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

The position vector of points A and B are `6 bara + 2barb and bara - 3barb.` If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara - barb.`

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

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.

If x = f(t) and y = g(t) are differentiable functions of t, so that y is function of x and `(dx)/dt ≠ 0` then prove that `dy/(dx) = (dy/dt)/((dx)/dt)`. Hence find `dy/(dx)`, if x = at², y = 2at.

What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?

The position vector of points A and B are `6bar "a" + 2bar "b"` and `bar "a" - 3bar "b"`. If point C divides AB in the ratio 3:2 then shows that the position vector of C is `3bar "a" - bar "b"`

The position vector of points A and B are 6`\overline"a"` + 2`\overline"b"` and `\overline"a" - 3\overline"b"`. If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3\overline"a" - \overline"b"`.

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 position vector of points A and B are `6bara` + `2barb` and `bara - 3barb`. If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara -  barb`.

The position vector of points A and B are `6bara + 2barb` and `bara -3barb`. If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara-barb`.

Prove that `tan^-1x + tan^-1  (2x)/(1 - x^2) = tan^-1  (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`

Determine whether `bara and barb` are orthogonal, parallel or neither.

`bara = - 3/5 hati+ 1/2 hatj + 1/3 hatk , barb= 5hati + 4hatj + 3hatk`

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

Determine whether `bara` and `barb` are orthogonal, parallel or neither.

`bara = - 3/5 hati + 1/2 hatj + 1/3 hatk, barb = 5hati + 4hatj + 3hatk`

Determine whether `bb(bara and barb)` are orthogonal, parallel or neither.

`bar a = -3/5hati + 1/2hatj + 1/3hatk, barb = 5hati + 4hatj + 3hatk`

Find the volume of the parallelopiped whose vertices are A (3, 2, −1), B (−2, 2, −3) C (3, 5, −2) and D (−2, 5, 4). 

If `barc = 3bara - 2barb` and `[bara     barb + barc     bara + barb + barc]` = 0 then prove that `[bara  barb  barc]` = 0

Determine whether `bb(bara and barb)` are orthogonal, parallel or neither.

`bara=-3/5hati+1/2hatj+1/3hatk,barb=5hati+4hatj+3hatk`