ISC Class 12 Maths Question Paper Solution 2020

Solving the ISC Class 12 Maths 2020 Question paper prepares students for the board exam. They get the exam-like feeling by practising the questions of past year papers. Moreover, they get well versed with the difficulty level of the Mathematics paper and changes made in the exam pattern over the years. A thorough understanding of it helps them make an exam strategy and prepare effectively for the board exam. To help them in doing so, we have provided the ISC Class 12 Maths Question Paper Solution 2020 PDF. It contains the step by step answer to each question with a detailed explanation.

Download ISC Class 12 Maths Question Papers Solutions 2020 PDF

The ISC Class 12 Maths 2020 exam was conducted on 11th March 2020. The exam started at 2 pm, and students were allotted 3 hours to complete the paper. They can download the ISC Class 12 Maths Question Paper Solution 2020 PDF from the link below.

Students can have a look at the ISC Class 12 Maths Question Paper Solution 2020 below. They can also access the year wise ISC Class 12 Maths Solved Previous Year Question Papers for more practice.

Difficult Topics of ISC Class 12 Maths 2020 Question Paper

Below we have listed down the topics which students found difficult while attempting the ISC 2020 Maths Question Paper.

• Continuity and derivability
• Modulus function
• Applications on derivatives
• Integration by substitution and by parts
• Applications integrals
• 3D geometry
• Inverse circular functions
• Mean value theorems, open and closed interval in Mean Value theorem.
• Probability, mutually exclusive and independent events, Product and sum rule of probability, dependent and independent events.
• Identification of the types of differential equations and their framing.
• Between the regression coefficients byx and bxy and regression lines y on x and x on y.
• Linear Programming Problems in identifying the constraints.
• Application of definite integrals: Sketching of curves, Identifying the area of the shaded region and finding the upper and lower limits from the graph.

ISC Class 12 Maths Question Paper 2020 With Solutions

Question 1:

(i) Determine whether the binary operation ∗ on R defined by a∗b = |a-b| is commutative. Also, find the value of ( -3)∗2.

(ii) Prove that:

tan²(sec^-1 2) + cot² (cosec^-1 3) = 11.

(iii) Without expanding at any stage, find the value of the determinant:

(iv)

(v) Find

(vi) The edge of a variable cube is increasing at the rate of 10 cm/sec. How fast is the volume of the cube increasing when the edge is 5 cm long?

(vii) Evaluate:

(viii) Form a differential equation of the family of the curves y² = 4ax.

(ix) A bag contains 5 white, 7 red and 4 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white?

(x) Let A and B be two events such that

find ‘p’ if A and B are independent events.

Answer:

(i) a*b = |a-b|

⇒a*b = b*a

b*a = b-a=a-b, hence commutative

(-3)*2 = |-3-2| = |-5| = 5 = |5|

(ii)

(iii)

(iv)

(v)

(vi) Let the edge of the cube be a,

da/dt = 10 cm/s

(vii)

(viii)

(ix)

(x)

Question 2:

Answer:

Question 3:

Answer: (a)

OR

(b)

Question 4: Using properties of determinants, show that

Answer:

Question 5: Verify Rolle’s theorem for the function, f(x) = -1 + cos x in the interval [0, 2π]

Answer:

Question 6:

Answer:

Question 7:

(a) The equation of tangent at (2, 3) on the curve y² = px³ + q is y = 4x-7. Find the values of ‘p’ and ‘q’.

OR

(b) Using L’ Hospital’s rule, evaluate:

Answer: (a)

Alternatively: If the candidate proves that y=4x−7 is not tangent to the curve at the point (2,3), it was accepted.

OR

(b)

Question 8:

Answer: (a)

OR

(b)

Question 9: Solve the differential equation

Answer:

Question 10:

Three persons A, B and C shoot to hit a target. Their probabilities of hitting the target are 5/6 4/5 and 3/4 respectively. Find the probability that:

(i) Exactly two persons hit the target.

(ii) At least one person hits the target.

Answer:

Question 11: Solve the following system of linear equations using matrices:

x-2y=10, 2x-y-z=8, -2y+z=7

Answer:

Question 12:

(a) Show that the radius of a closed right circular cylinder of given surface area and maximum volume is equal to half of its height.

OR

(b) Prove that the area of the right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Answer: (a)

(b)

Question 13:

(a) Evaluate:

(b) Evaluate:

Answer: (a)

OR

(b)

Question 14:

The probability that a bulb produced in a factory will fuse after 150 days of use is 0·05. Find the probability that out of 5 such bulbs:

(i) None will fuse after 150 days of use.

(ii) Not more than one will fuse after 150 days of use.

(iii) More than one will fuse after 150 days of use.

(iv) At least one will fuse after 150 days of use.

