Plus Two Maths Model Question Papers Paper 1 is part of Plus Two Maths Previous Year Question Papers and Answers. Here we have given Plus Two Maths Model Question Papers Paper 1.

## Plus Two Maths Model Question Papers Paper 1

Board | SCERT |

Class | Plus Two |

Subject | Maths |

Category | Plus Two Previous Year Question Papers |

**Time : 2 1/2 Hours**

**Cool off time : 15 Minutes**

**Maximum : 80 Score**

**General Instructions to Candidates :**

- There is a ‘Cool off time’ of 15 minutes in addition to the writing time.
- Use the ‘Cool off time’ to get familiar with questions and to plan your answers.
- Read questions carefully before you answering.
- Read the instructions careully.
- When you select a question, all the sub-questions must be answered from the same question itself.
- Calculations, figures and graphs should be shown in the answer sheet itself.
- Malayalam version of the questions is also provided.
- Give equations wherever necessary.
- Electronic devices except non programmable calculators are not allowed in the Examination Hall.

**QUESTIONS**

**Question 1 to 7 carry 3 scores each. Answer any six questions only **

Question 1.

a. Let * be a binary operation, defined by a * b = 3a + 4b – 2, find 4*5

b. Let A = N x N and * be a binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Also, find the identity element for * on A, if any.

Question 2.

Question 3.

a. If thematrixAis both symmetric and skew- symmetric, then A is a ……….. matrix

b. Find the inverse of A = [ ] by elemenatry row operation

Question 4.

Using properties of determinants, prove that

Question 5.

At what points will the tangent to the curve y = 2x^{3} – 15x^{2} + 36 x – 21 be parallel to the x- axis? Also find the equations of the tangents to the curve these points.

Question 6.

Question 7.

**Question 8 to 17 carry 4 scores each. Answer any eight questions only **

Question 8.

Consider the following system of equations :

Question 9.

Question 10.

Question 11.

a. At the point x = 0, the function f(x) = |x| is

(a) continuous, but not differentiable

(b) differentiable, but not continuous

(c) continuous and differentiable

(d) neither continuous not differentiable

Question 12.

a. A spherical bubble is decreasing in volume at the of 2c.c/s. Find the rate at which the surface area is diminishing when he radius i s 3cm.

b. Find the equations of the tangent to the curve y = x^{2} – 4x + 1 at (2,3)

Question 13.

Question 14.

Question 15.

a. Find the equation of the plane passing through (2, -3, 1) and is prependicular to the line through the points (3,4,-1) and (2,-1,5).

b. Find the distance from origin to the plane 3x-2y+6z+14 = 0.

Question 16.

Question 17.

**Question 18 to 24 carry 6 scores each. Answer any 5 questions only **

Question 18.

Show that the semi-vertical angle of a right circular cone of given surface area and maximum volume is sin^{-1} ( )

Question 19.

Question 20.

Consider an L.P.P. to minimize z = 3x+5y subject to the constraints :

x + 3y > 3, x + y > 2,x,y > 0

a. Draw the feasible region.

b. Write the comer points of the feasible region.

c. Find the minimum profit.

Question 21.

Find the following integrats:

Question 22.

Question 23.

a. Consider the differential equation

i. Show that it is a homogeneous differential equation.

ii. Solve the above differential equation.

Question 24.

Using integration find the area of the region bounded by the triangle whose vertices are (-1,0), (1,3) and (3,2).

**ANSWERS**

Answer 1.

Answer 2.

Answer 3.

Answer 4.

Answer 5.

Answer 6.

Answer 7.

Answer 8.

Answer 9.

Answer 10.

Answer 11.

Answer 12.

Answer 13.

Answer 14.

Answer 15.

Answer 16.

Answer 17.

Answer 18.

Answer 19.

Answer 20.

It can be seen that the feasible region is unbounded.

The comer points of the feasible region are

A(0),B (,) and C (0,2)

The values of Z at these comer are as follows.

As the feasible region is unbounded, therefore, 7 may or may not be the minimum value of Z.

For this, we draw the graph of the inequality, 3x + 5y < 7, and check whether the resulting half plane has points in common with the fea¬sible region or not.

It can be seen that the feasible region has np common point with 3x + 5y < 7 Therefore, the minimum value of Z is 7 at B (,)

Answer 21.

Find the Following integrals :

Answer 22.

Answer 23.

Answer 24.

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