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

10 months ago

Maths Class 12th

Let y = y(x), x > 1, be the solution of the differential equation

$(x - 1) \frac{d y}{d x} + 2 x y = \frac{1}{x - 1}, w i t h y (2) = \frac{1 + e^{4}}{2 e^{4}} .$ If y(3) = $\frac{e^{α} + 1}{β e^{α}}$ , then the value of α+β is equal to

0 Follower 4 Views

Payal Gupta

Contributor-Level 10

$\frac{d y}{d x} + \frac{2 x}{x - 1} \cdot y = \frac{1}{{(x - 1)}^{2}}$

IF $= e^{\int \frac{2 x}{x - 1} d x}$

= $e^{2 x} \cdot {(x - 1)}^{2}$

$y \cdot e^{2 x} {(x - 1)}^{2} = {e^{2 x} \frac{{(x - 1)}^{2}}{{(x - 1)}^{2}} d x + C$

y = $\frac{e^{2 x}}{2 {(x - 1)}^{2}} + \frac{C}{{(x - 1)}^{2}}$

y (2) = $\frac{1 + e^{4}}{2 e^{4}}, \Rightarrow C = \frac{1}{2}$

y (3) = $\frac{e^{α} + 1}{β e^{α}} = \frac{e^{6} + 1}{8 e^{6}}$

0 0

New answer posted

10 months ago

Maths Class 12th

Let $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k} a n d \vec{c}$ be a vector such that $\vec{a} + (\vec{b} * \vec{c}) = \vec{0} a n d \vec{b} . \vec{c} = 5 .$ Then, the value of $3 (\vec{c} . \vec{a})$ is equal to

0 Follower 33 Views

Payal Gupta

Contributor-Level 10

Data contradiction.

$\vec{a} * (\vec{b} * \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}$

0 0

New answer posted

10 months ago

Maths Maths Binomial Theorem

Let $n \geq 5$ be an integer. If 9ⁿ – 8n – 1 = 64α and 6ⁿ – 5n – 1 = 25β, then α - β is equal to

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

0 0

New answer posted

10 months ago

Maths Class 11th

Negation of the Boolean statement $(p \lor q) \Rightarrow ((\sim r) \lor p)$ is equivalent to

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

pva ⇒ $(\sim r v p)$

$\sim (p \lor q) \lor (\sim r v p)$

its negation as asked in question

$(p \lor q) \land (\sim p \land r)$

= $(p \land \sim p \land r) \lor (q \land r \land \sim p)$

= $(p \land r \land \sim p) [a s p \land \sim p i s f a l s e]$

0 0

New answer posted

10 months ago

Maths Class 11th

From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is

0 Follower 1 View

Payal Gupta

Contributor-Level 10

Let base = b

$t a n 60 ° = \frac{h}{b}$

$t a n 30 ° = \frac{h ? 20}{b}$

0 0

New question posted

10 months ago

Maths Class 11th

From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is

0 Follower

New answer posted

10 months ago

Maths Maths Statistics

The number of values of $a \in N$ such that the variance of 3, 7, 12, a, 43 a is a natural number is

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

$M e a n = \frac{3 + 12 + 7 + a + (43 - a)}{5} = 13$

Variance = $\frac{3^{2} + 1 2^{2} + 7^{2} + a^{2} + {(43 - a)}^{2}}{5} - {(13)}^{2}$

$\Rightarrow \frac{2 a^{2} - a + 1}{5} \to N a t u r a l n u m b e r$

Let 2a² – a + 1 = 5x

D = 1 – 4 (2) (1 – 5n)

= 40n – 7, which is not $4 λ o r 4 λ + 1 f r o m .$

As each square form is $4 λ o r 4 λ + 1$

0 0

New answer posted

10 months ago

Maths Relations and Functions

The probability that a relation R from ${x, y} t o {x, y}$ is both symmetric and transitive, is equal to

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

Total number of possible relation = $2^{n^{2}} = 2^{4} = 16$

Favourable relations = $?, {(x, x)}, {(y, y)}$

${(x, x), (y, y)}$

${(x, x), (y, y), (x, y), (y, x)}$

Probability = $\frac{5}{16}$

0 0

New answer posted

10 months ago

Maths Class 12th

Let A, B, C be three points whose position vectors respectively are

$\vec{a} = \hat{i} + 4 \hat{j} + 3 \hat{k}$

$\vec{b} = 2 \hat{i} + α \hat{j} + 4 \hat{k}, α \in R$

$\vec{c} = 3 \hat{i} - 2 \hat{j} + 5 \hat{k}$

If is the smallest positive integer for which $\vec{a}, \overset{\leftarrow}{b}, \vec{c}$ are noncollinear, then the length of the median, in $Δ A B C,$ through A is

0 Follower 8 Views

Payal Gupta

Contributor-Level 10

Mid point of BC is $\frac{1}{2} (5 \hat{i} + (α - 2) \hat{j} + 9 \hat{k})$

$\bar{A B} = \hat{i} + (α - 4) \hat{j} + \hat{k}$

$\bar{A C} = \hat{i} + (- 2 - α) \hat{j} + \hat{k}$

For = 1, $\bar{A B}$ and $\bar{A C}$ will be collinear. So for non collinearity

= 2

0 0

New answer posted

10 months ago

Maths Class 12th

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y +2z = 16. Let T be a plane passing through the point Q and contains the line $\vec{r} = - \hat{k} + λ (\hat{i} + \hat{j} + 2 \hat{k}), λ \in R .$ Then, which of the following points lies on T?

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

$\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 1}{2} = \frac{- 2 (1 + 4 + 2 - 16)}{1 + 2^{2} + 2^{2}}$

(x, y, z) = (3, 6, 5)

now point Q and line both lies in the plane.

So, equation of plane is

$| \begin{matrix} x & y & z + 1 \\ 3 & 6 & 6 \\ 1 & 2 \end{matrix} | = 0$

2x – z = 1

option (B) satisfies.

0 0

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
691k 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