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CBSE Class 12 Maths Board Exam: Important 6 marks questions

Important 6 Marks Questions for CBSE Class 12 Maths are provided here for students as per the latest exam pattern. Students can practice these questions to get good marks in the board exam. These questions are in accordance with the CBSE syllabus and NCERT curriculum. Maths can be a nightmare to many students as the subject requires conceptual knowledge and a good understanding. It is not a child’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 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 a good percentage:

Question 1- In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let

\(\begin{array}{l}\frac{3}{5}\end{array} \)
be the probability that he knows the answer and
\(\begin{array}{l}\frac{2}{5}\end{array} \)
 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability
\(\begin{array}{l}\frac{1}{3}\end{array} \)
, 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 = 3x2 and the line 2y = 3x + 12.

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

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

and

\(\begin{array}{l}\vec{r} .(2\hat{i} + 5\hat{j} + 3\hat{k}) = 9\end{array} \)

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

Question 4- Solve the differential equation

\(\begin{array}{l}\frac{dy}{dx}-3y \cot x = \sin 2x\end{array} \)
given
\(\begin{array}{l}y = 2\end{array} \)
 when
\(\begin{array}{l}x = \frac{\pi}{2}\end{array} \)
.

Question 5- The sum of surface areas of a sphere and a cuboid with sides

\(\begin{array}{l}\frac{x}{3}\end{array} \)
, 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- 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

\(\begin{array}{l}\in\end{array} \)
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

\(\begin{array}{l}\Delta ABC\end{array} \)
is isosceles if,

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

Question 9-  Let the function f: R – (4/3)→ 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 that 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

\(\begin{array}{l}2\hat{i} + 3\hat{j} + 4 \hat{k}\end{array} \)
to the plane
\(\begin{array}{l}\vec{r}.(2\hat{i} + \hat{j} +3\hat{k})- 26 = 0\end{array} \)
. Also determine the image of P in the plane.

Question 11- Determine the value for the given integral  ∫  1/cos4 x sin4 x dx

Question 12- Determine the area of the region bounded by the curve x2 = 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

\(\begin{array}{l}6 \sqrt{3}\end{array} \)
r.

Question 14- Find:

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

Question 15- Solve the differential equation

\(\begin{array}{l}(\tan^{-1}x – y)dx = (1 + x^{2})dy\end{array} \)
.

Question 16- If xy + yx = 1, then show that

\(\begin{array}{l}\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}} = \left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}\end{array} \)

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 is 

\(\begin{array}{l}\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{1}{p^{2}}\end{array} \)
.

Question 18- Calculate the coordinate points where the line passes through the points

\(\begin{array}{l}(3, -4, -5)\end{array} \)
and
\(\begin{array}{l}(2, -3, 1)\end{array} \)
, crosses the plane determined by the points
\(\begin{array}{l}(1, 2, 3)\end{array} \)
,
\(\begin{array}{l}(4, 2, -3)\end{array} \)
 and
\(\begin{array}{l}(0, 4, 3)\end{array} \)
..

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

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