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a year ago

Maths Class 11th

The number of values of x in the interval $(\frac{π}{4}, \frac{7 π}{4})$ for which 14 cosec²x – 2sin² x = 21 – 4cos²x holds, is………

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Vishal Baghel

Contributor-Level 10

Kindly consider the following answer

$\frac{?}{4} < x < \frac{?}{4}$

$\frac{14}{s i n^{2} x} ? 2 s i n^{2} x = 21 ? 4 + 4 s i n^{2} x$

$t = \frac{? 17 \pm \sqrt[]{289 + 336}}{12}$

$= \frac{? 17 \pm 25}{12} = \frac{8}{12}, \frac{? 42}{12}$

$= \frac{2}{3},$

No. of solutions = 4

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New question posted

a year ago

Maths Class 11th

The number of values of x in the interval $(\frac{π}{4}, \frac{7 π}{4})$ for which 14 cosec²x – 2sin² x = 21 – 4cos²x holds, is………

0 Follower 2 Views

New answer posted

a year ago

Maths Class 11th

Let the abscissae of the two points P and Q be the roots of 2x² – rx + p = 0 and the ordinates of P and Q be the roots of x² – sx – q = 0. If the equation of the circle described on PQ as diameter is 2(x² + y²) – 11x – 14y – 22 = 0, then 2r + s – 2q + is equal to….

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Vishal Baghel

Contributor-Level 10

$P (x_{1}, y_{1})$

$Q (x_{2}, y_{2})$

$x_{1} + x_{2} = \frac{r}{2}, x_{1} x_{2} = \frac{P}{2}$

$y_{1} + y_{2} = s, y_{1}, y_{2} = - 9$

$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$

$2 (x^{2} + y^{2}) - r x - 2 s y + p - 2 q = 0$

r = 11, s = 7, p – 2q = -22

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New answer posted

a year ago

Maths Class 12th

Let θ be the angle between the vectors $\vec{a} a n d \vec{b},$ where $| \vec{a} | = 4, | \vec{b} | = 3$ and $θ \in (\frac{π}{4}, \frac{π}{3})$ . Then ${| (\vec{a} - \vec{b}) * (\vec{a} + \vec{b}) |}^{2} + 4 {(\vec{a} . \vec{b})}^{2}$ is equal to…………

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Vishal Baghel

Contributor-Level 10

${| 2 (\vec{a} * \vec{b}) |}^{2} + 4 {(\vec{a} . \vec{b})}^{2}$

$4 {| \vec{a} |}^{2} {| \vec{b} |}^{2}$

= 4 * 16 * 9 = 576

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New answer posted

a year ago

Maths Class 11th

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is……….

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Vishal Baghel

Contributor-Level 10

$x_{1} + x_{2} = 6, 13 \to 6 + 6 = 12$

$\begin{array}{l} x_{1} + x_{2} = 4, 11, 18 \to 4 + 8 + 1 = 13 \\ x_{1} + x_{2} = 2, 9, 16 \to 2 + 9 + 3 = 14 \\ x_{1} + x_{2} = 7, 14 \to 7 + 5 = 12 \\ x_{1} + x_{2} = 5, 12 \to 5 + 7 = 12 \end{array}$

=63

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New answer posted

a year ago

Maths Class 11th

Let c_r denote the binomial coefficient of x^r in the expansion of (1 + x)¹⁰. If for $\in R,$ α, β c₁ + 3.2C₂ + 5.3C₃ + ….upto 10 terms = $\frac{α * 2^{11}}{2^{β} - 1} (C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + . . . . u p t o 10 t e r m s)$ then the value of a + b is equal to……….

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Vishal Baghel

Contributor-Level 10

$\sum_{k = 1}^{10} (2 k - 1) . k .^{10} C_{k}$

$= 2 \sum {k^{2}}^{10} C_{k} - \sum k .^{10} C_{k}$

$x = 1 \Rightarrow \sum_{k = 0}^{10} k .^{10} C_{k} = 10 . 2^{9}$

$x = 1 \Rightarrow \sum k^{2}^{10} C_{k} = 90 . 2^{8} + 10 . 2^{9} = 2^{8} (90 + 201) = 2^{8} . 110$

S = 2⁹ . 110 – 10.2⁹ = 2⁹ . 100

S = 2⁹ . 100

$\frac{2^{11} . 25}{2^{1} - 1}$

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New answer posted

a year ago

Maths Class 11th

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:

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Vishal Baghel

Contributor-Level 10

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

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

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

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

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

$l n | y | = \frac{?}{12}$

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New answer posted

a year ago

Maths Class 11th

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Vishal Baghel

Contributor-Level 10

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

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

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

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

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

$l n | y | = \frac{?}{12}$

0 0

New answer posted

a year ago

Maths Class 11th

0 Follower 1 View

Vishal Baghel

Contributor-Level 10

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

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

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

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

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

$l n | y | = \frac{?}{12}$

0 0

New answer posted

a year ago

Maths Class 11th

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0 Follower 3 Views

Vishal Baghel

Contributor-Level 10

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

0 0

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