﻿ Write the principal value of  from Class 12 CBSE Previous Year Board Papers | Mathematics 2013 Solved Board Papers

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# CBSE Class 12 Mathematics Solved Question Paper 2013

1.

If  then find the matrix A.

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2.

Prove that

We know that:

We have:

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3.

A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.

Let the award money given for honesty, regularity and hard work be Rs. x, Rs. y and Rs. z respectively.
Since total cash award is Rs. 6,000.

Three times the award money for hard work and honesty amounts to Rs.11,000.

Award money for honesty and hard work is double that given for regularity.

The above system of equations can be written in matrix form AX = B as:

Here,

Thus, A is non-singular. Hence, it is invertible.

Hence, x = 500,  y = 2000,  and z = 3500.
Thus, award money given for honesty, regularity and hardwork is Rs. 500, Rs.2000 and Rs. 3500 respectively.
The school can include awards for obedience.

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4.

Show that the function  is  continuous but not differentiable at x=3.

Let c be a real number.
Case I: c<3 Then f(c) = 3-c.

CaseII: c = 3. Then f(c) = 3 - 3 = 0
Since  f is continuous at x = 3.

Case III: C>3. Then f(c)  = c - 3

Since,
Therefore, f is a continuous function.
Now, we need to show that
Consider the left hand limit of f at x = 3

Consider the right hand limit of f at x = 3

Since the left and right hand limits are not equal, f is not differentiable at x = 3.
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5.

Find the value of the following:

We know that:

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6.

Find the value of a if

Equating the corresponding elements, we get,

Now consider the equations,
a - b = -1   and 2a - b = 0
Subtracting first equation from second, we get: a = 1
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# 7.Write the principal value of

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8.

Using properties of determinants prove the following:

Applying  we have

Expanding along R1, we have:

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9.

Write the value of

We know:

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10.

If  then write the value of x.

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