and a portable model that will cost Rs. 25000 and Rs. 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit, if he does not want to invest more than Rs. 70 lakh and if his profit on the desktop model Rs. 4500 and on portable model is Rs. 5000.

The number of odd numbers greater than $8000$ that can be formed using the digits $2,3,4,5$ and $8$, if repetition is not allowed is

(i) ${\tan }^{-1}\left\{\frac{x}{1+\sqrt{1-x^2}}\right\},-1<x<1$

If $f\left(x\right)=\{\begin{array}{cc}\frac{\sin x^2}{2x\cdot \tan x},& x\ne 0\\ a,& x=0\end{array}$ and $f\left(x\right)$ is continuous at $x=0,$ then value of $a$ is equal to



[1 mark]

The value of $\underset{x\to 1}{lim}\frac{1-\sqrt{x}}{({\cos }^{-1}x{)}^2}$ is

The $n^{\text{th}}$ term in the expansion of ${\log }_e\left(\frac{4}{3}\right)$ is

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?

Mark the correct alternative in each of the following :

$Ina\Delta ABC,if(c+a+b)(a+b-c)=ab,\text{then the measure of angle C is}$

The last digit of $(2137{)}^{754}$ is

If $\theta$ is the acute angle between the curves $y=x^3$ and $y=2^{x-1},$ then $\tan \theta$ is equal to

Which of the following function are monotonic in the interval (0,1) ?

A covered box of volume $72{\text{cm}}^3$ and the base sides in a ratio of $1:2$ is to be made. The length of all sides so that the total surface area is the least possible is

The sum of the series $1+\frac{1}{1+2}+\frac{1}{1+2+3}+...$ upto 10 terms, is

1. 3

Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is 9 will be

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is probability that the selected number is not divisible by 7?

If $A$ and $B$ are two mutually exclusive events, then

Solve
system of linear equations, using matrix method.

prove that one and only one out of every three consecutive positive integer is divisible by 3

An equilateral triangle
is inscribed in the parabola y² = 4 ax,
where one vertex is at the vertex of the parabola. Find the length of
the side of the triangle.

Which among the following is/are odd functions?

The value of $\int 8\cos \left(\frac{5x}{2}\right)\cdot \sin 2x\cdot \cos \left(\frac{3x}{2}\right)dx$ is

(where $C$ is constant of integration)

In a $\Delta ABC,\angle A={120}^{\circ }$. If the angle bisector of $A$ cut $BC$ at point $D$, such that length of $BD$ is twice of $CD$ and $AD=10$ unit, then $BC$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)