HSC Arts (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.

Find the area of the region bounded by the curve y = x², and the lines x = 1, x = 2, and y = 0.

Solve the following system of equations by the method of reduction:

x + y + z = 6, y + 3z = 11, x + z = 2y.

The principle solutions of the equation cos θ = `1/2` are ______.

Check whether the vectors `2hati+2hatj+3hatk,-3hati+3hatj+2hatk` and `3hati+4hatk` form a triangle or not.

In the triangle PQR, `bar(PQ)` = 2`bara` and `bar(QR)` = 2`barb`. The mid-point of PR is M. Find following vectors in terms of `bara` and `barb`.

1. `bar(PR)`
2. `bar(PM)`
3. `bar(QM)`

Check whether the vectors `2hati + 2 hatj + 3hatk, - 3hati + 3hatj + 2hatk and 3hati + 4hatk` From a triangle or not.  

Evaluate the following.

`int x^3/(sqrt1 + x^4) `dx

In the triangle PQR, `bar(PQ)=2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bara and barb`.

(i) `bar(PR)`  (ii) `bar(PM)`  (iii) `bar(QM)`

In the triangle PQR, `bar"PQ" = 2 bar" a" and bar"QR" = 2 bar"b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:

(i) `bar"PR"` (ii) `bar"PM"` (iii) `bar"QM"`

Evaluate `int (1 + "x" + "x"^2/(2!))`dx

Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.

Check whether the vectors `2 hati+2 hatj+3 hatk,-3 hati+3 hatj+2 hatk and 3 hati +4 hatk` form a triangle or not.

In the triangle PQR, `bar"PQ" = bar"2a", bar"QR" = bar"2b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:

(i) `bar"PR"` (ii) `bar"PM"` (iii) `bar"QM"`.

Check whether the vectors `2hati + 2hatj +3hatk, - 3hati + 3hatj + 2hatk and 3hati + 4hatk`  form a triangle or not. 

Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.

In the triangle PQR, `bar(PQ)` = 2`bara` and `bar(QR)` = 2`barb`. The midpoint of PR is M. Find the following vectors in terms of `bara` and `barb`.

(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`

Solve the differential equation:

(1 + y²) dx = (tan⁻¹ y − x) dy

Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`

In ΔABC, prove the following:

`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`