Arts (English Medium) Class 12 - CBSE Question Bank Solutions

If A = `[(0, 2),(3, −4)]` and kA = `[(0, 3"a"),(2"b", 24)]`, then the values of k, a and b respectively are:

For which value of m is the line y = mx + 1 a tangent to the curve y² = 4x?

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

`"sin"^"p" theta  "cos"^"q" theta` attains a maximum, when `theta` = ____________.

The point on the curves y = (x – 3)² where the tangent is parallel to the chord joining (3, 0) and (4, 1) is ____________.

The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan `"t"/2`)} at the point ‘t’ is ____________.

The tangent to the parabola x² = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.

The two curves x³ - 3xy² + 5 = 0 and 3x²y - y³ - 7 = 0

The distance between the point (1, 1) and the tangent to the curve y = e^2x + x² drawn at the point x = 0

The tangent to the curve y = 2x² - x + 1 is parallel to the line y = 3x + 9 at the point ____________.

The tangent to the curve y = x² + 3x will pass through the point (0, -9) if it is drawn at the point ____________.

Find a point on the curve y = (x – 2)². at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

Tangents to the curve x² + y² = 2 at the points (1, 1) and (-1, 1) are ____________.

The line y = x + 1 is a tangent to the curve y² = 4x at the point

Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis. 

Find the equation of the tangent line to the curve y = x² − 2x + 7 which is parallel to the line 2x − y + 9 = 0.

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

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

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

Evaluate `∫_0^(3/2)|x cosπx|dx`