­CBSE BOARD EXAM PAPER ANSWER - 2022

Class 12 - Mathematics Set – 1, Code - 65/1/1

 

General Instructions :

Read the following instructions very carefully and strictly follow them :

(i) The question paper contains three Sections – Section A, B and C.

(ii) Each Section is Compulsory.

(iii) Section – A has 6 short answer type I questions of 2 mark each.

(iv) Section – B has 4 short answer type II questions of 3 marks each.

(v) Section – C has 4 long answer type questions of 4 marks each.

(vi) There is an internal choice in some questions.

(viii) Question No. 14 is a case based problem with 2 subparts of 2 marks each.

 

SECTION A

Question 1:

Find the sum of the order and the degree of the differential equation :

x+dydx2 = dydx2 + 1

 

Question 2:

In a parallelogram PQRS, PQ  = 3i  - 2j  + 2k  and PS  = - i  - 2k . Find |PR |

and |QS |.

 

Question 3:

If ddxF(x)  = sec4xcosec4x  and Fπ4  = π4 , then find F(x) .

OR

Find : logx -3(log x)4  dx.

 

Question 4:

Let A and B be two events such that P(A) = 58 , P(B) = 12  and P(A|B) = 34 . Find the value of P(B|A).

 

Question 5:

Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let the variable X denotes the number of red balls. Find the probability distribution of X.

 

Question 6:

Find the values of λ , for which the distance of point (2, 1, λ ) from plane 3x + 5y + 4z = 11 is 22  units.

 

SECTION B

Question 7:

If a , b , c  and d  are four non-zero vectors such that a×b  = c×d  and a×c  =  4b×d , then show that (a  - 2d ) is parallel to (2b  - c ) where a  ≠  2d , c  ≠  2b .

OR

The two adjacent sides of a parallelogram are represented by 2i  - 4j  - 5k  and 2i  + 2j  + 3k . Find the unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram also.

 

 

 

Question 8:

Find the vector equation of the plane passing through the intersection of the places r .(2i  + 2j  - 3k ) = 7 and r .(2i  + 5j  + 3k ) = 9 and through the point (2, 1, 3).

 

Question 9:

Find : dxx + 3x .

OR

Evaluate : 0π2cos x(1+sinx)(4+sinx) dx.

 

Question 10:

Find the particular solution of the differential equation xdydx  + xcos2yx  = y; given that when x = 1, y = π4 .

 

SECTION C

Question 11:

Using integration, find the area of the region {(x, y) : 4x² + 9y² ≤  36, 2x+ 3y≥ 6}.

OR

Using integration, find the area of the region bounded by lines x - y + 1 = 0, x = -2, x = 3 and x-axis.

 

Question 12:

A card from a pack of 52 playing cards is lost. From the remaining cards, 2 cards are drawn at random without displacement, and are found to be both aces. Find the probability that lost card being an ace.

 

Question 13:

Evaluate : 0πx1+sinxdx

 

CASE BASED / DATA BASED QUESTION

Question 14:

Electrical transmission wires which are laid down in winters are stretched tightly to accommodate expansion in summers.

Two such wires lie along the following lines :

l₁ : x+13  = y-3-2  = z+2-1

l₂ : x-1  = y-73  = z+7-2

Based on the given information, answer the following questions :

(i) Are the lines l₁ and l₂ coplanar ? Justify your answer.

(ii) Find the point of intersection of the lines l₁ and l₂.

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