Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.

The differential equation of the family of curves y² = 4a(x + a) is ______.

The differential equation representing the family of circles x² + (y – a)² = a² will be of order two.

Differential equation representing the family of curves y = e^x (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0

The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is ______.

If `"x = a sin"  theta  "and  y = b cos"  theta, "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

If y `= "Ae"^(5"x") + "Be"^(-5"x") "x"  "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

Find: `int logx/(1 + log x)^2 dx`

Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`

The value of `int_2^3 x/(x^2 + 1)`dx is ______.

If A, B are non-singular square matrices of the same order, then (AB^–1)^–1 = ______.

If A and B are invertible square matrices of the same order, then which of the following is not correct?

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`

Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

Find the coordinate of the point P where the line through A(3, –4, –5) and B(2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0).
Also, find the ratio in which P divides the line segment AB.

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`