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Differential Equations

Multiple Choice Questions

Let be three unit vectors such that then the angle between is

3π/4
π/2
2π/3
5π/6

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If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

3a²−26a+55=0
3a²−32a+84=0
3a²−34a+91=0
3a²−34a+91=0

206 Views

3.
Let y(x) be the solution of the differential equation $left parenthesis straight x space log space straight x right parenthesis dy over dx space plus straight y space equals space 2 space straight x space log space straight x comma$ (x ≥1). Then, y (e) is equal to

e

0

2

2

Given differential equation is
$straight x left parenthesis log space straight x right parenthesis dy over dx space plus straight y space equals 2 space straight x space log space straight x comma rightwards double arrow space dy over dx space plus fraction numerator straight y over denominator straight x space log space straight x end fraction space equals 2$
This is a linear differential equation.
therefore, $IF space equals space straight e to the power of integral fraction numerator 1 over denominator straight x space log space straight x end fraction dx end exponent space equals space straight e to the power of log space left parenthesis log space straight x right parenthesis space end exponent space equals space log space straight x$
Now, the solution of given differential equation is given by
$straight y. space log space straight x space equals space integral log space straight x. space 2 dx straight y. space log space straight x space equals space space equals space 2 integral log space straight x space dx At space straight y. space log space straight x space equals space 2 left square bracket space straight x space log space straight x minus straight x right square bracket plus straight c straight x space equals space 1 straight c space equals 2 straight y. space log space straight x space equals space 2 left square bracket straight x space log space straight x minus straight x right square bracket plus 2 straight x space equals straight e straight y space equals space 2 space left parenthesis straight e minus straight e right parenthesis space plus 2 space rightwards double arrow straight y space equals space 2$

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If $left parenthesis 2 space sin space straight x right parenthesis space dy over dx space plus space left parenthesis space straight y space plus 1 right parenthesis space cos space straight x space equals space 0 space and space straight y left parenthesis 0 right parenthesis space equals 1 space then space straight y open parentheses straight pi over 2 close parentheses$ is equal to

4/3
1/3
-2/3
-2/3

220 Views

Let In ∫tan x dx,(n> 1) . I⁴ + I⁶ = a tan⁵x + bx⁵ + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

$open parentheses negative 1 fifth comma 0 close parentheses$
$open parentheses negative 1 fifth comma 1 close parentheses$
$open parentheses 1 fifth comma 0 close parentheses$
$open parentheses 1 fifth comma 0 close parentheses$

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How many real solutions does the equation x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0 have?

149 Views

Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

$\frac{3 \sqrt{5}}{2}$
$\sqrt{10}$
$2 \sqrt{10}$
$3 \sqrt{\frac{5}{2}}$

Consider the non-constant differentiable function f of one variable which obeys the relation $\frac{f (x)}{f (y)}$ f(x - y ). If f'(0)= p and f(y) . f'(5) = q, then f'(- 5) is