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

8 months ago

Maths Class 11th

Let $λ \neq 0$ be in R. If a and b are the roots of the equation x² – x + $2 λ = 0,$ and a and $γ$ are the roots of the equation 3x² – 10x + $27 λ = 0,$ then $\frac{β γ}{λ}$ is equal to_________.

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

a + b = 1 $α + γ = \frac{10}{3}$

$α β = 2 λ$ $α γ = 9 λ$

$\frac{β}{γ} = \frac{2}{9},$ $β - γ = 1 - \frac{10}{3} = - \frac{7}{3}$

$\Rightarrow β = \frac{2}{3}$ $γ = 3$

$α = \frac{1}{3}, λ = \frac{1}{9}$

$∴ \frac{β γ}{λ} = 18$

0 0

New answer posted

8 months ago

Maths Class 12th

Let a and b respectively be the points of local maximum and local minimum of the function F(x) = 2x³ – 3x² – 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4 A is equal to________.

0 Follower 10 Views

alok kumar singh

Contributor-Level 10

$f (x) = 2 x^{3} - 3 x^{2} - 12 x$

$f' (x) = 6 x^{2} - 6 x - 12$

= 6 (x – 2) (x + 1)

a = -1, b = 2

A = \int_{- 1}^{0} (2 x^{3} - 3 x^{2} - 12 x) d x - \int_{0}^{2} (2 x^{3} - 3 x^{2} - 12 x) d x = \frac{57}{2}

->4A = 114

0 0

New answer posted

8 months ago

Maths Class 11th

If $A_{k} = \sum_{i = 0}^{9} (\begin{matrix} 9 & i \end{matrix}) [\begin{matrix} 12 & 12 - k + i \end{matrix}] + \sum_{i = 0}^{8} (\begin{matrix} 8 & i \end{matrix}) [\begin{matrix} 13 & 13 - k + i \end{matrix}]$ and A₄ – A₃ = 190 p, then p is equal to__________.

0 Follower 4 Views

alok kumar singh

Contributor-Level 10

= coefficient of x⁴ in (1 + x)²¹ + coefficient of x⁴ in (1 + x)²¹

$=^{21} C_{4} +^{21} C_{4} = 2 .^{21} C_{4}$

$A_{3}$ = coefficient of x³ in (1 + x)²¹ + coefficient of x³ in (1 + x)²¹

0 0

New answer posted

8 months ago

Maths Class 12th

Let be the plane passing through the point (1, 2, 3) and the line of intersection of the planes $\vec{r} \cdot (\hat{i} + \hat{j} + 4 \hat{k}) = 16 a n d \vec{r} \cdot (- \hat{i} + \hat{j} + \hat{k}) = 6 .$

Then which of the following points does NOT lie on P?

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

Equation of required plane

$(x + y + 4 z - 16) + λ (- x + y + z - 6) = 0$ it passes (1, 2, 3)

$\Rightarrow - 1 + λ (- 2) = 0$

$\Rightarrow λ = - \frac{1}{2}$

$∴$ Equation of plane

$(1 - λ) x + (1 + λ) y + (4 + λ) z - 16 - 6 λ = 0$

$\frac{3}{2} x + \frac{1}{2} y + \frac{7}{2} z - 13 = 0$

$\Rightarrow 3 x + y + 7 z = 26$

(4, 2, 2) not satisfying the plane

0 0

New answer posted

8 months ago

Maths Class 11th

Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃ = 5i. If $z (\neq z_{1})$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then arg(z) is equal to:

0 Follower 4 Views

Vishal Baghel

Contributor-Level 10

$\frac{2}{- 4} = \frac{- 1}{2}$

y – 4 = 2 (x – 3)

y = 2x – 2

x² + (2x – 2)² = 25

$5 x^{2} - 8 x - 21 = 0$

$z (\frac{- 7}{5}, \frac{- 24}{5})$

0 0

New answer posted

8 months ago

Maths Class 11th

Let x = 2t, $y = \frac{t^{2}}{3}$ be a conic. Let S be the focus and B the point on the axis of the conic such that $S A ⊥ B A,$ where A is any point on the conic. If k is the ordinate of the centroid of the $Δ S A B,$ then $\underset{t \to 1}{l i m}$ k is equal to:

0 Follower 2 Views

Vishal Baghel

Contributor-Level 10

x = 2t $A (2 t, \frac{t^{2}}{3})$ $\frac{^{}}{}$

$y = \frac{t^{2}}{3}$ S (0, 3)

