HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

The joint equation of the angle bisectors of the angles between the lines 4x² – 16xy + 7y² = 0 is ______.

The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.

Evaluate `int_(-π/2)^(π/2) sinx/(1 + cos^2x)dx`

If the lines represented by 5x² – 3xy + ky² = 0 are perpendicular to each other, find the value of k.

If `int_0^π f(sinx)dx = kint_0^π f(sinx)dx`, then find the value of k.

Evaluate `int tan^-1x  dx`

Evaluate:

`int (sin(x - a))/(sin(x + a))dx`

If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv  dx - int(d/dx u)(intv  dx)dx`. Hence evaluate: `intx cos x  dx`

Evaluate:

`int1/(x^2 + 25)dx`

Find the approximate value of tan⁻¹ (1.002).
[Given: π = 3.1416]

Find the shortest distance between the lines `barr = (4hati - hatj) + λ(hati + 2hatj - 3hatk)` and `barr = (hati - hatj -2hatk) + μ(hati + 4hatj - 5hatk)`

Prove that the acute angle θ between the lines represented by the equation ax² + 2hxy+ by² = 0 is tanθ = `|(2sqrt(h^2 - ab))/(a + b)|` Hence find the condition that the lines are coincident.

Minimize `z=4x+5y ` subject to `2x+y>=7, 2x+3y<=15, x<=3,x>=0, y>=0` solve using graphical method.

If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx

Find `dy/dx if y=cos^-1(sqrt(x))`

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

Minimize: Z = 6x + 4y

Subject to the conditions:

3x + 2y ≥ 12,

x + y ≥ 5,

0 ≤ x ≤ 4,

0 ≤ y ≤ 4

If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `

(A) x

(B) 1/x

(C) 1

(D) 0

Given is X ~ B(n, p). If E(X) = 6, and Var(X) = 4.2, find the value of n.

Solve the following LPP by using graphical method.

Maximize : Z = 6x + 4y

Subject to x ≤ 2, x + y ≤  3, -2x + y ≤  1, x ≥  0, y ≥ 0.

Also find maximum value of Z.