Two high school classes took the same test. One class of 20 students made an average grade of 80 %; the other class of 30 students made an average grade of 70 %. The average grade for all students in both classes is:

Two high school classes took the same test. One class of 20 stude…

If $z_1,z_2,z_3$ are vertices of a triangle in argand plane such that $|z_1 -z_2| = |z_1 -z_3|$, then $arg\ \left( {\frac{{2{z_1} - {z_2} - {z_3}}}{{{z_3} - {z_2}}}} \right)$ is-

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The foci of the hyperbola $9{x^2} - 16{y^2} = 144$ are

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How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

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In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls

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If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks, then his chance of winning prize are

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If $\text{f(x)}=\cos(\log\text{x}),$ then value of $\text{f(x)}\text{f(4)}-\frac{1}{2}\Big\{\text{f}\Big(\frac{\text{x}}{4}\Big)+\text{f}(4\text{x})\Big\}$ is:

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Statement $1$ : The only circle having radius $\sqrt {10} $ and a diameter along line $2x + y = 5$ is $x^2 + y^2 - 6x +2y = 0$.
Statement $2$ : $2x + y = 5$ is a normal to the circle $x^2 + y^2 -6x+2y = 0$.

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Let $U$ be the universal set and $A \cup B \cup C = U$. Then $\{ (A - B) \cup (B - C) \cup (C - A)\} '$ is equal to

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Let $A = \left\{ {\left( {x,y} \right):\,y = mx + 1} \right\}$

$B = \left\{ {\left( {x,y} \right):\,\,{x^2} + 4{y^2} = 1} \right\}$

$C = \left\{ {\left( {\alpha ,\beta } \right):\,\left( {\alpha ,\beta } \right) \in A\,\,and\,\,\left( {\alpha ,\beta } \right) \in B\,\,and\,\alpha \, > 0} \right\}$ .

If set $C$ is singleton set then sum of all possible values of $m$ is

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Sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ ...\text{ is}$

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