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 question posted

3 months ago

Maths Class 11th

The locus of the mid - points of the perpendiculars drawn from points on the line, $x = 2 y$ to the line $x = y$ is:

0 Follower 6 Views

New answer posted

3 months ago

Maths Vector Algebra

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ . If $λ = \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ and $\vec{d} = \vec{a} * \vec{b} + \vec{b} * \vec{c} + \vec{c} * \vec{a}$ , then the ordered pair, $(λ, \vec{d})$ is equal to:

0 Follower 7 Views

alok kumar singh

Contributor-Level 10

$= \frac{128}{3}$

$3 + 2 (\overset{?}{a} \cdot \overset{?}{b} + \overset{?}{b} \cdot \overset{?}{c} + \overset{?}{c} \cdot \overset{?}{a}) = 0$

$\begin{array}{r} \overset{?}{a} \cdot \overset{?}{b} + \overset{?}{b} \cdot \overset{?}{c} + \overset{?}{c} \cdot \overset{?}{a} = - \frac{3}{2} \\ \overset{?}{d} = \overset{?}{a} * \overset{?}{b} + \overset{?}{b} * \overset{?}{c} + \overset{?}{c} * \overset{?}{a} \\ \overset{?}{d} = 3 (\overset{?}{a} * \overset{?}{b}) \end{array}$

0 0

New answer posted

3 months ago

Maths Maths Application of Integrals

The area (in sq. units of the region $\{(x, y) \in R^{2} ∣ 4 x^{2} \leq y \leq 8 x + 12\}$ is:

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

$x = 1$

$4 x^{2} = 8 x + 12$

Area $x = - 1,3$

$= \int_{- 1}^{3} ? [(8 x + 12) - 4 x^{2}] d x$

$= {[\frac{8 x^{2}}{2} + 12 x - \frac{4 x^{3}}{3}]}_{- 1}^{3}$

0 0

New answer posted

3 months ago

Maths Class 11th

Let $f (x)$ be a polynomial of degree 5 such that $x = \pm 1$ are its critical points. If ${l i m}_{x \to 0} ? (2 + \frac{f (x)}{x^{3}}) = 4$ , then which one of the following is not true?

0 Follower 7 Views

alok kumar singh

Contributor-Level 10

$f^{'} (x) = a (x + 1) (x - 1) x^{2}$

$f^{'} (x) = a x^{4} - x^{2} f$

$f (x) = \frac{a x^{5}}{5} - \frac{a x^{3}}{5} + C$
$? f (0) = 0 \Rightarrow c = 0$

${l i m}_{x \to 0} ? \frac{f (x)}{x^{3}} = 2$

$\Rightarrow a = - 6$

Minima at $∴ f^{'} (x) = - 6 (x^{2} - 1) (x^{2})$

Maxima at $x = - 1$

0 0

New answer posted

3 months ago

Maths Differential Equations

Let $y = y (x)$ be the solution curve of the differential equation, $(y^{2} - x) \frac{d y}{d x} = 1$ , satisfying $y (0) = 1$ . This curve intersects the $x -$ axis at a point whose abscissa is:

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

$f^{'} (x) = a (x + 1) (x - 1) x^{2}$

$f^{'} (x) = a x^{4} - x^{2} f$

$f (x) = \frac{a x^{5}}{5} - \frac{a x^{3}}{5} + C$
$? f (0) = 0 \Rightarrow c = 0$

${l i m}_{x \to 0} ? \frac{f (x)}{x^{3}} = 2$

$\Rightarrow a = - 6$

Minima at $∴ f^{'} (x) = - 6 (x^{2} - 1) (x^{2})$

Maxima at $x = - 1$

0 0

New answer posted

3 months ago

Maths Class 12th

Let $y = y (x)$ be a function of $x$ satisfying $y \sqrt[]{1 - x^{2}} = k - x \sqrt[]{1 - y^{2}}$ where $k$ is a constant and $y (\frac{1}{2}) = - \frac{1}{4}$ . Then $\frac{d y}{d x}$ at $x = \frac{1}{2}$ , is equal to:

0 Follower 4 Views

alok kumar singh

Contributor-Level 10

Differentiating

y. $\frac{- 2 x}{2 \sqrt[]{1 - x^{2}}} + \sqrt[]{1 - x^{2}} \cdot y^{'} = \frac{x \cdot 2 y y^{'}}{2 \sqrt[]{1 - y^{2}}} - \sqrt[]{1 - y^{2}}$

Put $x = \frac{1}{2}, y = - \frac{1}{4}$ and $x, y = - \frac{1}{8}$

$y^{'} = \frac{- \sqrt[]{5}}{2}$

0 0

New answer posted

3 months ago

Maths Integrals

The value of $α$ for which $4 α \int_{- 1}^{2} ? e^{- α | x |} d x = 5$ , is

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

$4 α \int_{- 1}^{0} ? e^{α x} d x + \int_{0}^{2} ? e^{- α x} d x = 5$

$\Rightarrow 4 α (\frac{1 - e^{- α}}{α} - \frac{e^{- 2 α} - 1}{- α}) = 5$

Let $e^{- α} = t$

$∴ 4 t^{2} + 4 t - 3 = 0$

$\Rightarrow t = \frac{1}{2}$

$α = l n ? 2$

0 0

New answer posted

3 months ago

Maths Maths Continuity and Differentiability

The value of $c$ in the Lagrange's mean value theorem for the function $f (x) = x^{3} - 4 x^{2} + 8 x + 11$ , when $x \in [0,1]$ is:

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

Using LMVT

$f^{'} (c) = \frac{f (1) - f (0)}{1 - 0}$

$3 c^{2} - 8 c + 8 = \frac{16 - 11}{1 - 0}$

$3 c^{2} - 8 c + 3 = 0$

$c = \frac{4 - \sqrt[]{7}}{3} \in (0,1)$

0 0

New answer posted

3 months ago

Maths Class 12th

Let $A = [a_{i j}]$ and $B = [b_{i j}]$ be two $3 * 3$ real matrices such that $b_{i j} = (3)^{(i + j - 2)} a_{j i}$ , where $i, j = 1,2, 3$ . If the determinant of is 81 , then the determinant of is:

0 Follower 5 Views

alok kumar singh

Contributor-Level 10

$| B | = |\begin{array}{l} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{array}| = |\begin{array}{l} 3^{0} a_{11} & 3^{1} a_{21} & 3^{2} a_{31} \\ 3^{1} a_{12} & 3^{2} a_{22} & 3^{3} a_{32} \\ 3^{2} a_{13} & 3^{3} a_{23} & 3^{4} a_{33} \end{array}|$

$81 = 3^{3} \cdot 3^{3} \cdot 3^{2} | A |$

$\Rightarrow | A | = \frac{1}{9}$

0 0

New answer posted

3 months ago

Maths Class 11th

If the sum of the first 40 terms of the series, $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \dots$ is (102) $m$ , then $m$ is equal to:

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

$3 + 4 + 8 + 9 + 13 + 14 + \dots .$ . upto 40 terms

$\Rightarrow 7 + 17 + 27 + \dots \dots . . 20$ terms

$S = \frac{20}{2} [2 * 7 + 19 * 10]$

$= 102 * 20 = 102 m$

$∴ m = 20$

0 0

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

On Shiksha, get access to

65k Colleges
1.2k Exams
679k Reviews
1800k 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