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$If{K}_{c}for{H}_{2\left(g\right)}+I_{2\left(g\right)}\to 2H{I}_{\left(g\right)}is50,then{K}_{c}forH{I}_{(}g)\frac{1}{2}{H}_2+\frac{1}{2}{I}_{2}is$

If $\frac{x^2}{f\left(4a\right)}+\frac{y^2}{f(a^2-5)}=1$ represents an ellipse with major axis as y-axis and f is a decreasing function, then

Let P(n) denote the statement that $n^2$ + n is odd. It

is seem that P(n) ⇒ P(n + 1), $P_n$ is true for all

Sum of integers from 1 to 100 that are divisible by 2 is a, by 5 is b and by both 2 and 5 is c. Find the sum of integers which are divisible 2 or 5.

${lim}_{x\to \infty }{\left\{\frac{3x^2+1}{4x^2-1}\right\}}^{\frac{x^3}{1+x}}$

Let $f\left(x\right)=\frac{a{x}^2+2(a+1)x+9a+4}{x^2-8x+32}$ and $g\left(x\right)=x-x^2-1.$ If $f\left(x\right)$ is less than $M+\frac{3}{4}$ for all $x\in R,$ where $M$ is the maximum value of $g\left(x\right),$ then set of values of $a$ lies in

1. 0

Raj was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?

Period of the function sin³x + cos³x=

If $x^3+5xy+y^2-2x+y-6=0$ and $y\left(1\right)=1$, then which of the following is/are true?

$(\text{where}{y}_1=\frac{dy}{dx},y_2=\frac{d^{2}y}{d{x}^2})$

$f:A\to B$ is a function defined as $f\left(x\right)=|x^2+1|.\text{If}A=\{-2,,0,1,2,3,4\},$ then the possible set $B$ could be:

If the roots of the equations $x^3-12x^2+39x-28=0$ are in A.P., then their common difference will be

$\text{For two sets}A=\{5,6,7,8\}\&B=\{7,8,9,11\}.A\cup B=$

The solution of the differential equation $y^{4}dx+2x{y}^{3}dy=\frac{ydx-xdy}{x^3{y}^3}$ is

(where $c$ is integration constant)

A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events :
(i) A = Both numbers are odd.

(ii) B = Both nnanbers are even.

(iii) C = sum of the numbers is less than 6

Also, find $A\cup B,A\cap B,A\cup C,A\cap C$.
Which pairs of events are mutually exclusive?

The value of $\left\{\frac{3^{2003}}{28}\right\},$ where $\{.\}$ denotes the fractional part function, is

If the Boolean expression $(p\wedge q)⊛(p\otimes q)$ is a tautology, then $⊛$ and $\otimes$ are respectively given by

A box contains 10 red balls and 15 blue balls. One ball from the box is lost. Two balls are then drawn from the box and are found to be red ones. Find the chance that the missing ball is a blue ball.

If $z=\frac{-2}{1+i\sqrt{3}}$, then the value of arg(z) is

Find the value of

The equation of the curve which passes through the point (1, 1) and whose slope is given by $\frac{2y}{x}$, is

Look at the following graph





The range of the graph is

For a circle of radius $r=2m$, the angle subtended by an arc of length $\frac{\pi }{2}m$ will be

The interval(s) of $x$ which satisfy the inequality $\frac{(1-3x{)}^7(1+5x{)}^4(x+5{)}^6}{(x^2-1)(x-6{)}^3(1-2x{)}^4}>0$ is/are

Write log₁₀95 = 0.24 in the exponential form