The Central Board of Secondary Education (CBSE) has released the date of examination for 12th boards. The exams will commence from March 5th till April 11th. The final board result will be calculated on the basis of practicals as well as board theory examination. As the board examination is nearing, it is the best time for students to begin practicing for their examination.

Most of the subjects in class 12 are vast, where some of them require not only memorization but also requires skill. One such is the subject of Mathematics, which seems to be a nightmare for students and requires a lot of practice to boost confidence. So we at BYJU’S provide students of Class 12 with important 2 marks question, which can be beneficial for them in their Board examination.

Students preparing for CBSE Class 12 Maths Board Examination are advised to practice the given question for Mathematics:

**Important 2 Marks Questions for Class 12 Maths Board are as follows-**

**Question 1:** Let the function f : R → R be defined by f (x) = cos x for all x ϵ R. Show that f is neither one-one nor onto.

**Question 2:** A box contains 11 balls of which some are red in color. If 5 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles. Find the initial number of red balls present in the box.

**Question 3:** How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all? Justify your answer.

**Question 4:** Find dy/dx when x and y are connected by the relation: sec (x + y) = xy

**Question 5:** Examine the continuity of the function f (x) = x3 + 2×2 – 1 at x = 1.

**Question 6:** A furniture dealer sells only tables and chairs. He has Rs. 50,000 to invest and a storing capacity for 80 items. He buys a table for Rs. 800 and a chair for Rs. 400. He gets a profit of Rs. 100 on selling a table and Rs. 50 on selling a chair. Assuming that he sell whatever he purchases, formulate the above as an LPP for maximum profit.

**Question 7:** Evaluate: cos‒1 (‒√3 /2) + π/6).

**Question 8:** Differentiate 8x/x8 with respect to x.

**Question 9:** If cos (tan‒1 x + cot ‒1 √3) = 0 then, calculate the value of x.

**Question 10:** Find the Cartesian equation of the line which passes through the point (-2.4.-5) and is parallel to the line \(\frac{x+3}{3} = \frac{4-y}{5} = \frac{z+8 }{6}\)

**Question 11:** If f (x) = |cos x ‒ sin x|, then find the value of f’(π/3).

**Question 12:** If x = 3sin t – sin 3t, y = 3 cos t – cos 3t, then find dy/dx.

**Question 13:** Find the adjoint of the matrix A = \(\begin{bmatrix} 1 & 2\\ 3 & -5 \end{bmatrix}\). Also verify that A (adj A) = \(\left | A \right | I\).

**Question 14:** Find the approximate change in the value of (1/x2), when x changes from x = 2 to x = 2.002.

**Question 15:** Find the next term of the series-

3, 4, 6, 9, 14, 21, ?

**Question 16:** The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. Find the rate at which its area increases, when side is 10 cm long.

**Question 17:** The two positive integers p and q are of the form-

\(p = a^{2}b^{3}\)

\(q = a^{3}b\),

where a, b are prime numbers.

Then verify:

LCM (p,q) \(\times\) HCF (p,q) = pq

**Question 18:** If A and B are two events such that P (A) = 0.4, P (B) = 0.8 and P (B|A) = 0.6, then find P (A|B).

**Question 19:** Find the value(s) of k for which the pair of linear equation \(kx+ y = k^{2}\) and x + ky = 1 have infinitely many solution.

**Question 20:** The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = \(0.005x^{3}+0.02x^{2} + 30x\). Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.

**Question 21:** Integrate: tan2x sec4x dx.

**Question 22:** Show that f (x) = tan-1 (sin x + cos x) is an increasing function in (0, π/4).

**Question 23:** Find the LCM of the given numbers-

\(\frac{10}{15}, \frac{13}{117}, \frac{30}{36}\)

**Question 24:** Find an angle q, where 0 < q < π/2, which increases twice as fast as its sine.

**Question 25:** Find dy/dx when x and y are connected by the relation: tan-1 (x2 + y2) = a

**Question 26:** Arun can solve 90 % of the problems given in a book whereas Amit can solve 70%. Find the probability that at least one of them will solve the problem, selected at random from the book?

**Question 27:** A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of them is a boy (ii) the older child is a boy.

**Question 28:** Verify that ax3 + by2 = 1 is a solution of the differential equation x (yy1 + y1) = yy1.

**Question 29:** Find the Cartesian and vector equations of the line which passes through the point (‒2, 4, ‒5) and parallel to the line given by (x + 3)/3 = (y ‒ 4)/5 = (8 ‒ z)/‒6.

**Question 30:** Find the Projection (vector) of 2 i ‒ j + k on i ‒ 2j + k.

**Question 31:** Find the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XZ plane.

**Question 32:** Solve the following Linear Programming Problem graphically:

Maximize: Z = 3 x + 4 y

Subject to: x + y ≤ 4, x ≥ 0 and y ≥ 0.