Answer:

It is a case of binomial distribution.

p=0.05, q=0.95, n=5

Binomial distribution (p+q)⁵

(i) None fuse: P(X=0) = (.95)⁵

(ii) Not more than one fuse

P(X=0)+ P(X=1)=5C₀q⁵ + 5qq⁴p¹

(.95)⁵+5(.95)⁴(.05)¹

(iii) More than one fuse

1-[(.95)⁵+5(.95)⁴(.05)¹]

(iv)

At least one fuses

1-(.95)⁵

Question 15:

(a) Write a vector of magnitude of 18 units in the direction of the vector

(b) Find the angle between the two lines:

(c) Find the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line joining the points (4, 5, 0) and (1, -2, 4).

Answer: (a)

(b)

(c) Passes through the point (2, -3, 1)

dr’s=<3, 7, -4>

Equation: 3(𝑥−2)+7(𝑦+3)−4(𝑧−1)=0

3𝑥+7𝑦−4𝑧+19=0

Question 16:

(a)

OR

(b) Using vectors, find the area of the triangle whose vertices are:

A (3, ̶ 1, 2), B (1, ̶ 1, ̶ 3) and C ( 4, ̶ 3, 1)

Answer: (a)

OR

(b)

Question 17:

(a) Find the image of the point (3, ̶ 2, 1) in the plane 3x ̶ y + 4z = 2

OR

(b) Determine the equation of the line passing through the point ( ̶ 1, 3, ̶ 2) and perpendicular to the lines:

Answer: (a)

OR

(b) Equation of a line passing through (-1. 3, -2) is:

Question 18: Draw a rough sketch of the curves y² = x and y² = 4 – 3x and find the area enclosed between them.

Answer:

Points of intersection are (1,-1) and (1,1)

Area between the curves:

Question 19:

(a) The selling price of a commodity is fixed at ₹ 60 and its cost function is

C (x) = 35 x + 250

(i) Determine the profit function.

(ii) Find the break even points.

(b) The revenue function is given by R(x) = 100x – x² – x³ . Find

(i) The demand function.

(ii) Marginal revenue function.

(c) For the lines of regression 4x – 2y = 4 and 2x – 3y + 6 = 0,

find the mean of ‘x’ and the mean of ‘y’.

Answer:

(a) p=60, C(x)=35x + 250

R(x)=60

(i) Profit function

P(x)=60x-35x-250

25x-250

(ii) Break even points

60x = 35x + 250

x=10

(b) R(x)=100x-x²-x³

(i) Demand function: p=100-x-x²

(ii) Marginal revenue = 100-2x-3x² is the marginal revenue

(c) 4x-2y=4

2x-3y=-6

On solving simultaneously, we get mean of x=3 and mean of y=4

Question 20:

(a) The correlation coefficient between x and y is 0.6. If the variance of x is 225, the variance of y is 400 , mean of x is 10 and mean of y is 20 , find

(i) the equations of two regression lines.

(ii) the expected value of y when x = 2

OR

(b) Find the regression coefficients b_yx , b_xy and correlation coefficient ‘r’ for the following data : (2,8), (6,8 ), (4,5), (7, 6), (5 ,2)

Answer: (a)(i)

(ii) When x=2, y=68/5

(b)

Question 21:

(a) The marginal cost of the production of the commodity is 30 + 2x, it is known that fixed costs are ₹ 200, find

(i) The total cost.

(ii) The cost of increasing output from 100 to 200 units.

OR

(b) The total cost function of a firm is given by

where the selling price per unit is given as ₹ 6. Find for what value of x will the profit be maximum.

Answer: (a)

OR

(b)

Question 22: A company uses three machines to manufacture two types of shirts, half sleeves and full sleeves. The number of hours required per week on machine M₁ , M₂ and M₃ for one shirt of each type is given in the following table:

None of the machines can be in operation for more than 40 hours per week. The profit on each half sleeve shirt is ₹ 1 and the profit on each full sleeve shirt is ₹1·50. How many of each type of shirts should be made per week to maximise the company’s profit?

Answer:

The corner points of the feasible region are

A(0,20), B(10,15), C(15,10), D(20,0), O(0,0)

At A(0,20) Z=30

At B(10,15) Z=32.50

At C(15,10) Z=30

At D(20,0) Z=20

At O(0,0) Z=0 Finding values of 𝑥 and 𝑦 for maximum profit

The company should make 10 half sleeve shirts and 15 full sleeve shirts, each week for the maximum profit.

Note: For questions having more than one correct answer/solution, alternative correct answers/solutions, apart from those given above, have also been accepted.

We hope students must have found this information on “ISC Class 12 Maths Question Papers Solutions 2020” helpful for their studies. To get the year-wise ISC Class 12 Previous Years Question papers along with solutions for other subjects, click here. Keep learning and download the BYJU’S App to access interactive study videos.