Class 12 Mathematics Sample Paper With Solutions Set G

Please refer to Class 12 Mathematics Sample Paper With Solutions Set G below. These Class 12 Mathematics Sample Papers will help you to get more understanding of the type of questions expected in the upcoming exams. All sample guess papers for Mathematics Class 12 have been designed as per the latest examination pattern issued by CBSE. Please practice all CBSE Sample Papers for Mathematics in Standard 12.

Sample Paper Class 12 Mathematics With Solutions Set G

Part–A
Section – I

All questions are compulsory. In case of internal choices attempt any one.

Q1. Check whether the function f : R → R is defined by f(x) = |x| + x is one-one or not. 
Answer : f (x) is not one-one

OR

Relation R defined in set A such that (a, b) ∈ R and (b, a) ∈ R for all the ordered pairs present in R and a, b ∈ A. Name the relation.
Answer : Symmetric relation.

Q2. In a relation R = {(1, 4), (2, 3), (3, 7)}, write the Domain and Range of R.
Answer : Domain : {1, 2, 3}; Range : {3, 4, 7}

Q3. Find the positive angles less than 2p for which q = sin−1 1/√2.
Answer : q = π/4 and 3π/4 

OR

Write the principal value branch of tan–1 x.
Answer : (–π/2 , π/2)

Q4. Write the number of elements in matrix

Answer : 9 elements

Q5. Find the area of the triangle with vertices at the points given as (– 2, – 3), (3, 2), (– 1, – 8) 
Answer : 15 sq. units

OR

If A and B are square matrices of order 3 such that |A| = – 1, |B| = 3, then find the value of |3 AB|.
Answer : –9

Q6. Find the adjoint of A

Answer :   

Q7. Evaluate:  

Answer : –1/2 cot x + C

OR

Evaluate:  

Answer : √2

Q8. Write the area bounded by two curves y = f(x) and y = g(x) (see fig.), which are intersected by the ordinates x = a and x = b.

Answer :

Q9. Find the integrating factor of the differential equation: x dy/dx – y = 2x².
Answer : 1/x

OR

Find the degree of the differential equation (Image)
Answer : Not defined.

Q10. Write two different vectors having same magnitude. 
Answer : a̅ = 2𝑖̂ +3𝑗̂ + 6𝑘̂ and b̅ = 3𝑖̂ +6𝑗̂ + 2𝑘̂

Q11. Write the scalar and vector components of the vector r̅ = 2𝑖̂ + 3𝑗̂ – 7𝑘̂.
Answer : Scalar components : 2, 3, –7; Vector components : 2𝑖̂ ,3𝑗̂ – 7𝑘̂ˆ

Q12. Find the values of x and y so that the vectors 2𝑖̂ + 3𝑗̂ and x𝑖̂ + y𝑗̂are equal. 
Answer : x = 2, y = 3

Q13. If P is (6, 2, – 3), find the direction cosines of OP. 
Answer : 6/7 ,–2/7 , –3/7

Q14. Find unit normal vector to the plane x + 2y + 3z – 6 = 0. 
Answer : 

Q15. If P(A) = 0.3, P(B) = 0.5 and P(A|B) = 0.4, find P(A ∩ B) and P(B|A). 
Answer : P(A ∩ B) = 0.2 and P(B|A) = 2/3

Q16. An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement.
Find the probability of getting 2 blue balls.
Answer : 16/121

Section-II
Both the Case study-based questions are compulsory. Attempt any 4 sub-parts from each question (17–18). Each sub-part carries 1 mark.

Q17. A jet of an enemy is flying along the curve y = x² + 2 . A soldier is placed at the point (3,2).   

Based on the above information answer the following:
(i) Distance between the soldier and the jet in terms of x is 
(a) (x–3)² + x4
(b) (x+3)² + x4
(c) (x+3)² + x3
(d) (x–3)² + x3
Answer : A

(ii) For maximum or minimum value of distance, equation will be 
(a) 4x² + 2x – 6 = 0
(b) 4x³ + 2x –6 =0
(c) 4x³ + 2x + 6 = 0
(d) 4x² + 2x + 6 = 0
Answer : B

(iii) Minimum value of distance in terms of x is 
(a) 10x² – 2
(b) 12x² –2
(c) 12x² + 2
(d) 10x² + 2
Answer : C

(iv) Minimum value of distance at x = 1
(a) 12
(b) 13
(c) 16
(d) 14
Answer : D

(v) Distance between the soldier and jet is 
(a) 2
(b) 3
(c) 5
(d) 7
Answer : C

Q18. On Diwali festival, I bought a lot of 30 bulbs. From a lot of 30 bulbs which include 6 defective, a sample of 4 bulbs is drawn at random with replacement. 

Based on the above information answer the following:

(i) Find P(X = 0) where X denotes the number of defective bulb in 4 draws with replacement. 
(a) 256/625
(b) 265/625
(c) 256/265
(d) 256/652
Answer : A

(ii) Find the probability that the number of defective bulb is 1 out of 4 draws with replacement. 
(a) 256/625
(b) 265/625
(c) 256/652
(d) 265/652
Answer : A

(iii) Find the probability that the number of defective bulb is 2 out of 4 draws with replacement. 
(a) 69/625
(b) 96/625
(c) 16/625
(d) 86/625
Answer : B

(iv) Find the probability that the number of defective bulb is 3 out of 4 draws with replacement. 
(a) 61/625
(b) 16/526
(c) 16/625
(d) 16/265
Answer : C