CBSE/12th Class/Maths/2013/SET-1

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S.No Questions Answers Q.1

Sol.1

푡푎푛 휋4 = 1

푡푎푛 =휋4

cos2휋3 = −

12

푐표푠 −12 =

2휋3

∴ 푡푎푛 + 푐표푠 −12 =

휋4 +

2휋3 =

11휋12

Q.2 Write tha Value Of tan (2푡푎푛 ).

Sol.2

Q.3 Find tha a value of ‘a’ if 푎 − 푏 2푎 + 푐

2푎 − 푏 3푐 + 푑 = −1 50 13 Sol.3

푎 − 푏 = −1 ------------------------(1) 2푎 + 푐 = 5 ------------------------(2) 2푎 − 푏 = 0 ------------------------(3) 3푐 + 푑 = 13 ----------------------(4) From equation (1) & (3)

(푎 − 푏) = −12푎 − 푏 = 0

−푎 = −1푎 = 1

Q.4

Sol.4

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Q.5

Sol.5

Q.6 Write the degree of differential equation:

Sol.6

The highest order derivative present in the given differential equation is . Its power is 2.

So, the degree of the given differential equation is 2. Q.7

If and aretwo equal vectors, then write the value of x + y +z.

Sol.7

Given, and are equal vector Therefore, the value of x+ y + z is 0.

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Q.8

Sol.8

Let bethe unit vector.

Q.9 Find the Cartesianequation of the line which passes through the point

(−2, 4, −5)and is parallel to the line .

Sol.9 The equation of thegiven line is

The required line isparallel to the given line. Therefore, direction ratios of therequired line are same as the direction ratio of the given line. So, the direction ratios of the required line are 3, − 5, 6.The equation of thestraight line passing through (− 2, 4, − 5) and having

direction ratios 3, − 5, 6 is

( ) = ( ) = ( ) = ( ) = 푧 −

i.e., = = [Equation of the line passes through (푥1, 푦1,푧1)

Q.10

Sol.10

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Q.11

Sol.11

Q.12

Sol.12

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OR

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Q.13

Sol.13

Q.14

Sol.14

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Q.15

Sol.15

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Q.16

Sol.16

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OR

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Q.17

Sol.17

I= ∫ ( )

( ) 푑푥

∫ ( )( ) 푑푥

∫ ( ) ( )( ) 푑푥

∫(푐표푎2푎 − 푐표푡 푡 푠푖푛2푎)푑푡 푐표푠 2푎 푡 − 2푠푖푛2푎 푙표푔|푠푖푛 푡| + 푐 푐표푠2푎 푥 + 푎 − 푠푖푛2푎 푙표푔|푠푖푛 푥 + 푎| + 푐

OR

CBSE/12th Class/Maths/2013/SET-1

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Q.18

Sol.18

Q.19

Sol.19

[풙

ퟐ

ퟐ+ (풙 ퟐ)ퟐ

ퟐ+ (풙 ퟒ)ퟐ

ퟐ]

ퟒퟐ

ퟐ+ ퟐퟐ

ퟐ+ ( ퟐ)ퟐ

ퟐ+ ( ퟒ)ퟐ

ퟐ

8+2+2+8 20

Q.20

Sol.20

If two vectors are are perpendicular, Then their scalar product must be zero.

CBSE/12th Class/Maths/2013/SET-1

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Q.21

OR

Find the vector equation of the plane which contains the line of intersection of the planes which is

perpendicular to the plane

Sol.21

Let 0 be the angle between the given line and the plane.

Thus, the angle between the given line and the given plane is

OR The equation of the given planes are

The equation of the plane passing through the intersection of the planes(1) and (2) is

Given, the plane(3) is perpendicular to the plane

This is the equation of the required plane.

Q.22 A speak truth in 60% of the cases ,while B in 90% of the cases. In Sol.22

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what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of classes than A?

Let the probability that A and B speak truth be P(A) and P(B) respectively

Therefore, P (A) = and P (B) = A and B can contradict in starting a fact when one is speaking the truth and other is not speaking the truth. Case 1: A is speaking the truth and B is not speaking the truth. Required probability :

P (A) Case 2: A is not speaking the truth and B is speaking the truth Required probability :

1-P (A) × P (B)

From case 1,it is clear that it is not necessary that the statement of B will carry more weight as he speaks truth in more number of case than A.

Q.23 A school want to award its students for the values of honesty, Regularity and hard work with 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 algebracially 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.

Sol.23 Let the award money given for Honesty, Regularity, and Hard work be Rs x, Rs y and Rs z respectively. Since the total cash award is Rs 6,000

Three times the award money for Hard work and Honesty amounts Rs 11,000.

Award money for Honesty and Hard work is double the one given for regularity.

The above systems for equations can be written in matrix form AX=B as∴

Here,

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

CBSE/12th Class/Maths/2013/SET-1

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Hence, x=500, y=2000, and z=3500 Thus, award money given for Honesty, Regularity and hard work are Rs 500, Rs 2000 and Rs 3500 respectively School can include awards for obedience.

Q.24

OR

Sol.24

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OR

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Q.25 Using intergation,find the area of the region enclosed between the two OR

circles

Sol.25

Let A and B be the points of intersection of the line and parabola.

Coordinates of Point A are .Coordinates of Point B are (2,1).

=푥 + 2

4 −푥4 푑푥

= ( ( + 2푥) − )2

= Units OR

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Q.26

Sol.26

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Put the value of v, we get

Put the value of C in equation (2), we get

Which is the particular solution of the given differential equation.

Q.27

Sol.27

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Q.28 A co-operative society of farmers has 50 hectares of land to grow two

crops A and B. The profiits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, liquid herbicide has to be used for crops Aand B at the rate of 20 litres and 10 litres per hectare, respectively. Futher not more than 800 litres of herbicide sould be used in order to protect fish and wildlife using a pond which collects drainage from this land. Keepng in mind that the protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance of environment?

Sol.28

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Q.29 Assume that the chances of a patient having a heart attack is 40%.

Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probablities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probablity that the patient followed a course of meditation.

Sol.29

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