Most students studying in the plus two are well aware of the significance of Class 12 Maths in their life. Since they are well aware of how crucial the year is for them, students are on the hunt to find as many resources or study material as they can so that they can prepare well for the exams. BYJUâ€™s come to the help of these students by compiling here the Kerala Plus Two Maths Important Questions.

These questions are useful for students as it covers almost all the main topics and concepts of subject. It gives the students an overview of the type of questions that are normally asked in the exams. Students who have prepared from this also feel quite confident to write the exam, as they are more acquainted with the exam pattern.

### Download Kerala Board plus two Maths important Question PDF

Here are some of the important questions, we have compiled for you:

**1.** If

**2.** Find f.

**3.** (a) Identify the functions from the below graph:

(b) Find the domain and range of the function represented in the above graph.

(C) Prove that

**4.** Consider the below figure:

- Find the point of intersection â€˜pâ€™ of the circle x + y= 50 and the line y=x
- Find the area of the shaded region

**5.** (a) Prove that any of the vectors

(b) Show that if

are coplanar then

are also coplanar

**6.** (a) Find the equation of a plane, which makes X,Y,Z intercepts respectively as 1,2,3

(b) Find the equation of a plane passing through the point (1,2,3), which is parallel to the above plane

**7.** (a) Prove that the function defined by f(x)=cos(x) is a continuous function

(b) If

show that \(\frac{dy}{dx}\)

= \(\frac{ae^{acos^{-1_{x}}}}{\sqrt{1-x^{2}}}\)

**8.** (a) Find

and

if

(b) Express the matrix \(\begin{bmatrix} 2, -2, 4 \\ 1, 3, 4 \\ 1, -2,-3 \end{bmatrix}\)

as the sum of a symmetric and a skew symmetric matrices

**9.** Evaluate the following:

(i) sin mx dx

and

(ii) \(\int \frac{x dx}{\left ( x+1 \right )\left ( x+2 \right )}\)

And

(iii) \(\int \frac{1 dx}{\sqrt{x^{2}+2x+2}}\)

**10.** (a) Find the angle between the lines:

(b) Find the shortest distance between the pair of lines:

**11.** (a) Let R be a relation defined on A = by R = { (1,3), (3,1), (2,2). R is

(i) Reflexive (ii) Symmetric

(iii) Transitive (iv) Reflexive but not symmetric

(b) Find fog and gof if f(x) = I x +1 I and get gx=2x-1.

(c) Let * be a binary operation defined on N x N by

(a, b) * (c, d) = (a+c, b+d)

Find the identity element for * if it exists

**12.** Consider the linear programming problem:

Maximize Z= 50x +40y

Subject to the constraints

x + 2y 10

3x + 4y 24

x 0, y 0

- Find the feasible region
- Find the corner points of the feasible region
- Find the maximum value of Z

**13.** (a) The angle between the vectors + and + is

(i) 60 (ii) 30 (iii) 45 (iv) 90

(b) If \(\vec{a},\vec{b},\vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}\) =0, find the value of \(\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}\)

**14.** (a) If A= \(\begin{bmatrix} a 1 \\ 1 0 \end{bmatrix}\) is such that A= 1, then A equals

(i) 1 (ii) -1 (iii) 0 (iv) 2

(b) solve the system of equations

x-y+z= 4

2x+y-3z=0

x+y+z=2 using the matrix method

**15.** (a) Area bounded by the curves y=cos x, x=, x=0, y=0 is

(i) Â½ (ii) 2/x (iii) 1 (iv)

(b) Find the area between the curves yÂ²=4ax and xÂ²=4ay, a> 0.

**16.** (a) The function f: NN, given by f(x)=2x is

(i) one-one and onto (ii) one-one but not onto

(iii) not one-one and not onto (iv) onto but not one-one

(b) find gof(x), if f(x)= 8xÂ³ and g(x) = \(x^{1/3}\)

(c) Let * be an operation such that a * b= LCM of a and b defined on the set A={1, 2,3,4,5}. Is * a binary operation? Justify your answer.

**17.** (a) Prove that

(b) Find

(c) Find

**18.** Find the shortest distance between the lines

**19.** (a) Equation of the plane with intercepts 2,3,4 on the x,y and z axis respectively is

(i) 2x+3y+4z= 1 (ii) 2x+3y+4z=12 (iii) 6x+4y+3z=1 (iv)6x+4y+3z=12

(b) Find the cartesian equation of the plane passing through the points A(2, 5, -3), B(-2, -3, 5) and C(5,3,-3).

**20.** (a) If P(A)=0.3, P(B)= 0.4, then the value of P(AB), where A and B are independent events is

(i) 0.48 (ii) 0.51 (iii) 0.52 (iv) 0.58

(b) A card from a pack of 52 cards is lost. From the remaining cards of the pack, 2 cards are drawn and are found to be diamonds. Find the probability of the lost card being a diamond.