Maths can be a nightmare to many students as the subject requires conceptual knowledge and a good understanding. It is not a childâ€™s play to excel in the subject without having a masterly skill and excellent grip on the concepts. As CBSE Class 12 Maths subject requires a lot of practice to learn theorems and their proofs, it also requires timely revision, otherwise, it is easy to forget the concepts within a matter of time.

In class 12 Maths, the long type answers which carry 10 marks should contain two subdivisions. The marks allotted to each of a question should be either 4 marks or 6 marks. Get 12th Maths important 10 marks pdf at BYJU’S.

**Also, get:** Important 4 Marks Questions for CBSE Class 12 Maths

## Important 6 Marks Questions for Class 12 Maths CBSE Board

So here are a few important 6 marks questions, which is a part of 12th maths important 10 marks questions for students, who aim to secure good percentage:

**Question 1- **In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let \(\frac{3}{5}\) be the probability that he knows the answer and \(\frac{2}{5}\) be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability \(\frac{1}{3}\), what is the probability that the student knows the answer given that he answered it correctly?

**Question 2- **Using integration, find the area enclosed by the parabola 4y = 3x^{2} and the line 2y = 3x + 12.

**Question 3****– **DetermineÂ the vector and cartesian equations of the plane that passes through the line of intersection of the planes

\(\vec{r} .(2\hat{i} + 2\hat{j} – 3\hat{k}) = 7\)

and \(\vec{r} .(2\hat{i} + 5\hat{j} + 3\hat{k}) = 9\)

such that the intercept made by the plane on x-axis and z-axis should be equal.

**Question 4- **Solve the differential equation \(\frac{dy}{dx}-3y \cot x = \sin 2x\) given \(y = 2\) when \(x = \frac{\pi}{2}\).

**Question 5- **The sum of surface areas of a sphere and a cuboid with sides \(\frac{x}{3}\), x and 2x, is constant. Show that the sum of their volumes is minimum if x is equal to three times the radius of the sphere.

**Question 6-Â **A bag contains 4 white, 5 black and 7 red balls. From the bags, two balls are drawn at random. Calculate the probability that both the balls are white balls.

**Question 7- **Show that the given binary operation * on A = R – {-1} described as a*b = a + b + ab for all a, b \(\in\) A is commutative and associative on A. Also, determine the identity element of the binary operation * in A and show that every element of A is invertible.

**Question 8- **Using the properties of determinants, show that \(\Delta ABC\) is isosceles if,

\(\begin{vmatrix} 1 & 1 & 1\\ 1 + \cos A & 1+ \cos B & 1+ \cos C \\ \cos^{2}A + \cos A & \cos^{2}B + \cos B & \cos^{2}C + \cos C \end{vmatrix} = 0\)

**Question 9-Â Â **Let the function f: R – (4/3)â†’Â R – (4/3) is defined by f(x) = (4x+3)/(3x+4). Prove that the given function is bijective. And, find the inverse of the function and f^{-1}(0) and the value of x, such thatÂ f^{-1}(x) = 2.

**Question 10- **Calculate the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector \(2\hat{i} + 3\hat{j} + 4 \hat{k}\) to the plane \(\vec{r}.(2\hat{i} + \hat{j} +3\hat{k})- 26 = 0\). Also determine the image of P in the plane.

**Question 11-**Â Determine the value for the given integralÂ âˆ«Â 1/cos^{4} x sin^{4} x dx

**Question 12-Â **Determine the area of the region bounded by the curve x^{2} = 4y and the line equation is given as x = 4y -2 using integration method.

**Question 13- **Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is \(6 \sqrt{3}\)r.

**Question 14- **Find:

\(\int \frac{\cos \theta}{(4 + \sin^{2}\theta)(5 – 4\cos^{2}\theta)} d\theta\)

**Question 15- **Solve the differential equation \((\tan^{-1}x – y)dx = (1 + x^{2})dy\).

**Question 16- **IfÂ xy + yx = 1, then show that \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}} = \left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}\)

**Question 17- **A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axis at A, B and C. Show that the locus of the centroid of triangle ABC isÂ \(\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{1}{p^{2}}\).

**Question 18-Â **Calculate the coordinate pointsÂ where the linepasses through the points \((3, -4, -5)\) and \((2, -3, 1)\), crosses the plane determined by the points \((1, 2, 3)\), \((4, 2, -3)\) and \((0, 4, 3)\)..

**Question 19- **Show that the surface area of a closed cuboid with a square base and given volume is minimum when it is a cube.

**Question 20-Â **Solve the system of equations using matrices: x+y-2z= -3, 2x-3y+5z=11, and 3x+2y-4z=-5.