Class 12 ISC term2 Maths Specimen 2022

BOARD -

CLASS -

SUBJECT -

ISC

12th

MATHEMATICS

Paper Pattern for Written Term-II

TIME -

MARKS -

1 Hour 30 Minutes

40

Visit CISCE OFFICIAL PAGE for Regulations and Syllabus of Class 12th ISC

Solved Specimen Paper Semester-2 2022

Question 1 [MATHEMATICS Specimen Paper Semester-2 2022]

Choose the correct answers to the questions from the given options. (Do not copy the question, Write the correct answer only.)

(i) If ∫
(log x) 2 / x
dx =
(log x) 𝑘 / 𝑘
+ 𝑐, then the value of 𝑘 is:

  1. 3
  2. 2
  3. 1
  4. None of the above options

Solution

(ii) ∫ 0 2a 𝑓(𝑥) 𝑑𝑥 = ∫ 0 a 𝑓(𝑥) 𝑑𝑥 + ∫ 0 a 𝑓(𝑘 − 𝑥) 𝑑𝑥 , then the value of 𝑘 is:

  1. 𝑎
  2. 2𝑎
  3. Independent of 𝑎
  4. None of the above options

Solution

(iii)The degree of the differential equation
d 2y / dx 2
+3 (
dy / dx
)2 = x2 (
d 2y / dx 2
)2 is:

  1. 1
  2. 2
  3. 3
  4. 4

Solution

(iv) ∫ ex (
x-1 / x 2
) dx = ex 𝑓(𝑥) + 𝑐. Then 𝑓(𝑥) satisfying the equation is:

  1. x
  2. 𝑥 2
  3. 1/x
  4. None of the above options

Solution

(v) Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card being a king and second card not being a king is:

  1. 48/663
  2. 24/663
  3. 12/663
  4. 4/663

Solution

(vi)If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:

  1. 1/66
  2. 3/66
  3. 19/66
  4. 47/66

Solution

Question 2 [MATHEMATICS Specimen Paper Semester-2 2022]

(a)Evaluate : ∫
x3-x2+x-1 / x-1
dx

Solution

OR

(b)Evaluate : ∫log 10 x dx

Solution

Question 3 [MATHEMATICS Specimen Paper Semester-2 2022]

(a)Solve the differential equation : 𝑐𝑜𝑠𝑒𝑐3𝑥 𝑑𝑦 − cosec 𝑦 𝑑𝑥 = 0

Solution

OR

(b)Solve the differential equation :
dy / dx
= 2-y

Solution

Question 4 [MATHEMATICS Specimen Paper Semester-2 2022]

∫ 2 8
√10-x / √x+ √10-x
dx

Solution

Question 5 [MATHEMATICS Specimen Paper Semester-2 2022]

(a)A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.

Solution

OR

(b)A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.

Solution

Question 6 [MATHEMATICS Specimen Paper Semester-2 2022]

Evaluate : ∫
1+sinx / 1-sinx
dx

Solution

Question 7 [MATHEMATICS Specimen Paper Semester-2 2022]

In a bolt factory, machines X, Y and Z manufacture 20%, 35% and 45% respectively of the total output. Of their output 8%, 6% and 5% respectively are defective bolts. One bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured in the machine Y?

Solution

Question 8 [MATHEMATICS Specimen Paper Semester-2 2022]

(a) Evaluate: ∫
dx / sinx + sin 2x

Solution

OR

(b) Evaluate: ∫ 0 Π/4 log(1+tanx) dx

Solution

Question 9 [MATHEMATICS Specimen Paper Semester-2 2022]

(i) The equation of the plane which is parallel to 2𝑥 − 3𝑦 + 𝑧 = 0 and which passes through (1, −1, 2) is:

  1. 2𝑥 − 3𝑦 + 𝑧 − 7 = 0
  2. 2𝑥 − 3𝑦 + 𝑧 + 7 = 0
  3. 2𝑥 − 3𝑦 + 𝑧 − 8 = 0
  4. 2𝑥 − 3𝑦 + 𝑧 + 6 = 0

Solution

OR

(ii) Evaluate: The intercepts made on the coordinate axes by the plane 2𝑥 + 𝑦 − 2𝑧 = 3 are:

  1. −3/2 , −3, −3/2
  2. 3/2, 3 , -3/2
  3. 3/2, -3 , -3/2
  4. 3/2, 3 , 3/2

Solution

Question 10 [MATHEMATICS Specimen Paper Semester-2 2022]

Find the equation of the plane passing through the point (1, 1, 1) and is perpendicular to the line
x-1 / 3
=
y-2 / 0
=
z-3 / 4
. Also, find the distance of this plane from the origin.

Solution

Question 11 [MATHEMATICS Specimen Paper Semester-2 2022]

Using integration, find the area of the region bounded between the line 𝑥 = 4 and the parabola 𝑦2 = 16𝑥.

Solution

Question 12 [MATHEMATICS Specimen Paper Semester-2 2022]

(i) If the regression line of 𝑥 𝑜𝑛 𝑦 is, 9𝑥 + 3𝑦 − 46 = 0 and 𝑦 𝑜𝑛 𝑥 is, 3𝑥 + 12𝑦 − 7 = 0, then the correlation coefficient ‘r’ is equal to:

  1. -1/12
  2. 1/12
  3. -1/(2√3)
  4. 1/(2√3)

Solution

(ii) If 𝑋̅ = 40, 𝑌̅ = 6, 𝜎𝑥 = 10, 𝜎𝑦 = 1.5 𝑎𝑛𝑑 𝑟 = 0.9 for the two sets of data X and Y, then the regression line of X on Y will be :

  1. 𝑥 − 6𝑦 − 4 = 0
  2. 𝑥 + 6𝑦 − 4 = 0
  3. 𝑥 − 6𝑦 + 4 = 0
  4. 𝑥 + 6𝑦 + 4 = 0

Solution

Question 13 [MATHEMATICS Specimen Paper Semester-2 2022]

For 5 observations of pairs (x, y) of variables X and Y, the following results are obtained: ∑ 𝑥 = 15, ∑ 𝑦 = 25, ∑ 𝑥2 = 55 , ∑ 𝑦2 = 135, ∑ 𝑥𝑦 = 83. Calculate the value of 𝑏𝑥𝑦 𝑎𝑛𝑑 𝑏𝑦𝑥 .

Solution

Question 14 [MATHEMATICS Specimen Paper Semester-2 2022]

A manufacturer wishes to produce two commodities A and B. The number of units of material, labour and equipment needed to produce one unit of each commodity is shown in the table given below. Also shown is the available number of units of each item, material, labour, and equipment.

Solution

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