Class 12 is a very crucial year for the Rajasthan Board students as it is the time for them to acquire more in-depth knowledge in their stream of choice. A student who has passed the year successfully can then go for further studies or professional colleges of their choice. In order to score well, Science stream students will then have to practice hard and learn the concepts of subjects like Maths, Physics, Chemistry and Biology thoroughly. Rajasthan Board Class 12 Maths Important Questions is a significant resource for the students.

To help the students with their preparation for the Rajasthan Board Class 12 exams, we have compiled here some important questions from the Class 12 Maths. These questions will help the students to also self- assess their current preparation level.

We have prepared these after careful analysis of the previous year question papers and sample papers so that students get an idea about the type of questions asked in Board exams.

## Download Rajasthan Board Class 12 Maths Important Questions PDF

1) If the points (x,-2), (5,2), (8,8) are colinear, then find the value of x.

2) Find the unit vector along with the sum of vectors

.

3) If 2P(A)=P(B)=5/13 and P(A/B) = â…– then find P (A âˆª B).

4) f f : R â†’ R, f(x) = x^{2} â€“ 5x + 7, then find the value of f ^{â€“1}(1).

5) Find A, if 2A –

6) Find the direction cosines of the line (x-2) /2 = (y+1) / -2 = (z-1) /1.

7) Find

8) Find the angle between planes

.

9) From a pack of 52 cards, two cards are drawn randomly one by one without replacement. Find the probability that both of them are red.

10) Show the region of a feasible solution under the following constraints xy+â‰¥28x,â‰¥0y,â‰¥0 in the answer book.

11) Examine continuity at x= 1 of function f (x) = f | x -1 |

12) Find

13) If

then find 2A^{2}-3B.

14) Examine the continuity of the function f defined by

15) Prove that the relation R in a set of real numbers R defined as R {( , ab): a=â‰¥b} is reflexive and transitive but not symmetric.

16) Solve 2 tan^{-1} (sin x)=tan^{-1}(2sec x), 0 < x< Ï€ /2 .

17) Find the intervals in which the function f given by f (x) = x^{2} â€“ 6x+5 is

a) Strictly increasing

b) Strictly decreasing

18) Prove that the relation R defined on set Z as a R b â‡” a âˆ’ b is divisible by 3, is an equivalence relation.

19) Prove that

20) If the radius of a sphere is measured as 9 cm with an error of 0Â·02 cm, then find the approximate error in calculating its volume.

21) Find two positive numbers x and y, the sum of them is 60 and xy^{3} is maximum.

22) Solve the equation cos ^{-1} x + cos ^{-1} 2x = (2Ï€) /3

23) Solve the following system of equations by using Cramer’s rule.

5x â€“ 4y = 7

x + 3y = 9

24) Using integration find the area of a triangular region whose sides have the equations y = x + 1, y = 2x + 1 and x = 2.

(Draw the figure in answer book)

25) Find the area of the triangle whose vertices are A ( 1, 1, 1 ), B ( 1, 2, 3 ) and C ( 2, 3, 3 ).

26) Prove that

.

27) A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is 6. Find the probability that it is actually 6.

28) Bag A contains 2 red and 3 black balls while another bag B contains 3 red and 4 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from bag B.

29) Prove that if a plane has the intercepts a, b, c and is at distance p units from the origin, then prove that (1/ a^{2}) + (1/b^{2 }) + (1/c^{2})= (1/p^{2}).

30) A dice is thrown twice and the sum of the numbers appearing is observed to be 7. Find the conditional probability that the number 3 has appeared at least once.

31) Find the equation of the plane through the line of intersection of the 1+y + z = and 2x + 3y + 4z = 5 which is perpendicular to the x- y + z =3.