Maths

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

In this question we get $2$ options that is (i) Either all $3$ will go Then remaining students in class are: \[25\text{ }-\text{ }3\text{ }=\text{ }22\] Number of students remained to be chosen for...

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In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

The student can choose $3$ questions from $part\;I$ and $5$ from $part\;II$ Or $4\;questions$ from $part\;I$ and $4$ from $part \;II$ $5$ questions from $part\;I$ and $3$ from $part \;II$

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In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.
(a) 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0
(b) 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0

Solution: (a) $2 x-2 y+4 z+5=0$ and $3 x-3 y+6 z-1=0$ It is given that The eq. of the given planes are $2 x-2 y+4 z+5=0$ and $x-2 y+5=0$ It is known to us that, two planes are $\perp$ if the...

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In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.
(a) 7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
(b) 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0

Solution: (a) $7 x+5 y+6 z+30=0$ and $3 x-y-10 z+4=0$ It is given that The eq. of the given planes are $7 x+5 y+6 z+30=0$ and $3 x-y-10 z+4=0$ Two planes are $\perp$ if the direction ratio of the...

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Write which of the following statements are true? Justify your answer. (i) The sets P = {a} and B = {{a}} are equal. (ii) The sets A={x: x is a letter of word “LITTLE”} AND, b = {x: x is a letter of the word “TITLE”} are equal.

Answers: (i) This statement is False P = {a} B = {{a}} But {a} = P B = {P} P and B are not equal (ii) This statement is True A = For “LITTLE” A = {L, I, T, E} = {E, I, L, T} B = For “TITLE” B = {T,...

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