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SEAT NUMBER
A.B.JICHKAR’S
IDEAL ACADEMY OF SCIENCE
SET PAPER – V(ANSWER KEY)
MATHAMETICS
TIME : 3 Hrs. CLASS : XII (State Board)
Max. Marks. : 80 DATE : 08.Feb.2024
General Instructions:
1. There are a total of 34 questions and four sections in the question paper. All questions are
compulsory.
2. Section A contains question numbers 1 to 2, multiple choice questions of two mark each and one sentence for
one mark each .
Section B contains question numbers 3 to 14, short answer type I questions of two marks each.
Section C contains question numbers 15 to 26, short answer type II questions of three marks each.
Section D contains question number 27 to 34, long answer type questions of four marks each.
________________________________________________________________________________________
SECTION A (16 + 4 = 20)
Q. 1) Select and write the correct answer for the following multiple choice types of questions . 16 m
i. The statement p → ( q → p) is equivalent to :
a) p → (p → q) b) p → (p ∨ 𝑞) c) p → (p ∧ 𝑞) d) p → (p ↔ 𝑞)
4 2
ii. The value of tan (𝑐𝑜𝑠 −1 5 + tan−1 3)
6 7 17 16
a) 17 b) 16 c) d)
6 7
𝑥+1 𝑦−3 𝑧+1
iii. The distance of the point (2 , -3 , 1) from the line = = , 𝑖𝑠
2 3 −1
a) √35 b) √37 c) √38 d) √39
iv. The joint equation of the angle bisectors of the angles between the lines 4x2 – 16xy + 7y2 = 0 is :
a) 8𝑥 2 − 3𝑥𝑦 + 8𝑦 2 = 0 b) 8𝑥 2 + 3𝑥𝑦 + 8𝑦 2 = 0
c) 8𝑥 2 + 3𝑥𝑦 − 8𝑦 2 = 0 d) 8𝑥 2 − 3𝑥𝑦 − 8𝑦 2 = 0
v. If 𝜃 is the acute angle between the vector 𝑖̂ + 𝑗̂ + 𝑘̂ and 2𝑖̂ − 𝑗̂ + 𝑘̂, then tan 𝜃 is :
7 √7 7 2
a) b) c) √2 d)
2 2 √7
cos ec xdx =
4
vi.
1 1
a) cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 + 𝑐 b) cot 𝑥 − 𝑐𝑜𝑡 3 𝑥 + 𝑐
3 3
1 1
c) − (cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 ) + 𝑐 d) − (cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 ) + 𝑐
3 3
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vii. The differential equations for 𝑎2 𝑦 = log 𝑥 + 𝑏, 𝑖𝑠
𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦
a) 𝑥 𝑑𝑥 2 − 𝑑𝑥 = 0 b) 𝑥 𝑑𝑥 2 − 𝑥 𝑑𝑥 = 0 c) 𝑥 𝑑𝑥 2 − 𝑥 2 =0 d) 𝑥 𝑑𝑥 2 + 𝑑𝑥 = 0
𝑑𝑥
1−𝑥 𝑑𝑦
viii. If 𝑦 = √1+𝑥 , then ( 1 – x2) 𝑑𝑥 + 𝑦 =
a) 1 b) 0 c) -1 d) 2
Q. 2) Attempt the following question: 4m
i. Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12
𝑑𝑦
ii. Find the solution of the differential equation y – x 𝑑𝑥 = 0
2
iii. Evaluate : sin 8 xdx
0
iv. Find the co-ordinates of the point of intersection of pair of lines
6𝑥 2 + 5𝑥𝑦 − 4𝑦 2 + 7𝑥 + 13𝑦 − 3 = 0.
EklavyaTestSeries
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SECTION B( 2 8 = 16)
Attempt any Eight of the following: 16 m
3) Write the dual of (p → q) ∨ (q → p).
4 12
4) If 𝑠𝑖𝑛−1 5 + 𝑐𝑜𝑠 −1 13 = 𝑠𝑖𝑛−1 𝛼, 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝛼.