${\frac{}{}}^{}$ $3 y = {(\frac{x}{2})}^{2}$ $B (0, λ)$

$3 k = \frac{t^{2}}{3} + 3 + λ = \frac{2 t^{2}}{3} + 3 - \frac{12 t^{2}}{9 - t^{2}}$

$\underset{t \to 1}{l i m} 3 k = \frac{2}{3} + 3 - \frac{12}{8} = 3 - \frac{5}{6} = \frac{13}{6}$

0 0

New answer posted

8 months ago

Maths Differential Equations

If the solution curve y = y(x) of the differential equation y²dx + (x² – xy + y²)dy = 0, which passes through the point (1, 1) and intersects the line y = $\sqrt[]{3} x$ at the point $(α, \sqrt[]{3} α),$ then value of $l o g_{e} (\sqrt[]{3} α)$ is equal to:

0 Follower 2 Views

Vishal Baghel

Contributor-Level 10

$y^{2} d x + (x^{2} - x y + y^{2}) d y = 0$

$\frac{d x}{d y} + \frac{x^{2} - x y + y^{2}}{y^{2}} = 0 \Rightarrow \frac{d x}{d y} + {(\frac{x}{y})}^{2} - (\frac{x}{y}) + 1 = 0$

Put x = vy $\Rightarrow v + y \frac{d v}{d y} + v^{2} - v + 1 = 0$

$\Rightarrow \frac{y d v}{d y} + v^{2} + 1 = 0$

$\Rightarrow \frac{π}{6} + l n | y | = \frac{π}{4}$

$l n | y | = \frac{π}{12}$

0 0

New answer posted

8 months ago

Maths Class 11th

The statement $(p \Rightarrow q) \lor (p \Rightarrow r)$ is NOT equivalent to

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

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

(B) $q \lor (- r \lor p)$

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

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

Using Venn diagram we get B as the correct option.

0 0

New answer posted

8 months ago

Maths Relations and Functions

The domain of the function f(x) = $s i n^{- 1} (\frac{x^{2} - 3 x + 2}{x^{2} + 2 x + 7}) i s :$

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

$- 1 \leq \frac{x^{2} - 3 x + 2}{x^{2} + 2 x + 7} \leq 1$

$\Rightarrow 0 \leq \frac{2 x^{2} - x + 9}{x^{2} + 2 x + 7} & \frac{- 5 x - 5}{x^{2} + 2 x + 7} \leq 0$

$x \in R & - 1 \leq x < \infty$

0 0

New answer posted

8 months ago

Maths Class 12th

Let $\vec{a}, \vec{b}, \vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $(\vec{a} * \vec{b}) . (\vec{b} * \vec{c}) + (\vec{b} * \vec{c}) . (\vec{c} * \vec{a}) + (\vec{c} * \vec{a}) . (\vec{a} * \vec{b})$ = 168, then $| \vec{a} | + | \vec{b} | + | \vec{c} |$ is equal to

0 Follower 18 Views

Payal Gupta

Contributor-Level 10

Given : $\hat{a} \cdot \hat{b} = \hat{b} \cdot \hat{c} = \hat{c} \cdot \hat{a} = c o s θ (s a y)$

$| \vec{a} | | \vec{b} | | \vec{c} | = 14$

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

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

$= (\vec{a} \cdot \vec{b}) (\vec{b} \cdot \vec{c}) - {| \vec{b} |}^{2} \vec{a} \cdot \vec{c}$

$= | \vec{a} | {| \vec{b} |}^{2} | \vec{c} | (c o s^{2} θ - c o s θ) = 14 | \vec{b} | (c o s^{2} θ - c o s θ)$

Similarly, $(\vec{b} * \vec{c}) \cdot (\vec{c} * \vec{a})$

= $| \vec{b} | {| \vec{c} |}^{2} | \vec{a} | (c o s^{2} θ - s i n θ) = 14 | \vec{c} | (c o s 2 θ - s i n θ) & (\vec{c} * \vec{a}) \cdot (\vec{a} * \vec{b})$

$= | \vec{c} | {| \vec{a} |}^{2} | \vec{b} | (c o s^{2} θ - s i n θ) = 14 | \vec{a} | (c o s^{2} θ - s i n θ)$

Given : 14 $(c o s^{2} θ - c o s θ) (| \vec{a} | + | \vec{b} | + | \vec{c} |) = 168$

$| \vec{a} | + | \vec{b} | + | \vec{c} | = \frac{12}{c o s^{2} θ - c o s θ} = \frac{12}{\frac{1}{4} - (- \frac{1}{2})} = \frac{12}{\frac{3}{4}} = 16$

Given : $\vec{a}, \vec{b}, \vec{c}$ are coplanar & pair wise equal angle.

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
687k 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