HSC Arts (Marathi Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Differentiate the following w.r.t.x:

(x³ – 2x – 1)⁵

Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)

If A = `[(2, 3),(4, 5)]`, show that A² – 7A – 2I = 0

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

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

Evaluate the following integrals : `int_0^1 log(1/x - 1)*dx`

Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis

In the triangle PQR, `bar("P""Q")`= `2 bar"a"` and `bar ("QR")` = `2 barb`.The mid - point of PR is M. Find following vector in term of  `bar a ` and `barb.`

1. `bar("P""R")` 
2. `bar("P""M")`
3. `bar("Q""M")`

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

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

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

Check whether the vectors `2hati + 2hatj + 3hat k, -3hati + 3hatj + 2hat k` 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)` = `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)`

Find `dy/dx` if ,

`x= e^(3t) , y = e^(4t+5)`

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.

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

Two kinds of foods A and B are being considered to form a weekly diet. The minimum weekly requirements of fats, Carbohydrates and proteins are 12, 16 and 15 units respectively. One kg of food A has 2, 8 and 5 units respectively of these ingredients and one kg of food B has 6, 2 and 3 units respectively. The price of food A is Rs. 4 per kg and that of food B is Rs. 3 per kg. Formulate the L.P.P. and find the minimum cost.

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

Prove that `int_0^(2a) f(x)dx = int_0^a[f(x)  + f(2a - x)]dx`