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

Evaluate:

`int sqrt((a - x)/x) dx`

If in ΔABC, `sin  A/2 * sin  C/2 = sin  B/2` and 2s is the perimeter of the triangle, then s = ______.

Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`

Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.

From the following set of statements, select two statements which have similar meaning.

1. If a man is judge, then he is honest.
2. If a man is not a judge, then he is not honest.
3. If a man is honest, then he is a judge.
4. If a man is not honest, then he is not a judge.

The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.

`int "cosec"^4x  dx` = ______.

The differential equation for a²y = log x + b, is ______.

Evaluate:

`int sin^2(x/2)dx`

Solve the differential equation

cos²(x – 2y) = `1 - 2dy/dx`

If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m²y²

`int x^2/sqrt(1 - x^6)dx` = ______.

If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)

Form the differential equation whose general solution is y = a cos 2x + b sin 2x.

`int 1/(sin^2x cos^2x)dx` = ______.

Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

1. Seema is thin and happy.
2. If Seema is fat then she is unhappy.

Evaluate:

`int(cos 2x)/sinx dx`

The perimeter of ΔABC is 20, ∠A = 60°, area of ΔABC = `10sqrt(3)`, then find the values of a, b, c.

Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`

The sum of the slopes of the lines given by x² – 2λxy – 7y² = 0 is 4 times their product, then the value of λ is ______.