HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Choose the correct option from the given alternatives : 

`int_0^(pi/2) (sin^2x*dx)/(1 + cosx)^2` = ______.

Verify which of the following is p.d.f. of r.v. X:

f(x) = x, for 0 ≤ x ≤ 1 and 2 - x for 1 < x < 2

Verify which of the following is p.d.f. of r.v. X:

 f(x) = 2, for 0 ≤ x ≤ 1.

It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is non-negative

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is odd

Solve the following :

The following probability distribution of r.v. X

Find the probability that

X is even

Evaluate the following.

`int e^x (1/x - 1/x^2)`dx

The acute angle between the lines represented by x² + xy = 0 is ______.

Find the measure of the acute angle between the lines given by x² − 4xy + y² = 0 

Find the value of h, if the measure of the angle between the lines 3x² + 2hxy + 2y² = 0 is 45°. 

If θ is the acute angle between the lines given by ax² + 2hxy + by² = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x² + 7xy + 3y² = 0 

If the angle between the lines represented by ax² + 2hxy + by² = 0 is equal to the angle between the lines 2x² − 5xy + 3y² = 0, then show that 100(h² − ab) = (a + b)²

The value of x, y, z for the following system of equations x + y + z = 6, x − y+ 2z = 5, 2x + y − z = 1 are ______

System of equations x + y = 2, 2x + 2y = 3 has ______

If A = `[(2, 0),(0, 1)]` and B = `[(1),(2)]`, then find the matrix X such that A⁻¹X = B.

Transform `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]` into an upper triangular matrix by using suitable row transformations

Solve the following by inversion method 2x + y = 5, 3x + 5y = −3

Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices

Solve the following equations by using inversion method.

x + y + z = −1, x − y + z = 2 and x + y − z = 3