Tags Maths

Maths

Get insights from 6.5k questions on Maths, answered by students, alumni, and experts. You may also ask and answer any question you like about Maths

Follow Ask Question

6.5k

Questions

Discussions

Active Users

Followers

New answer posted

a year ago

Maths Sets

Consider the line L given by the equation $\frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1} .$ Let Q be the mirror image of the point (2, 3, -1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is one the plane P?

0 Follower 6 Views

Vishal Baghel

Contributor-Level 10

Equation of plane $⊥^{r}$ to line $\frac{x - 3}{2} = \frac{x - 1}{1} = \frac{x - 2}{1}$ and passes through the point

(2, 3, -1) is 2(x – 2) + 1(y – 3) + 1 (z + 1) = 0

=> 2x + y + z – 6 = 0 .(i)

Hence point (1, 2, 2) satisfies equation (i)

$z = \frac{1}{1 - c o s θ + 2 i s i n θ} = \frac{1 - c o s θ - 2 i s i n θ}{{(1 - c o s θ)}^{2} - {(2 i s i n θ)}^{2}} = \frac{2 s i n^{2} \frac{θ}{2} - 2 i s i n θ}{{(1 - c o s θ)}^{2} + 4 s i n^{2} θ}$

$∴ R e (z) = \frac{2 s i n^{2} \frac{θ}{2}}{4 s i n^{2} \frac{θ}{2} (s i n^{2} \frac{θ}{2} + 4 c o s^{2} \frac{θ}{2})} = \frac{1}{2 (1 + 3 c o s^{2} \frac{θ}{2})} = \frac{1}{5} \Rightarrow c o s^{2} \frac{θ}{2} = \frac{1}{2}$

$\Rightarrow θ = \frac{π}{2} ∴ \int_{0}^{\frac{π}{2}} s i n x d x = 1$

0 0

New answer posted

a year ago

Maths Class 11th

If the sum of the coefficients in the expansion of (x + y)ⁿ is 4096, then the greatest coefficient in the expansion is_________.

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

2ⁿ = 4096 -> n = 12

¹²C₆ = 924 (the greatest coefficient)

0 0

New answer posted

a year ago

Maths Class 11th

A man starts walking from the point P(-3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50(PR)² + (RQ)² is equal to__________.

0 Follower 38 Views

alok kumar singh

Contributor-Level 10

$\Rightarrow \frac{6}{3} = \frac{2}{- t} \Rightarrow t = - 1$

->R (-1,0)

$P R^{2} + R Q^{2} = 20 + 5 = 25$

0 0

New answer posted

a year ago

Maths Class 12th

Let f(x) be a polynomial of degree 3 such that f(k) = $- \frac{2}{k}$ for k = 2, 3, 4, 5. Then the value of 52 – 10 f(10) is equal to________.

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

xf (x) + 2 = $λ$ (x – 2) (x – 3) (x – 4) (x – 5)

$x = 0 \Rightarrow λ = \frac{1}{60}$

x = 10 -> 10f (10) = 26

0 0

New answer posted

a year ago

Maths Class 11th

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is________.

0 Follower 12 Views

alok kumar singh

Contributor-Level 10

0 0

New answer posted

a year ago

Maths Relations and Functions

Let [t] denote the greatest integer $\leq t .$ The number of points where the function f(x) = $[x] | x^{2} - 1 |$ + sin $(\frac{π}{[x] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is__________.

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

$f (x) = {\begin{cases} - 2 x^{2} + 3, - 2 < x < - 1 \\ x^{2}, - 1 \leq x < 0 \\ \frac{\sqrt[]{3}}{2} - 1, 0 \leq x < 1 \\ x^{2} - 3 + \frac{1}{\sqrt[]{2}}, 1 \leq x < 2 \end{cases}$

$f (- 1^{-}) = f (- 1^{+}) = f (- 1) = 1$

$f (1^{+}) = f (1) = \frac{1}{\sqrt[]{2}} - 2$

Points of discontinuity

x = 0, 1

0 0

New answer posted

a year ago

Maths Class 12th

Let $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} a n d \vec{b} = \hat{i} + 2 \hat{j} - \hat{k} .$ Let a vector $\vec{v}$ be in the plane containing $\vec{a} a n d \vec{b} .$ If $\vec{v}$ is perpendicular to the vector $3 \hat{i} + 2 \hat{j} - \hat{k}$ and its projection on $\vec{a}$ is 19 units, then ${| 2 \vec{v} |}^{2}$ is equal to_________.

0 Follower 39 Views

alok kumar singh

Contributor-Level 10

$\vec{v} = l \vec{a} + m \vec{b}$

$= (2 l + m, - l + 2 m, 2 l = m)$

$\vec{v} . (3, 2, - 1) = 0 \Rightarrow l = - 4 m . . . . . . . (i)$

$| \vec{v} . \hat{a} | = 19 \Rightarrow 9 l - 2 m = 57 . . . . . . . . (i i)$

(i) & (ii) Þ l = 6, m = $\frac{- 3}{2}$

$\Rightarrow 2 \vec{v} = (21, - 18, 27)$

${| 2 \vec{v} |}^{2} = 1494$

0 0

New answer posted

a year ago

Maths Class 12th

Let f(x) = $x^{6} + 2 x^{4} + x^{3} + 2 x + 3, x \in R .$ Then the natural number n for which $\underset{x \to 1}{l i m} \frac{x^{n} f (1) - f (x)}{x - 1} = 44$ is_________.

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

$\underset{x \to 1}{l i m} \frac{x^{n} f (1) - f (x)}{x - 1}$

$= \underset{x \to 1}{l i m} \frac{9 x^{n} - (x^{6} + 2 x^{4} + x^{3} + 2 x + 3)}{x - 1}$

= 9n – 19 = 44 -> n = 7

0 0

New answer posted

a year ago

Maths Class 11th

Let the points of intersection of the lines x – y + 1 = 0, x – 2y + 3 = 0 and 2x – 5y + 11 = 0 are the mid points of the sides of a triangle ABC. Then the area of the triangle ABC is_____.

0 Follower 27 Views

alok kumar singh

Contributor-Level 10

ar (ABC) = 4ar (DEF)

$= 4 * \frac{1}{2} * | 2 (2 - 5) + 1 (5 - 3) + 7 (3 - 2) | = 2 | - 6 + 2 + 7 | = 6$

0 0

New question posted

a year ago

Maths Class 11th

If for the complex numbers z satisfying $| z - 2 - 2 i | \leq 1,$ the maximum value of is attained at then a + b is equal to__________.

0 Follower 4 Views

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

66k Colleges
1.2k Exams
711k Reviews
1850k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Need guidance on career and education? Ask our experts

Your Question

Maths

Questions

Discussions

Active Users

Followers

All

Discussions

Unanswered Questions

Share Your College Life Experience