EklavyaTestSeries
SEAT NUMBER
A.B.JICHKAR’S
IDEAL ACADEMY OF SCIENCE
SET PAPER – V(ANSWER KEY)
MATHAMETICS
TIME : 3 Hrs. CLASS : XII (State Board)
Max. Marks. : 80 DATE : 08.Feb.2024
General Instructions:
1. There are a total of 34 questions and four sections in the question paper. All questions are
compulsory.
2. Section A contains question numbers 1 to 2, multiple choice questions of two mark each and one sentence for
one mark each .
Section B contains question numbers 3 to 14, short answer type I questions of two marks each.
Section C contains question numbers 15 to 26, short answer type II questions of three marks each.
Section D contains question number 27 to 34, long answer type questions of four marks each.
________________________________________________________________________________________
SECTION A (16 + 4 = 20)
Q. 1) Select and write the correct answer for the following multiple choice types of questions . 16 m
i. The statement p → ( q → p) is equivalent to :
a) p → (p → q) b) p → (p ∨ 𝑞) c) p → (p ∧ 𝑞) d) p → (p ↔ 𝑞)
4 2
ii. The value of tan (𝑐𝑜𝑠 −1 5 + tan−1 3)
6 7 17 16
a) 17 b) 16 c) d)
6 7
𝑥+1 𝑦−3 𝑧+1
iii. The distance of the point (2 , -3 , 1) from the line = = , 𝑖𝑠
2 3 −1
a) √35 b) √37 c) √38 d) √39
iv. The joint equation of the angle bisectors of the angles between the lines 4x2 – 16xy + 7y2 = 0 is :
a) 8𝑥 2 − 3𝑥𝑦 + 8𝑦 2 = 0 b) 8𝑥 2 + 3𝑥𝑦 + 8𝑦 2 = 0
c) 8𝑥 2 + 3𝑥𝑦 − 8𝑦 2 = 0 d) 8𝑥 2 − 3𝑥𝑦 − 8𝑦 2 = 0
v. If 𝜃 is the acute angle between the vector 𝑖̂ + 𝑗̂ + 𝑘̂ and 2𝑖̂ − 𝑗̂ + 𝑘̂, then tan 𝜃 is :
7 √7 7 2
a) b) c) √2 d)
2 2 √7
cos ec xdx =
4
vi.
1 1
a) cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 + 𝑐 b) cot 𝑥 − 𝑐𝑜𝑡 3 𝑥 + 𝑐
3 3
1 1
c) − (cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 ) + 𝑐 d) − (cot 𝑥 + 𝑐𝑜𝑡 3 𝑥 ) + 𝑐
3 3
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vii. The differential equations for 𝑎2 𝑦 = log 𝑥 + 𝑏, 𝑖𝑠
𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦 𝑑2 𝑦 𝑑𝑦
a) 𝑥 𝑑𝑥 2 − 𝑑𝑥 = 0 b) 𝑥 𝑑𝑥 2 − 𝑥 𝑑𝑥 = 0 c) 𝑥 𝑑𝑥 2 − 𝑥 2 =0 d) 𝑥 𝑑𝑥 2 + 𝑑𝑥 = 0
𝑑𝑥
1−𝑥 𝑑𝑦
viii. If 𝑦 = √1+𝑥 , then ( 1 – x2) 𝑑𝑥 + 𝑦 =
a) 1 b) 0 c) -1 d) 2
Q. 2) Attempt the following question: 4m
i. Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12
𝑑𝑦
ii. Find the solution of the differential equation y – x 𝑑𝑥 = 0
2
iii. Evaluate : sin 8 xdx
0
iv. Find the co-ordinates of the point of intersection of pair of lines
6𝑥 2 + 5𝑥𝑦 − 4𝑦 2 + 7𝑥 + 13𝑦 − 3 = 0.
EklavyaTestSeries
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SECTION B( 2 8 = 16)
Attempt any Eight of the following: 16 m
3) Write the dual of (p → q) ∨ (q → p).
4 12
4) If 𝑠𝑖𝑛−1 5 + 𝑐𝑜𝑠 −1 13 = 𝑠𝑖𝑛−1 𝛼, 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝛼.
EklavyaTestSeries
