DR R. B.

PATIL MAHESH P U COLLEGE

PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 1 DATE: 22.02.2024

1) A relation R in a set A, if each element of A is related to every element of A then R is called

a) empty b) universal c)equivalence d)Reflexive
2) If the function f: N → N given by f(x) = 2x then f is
a) one-one but not onto b)bijective
c) Onto but not one-one d) neither one-one nor onto
−1
3) The domain of the function f(x) = cot x is
π
a)(−1,1) b) (−∞, ∞) c) R − (−1,1) d)R − (0, )
2
4) If a matrix has 8 elements , then total number of the possible different orders matrices
a) 8 b)6 c)4 d)2
1 sinθ 1
5) Let A = [−sinθ 1 sinθ] where 0 ≤ θ ≤ 2π then
−1 −sinθ 1
| |
a) A = 0 b) A ∈ (2, ∞)
| | c) |A| ∈ (2,4) d) |A| ∈ [2,4]
6) If f(x) = cos −1 x then the domain of f ′ (x) is
π π
a)[−1,1] b) (−1,1) c)R d) (− , )
2 2
dy
7) If y = e2logx then =
dx
a) ex b)2 c)elogx d)2x
2
8) The point on the curve x = 2y which is nearest to the point (0,5) is
a) (2√2, 4) b) (2√2, 0) c)(0,0) d)(2,2)
1
9) ∫ x 2 (1 − x2) dx =
x3 x3
a) + x + c b)x 3 − x + c c) −x+c d) x 2 − x + c
3 3
x(
10) ∫ e sinx + cosx) dx =
a) ex cosx + c b) ex sinx + c c)ex + c d)ex tanx + c
11) The projection of a vector i − j on i + j is
1
a) 0 b)√2 c) d)1
√2
12) Let a⃗ and ⃗b be two unit vectors and θ is the angle between them , then a⃗ + ⃗b is a unit vector if
θ=
π π π 2π
a) b) c) d)
4 3 2 3
13) If the direction cosines of a line are (k, k, k) then k is
1 1 1
a) b) c)1 d)
√3 2 3
14) The corner points of the feasible region determined by the system of linear constraints are
(0,0), (0,5), (30,0), (20,30) the objective function is z = 4x + y , then maximum value of Z is
a) 210 b)150 c)110 d)120
3 1
15) If A and B are independent events , P(A) = and P(B) = then P(A ∩ B) is
5 5
1 3 22 2
a) b) c) d)
3 25 25 3

*****ALL THE BEST*****

 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST KEY ANSWERS SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 1 DATE: 22.02.2024

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

b a b c d b d a c b a d a d b
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 2 DATE: 22.02.2024

1) The relation R in the set {1,2,3} given by {(1,2)} is Only

a) reflexive b)symmetric c)transitive d)None
2) If f: Z → Z defined by f(x) = [x] then the function f is
a) one-one but not onto b)onto but not one-one
c) Bijective d) Neither one-one nor onto
−1
3) Principal value branch of cosec x is
π π π π π
a) [0, π] b) [− , ] c) [− , ] − {0} d) [0, π] − { }
2 2 2 2 2
4) A square matrix A = [aij ] m×n in which aij = 0 if i ≠ j , aij ≠ 0 if i = j then the matrix is
a) identity b)scalar c)diagonal d)None
5) Let A be a square matrix of order 3 × 3 , such that A. adjA = 5I then |adjA| =
a) 125 b)0 c)−2 d)25
6) Which of the following x belongs to domain of greatest integer function f(x) = [x]
0 < x < 3 is not differentiable
a) 2 and 3 b)1 and 2 c)0 and 2 d)1 and 3
dy
7) If y = log 5 (10) then =
dx
1 1 1 1 1
a) × b) × 1c) d)0
log5 10 log10 5 10
2
8) The point on the curve x = 2y at which function attains minima
a) (√2, 1) b) (1, √2) c) (0,0) d)None
sec2 x
9) ∫ cosec2x dx =
a) sec 2 x b) tan2 x c)tanx − x + c d)None
ex 1
10) ∫ (1 − ) dx =
x x
1 1 1 1
a) e−x . +c b) e−x . + c c) ex . ( ) + c d) ex ( 2 ) + c
x x2 x x
√2
11) Let the vectors a⃗ and ⃗b be such that |a⃗| = 3 , |b
⃗|= then a⃗ × ⃗b is a unit vector if the angle
3
⃗ is
between a⃗ and b
π π π π
a) b) c) d)
6 4 3 2
12) The unit vector in the direction of the vector a⃗ = 2i − j + 3k is
2i−j+3k 2i+j+3k 2i−j−3k 2i−j+3k
a) b) c) d)
√14 √14 √14 14
13) The direction cosines of Z axis are
a)0,0,1 b) 1,0,0 c)0,1,0 d) None
14) Optimization of the objective function is a process of
a) maximizing the objective function
b) minimizing the objective function
c) maximizing and minimizing the objective function
d) None
B
15) If A and B are two events such that P(A) ≠ 0 and P ( ) = 1 then
A
a) A ⊂ B b)B ⊂ A c) B = ∅ d) A = ∅
***ALL THE BEST ***
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST KEY ANSWERS SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 2 DATE: 22.02.2024

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

c c c c d b d c c c b a a c a
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 3 DATE: 22.02.2024

1) Consider the non-empty set containing of children in a family and a relation 𝑅 defined by 𝑅 =
{(𝑎, 𝑏) ∶ 𝑎 𝑖𝑠 𝑏𝑟𝑜𝑡ℎ𝑒𝑟 𝑜𝑓 𝑏} , then 𝑅 is
a)symmetric but not transitive b)Transitive but not symmetric
c) Neither symmetric nor transitive d)Both symmetric and transitive
2) Let 𝑓: 𝑅 → 𝑅 𝑎𝑛𝑑 𝑔: 𝑅 → 𝑅 be defined by 𝑓(𝑥) = 𝑐𝑜𝑠𝑥 𝑎𝑛𝑑 𝑔(𝑥) = 3𝑥 2 respectively then
𝑓𝑜𝑔(𝑥) is
a)3 cos2 𝑥 b)cos(3𝑥 2 ) c)cos(2𝑥 3 ) d)2 cos3 𝑥
3𝜋
3) The value of cos −1 [𝑐𝑜𝑠 ] is
2
𝜋 3𝜋 5𝜋 7𝜋
a) b) c) d)
2 2 2 2
4) If 𝐴 𝑎𝑛𝑑 𝐵 are symmetric matrices of same order then (𝐴𝐵 − 𝐵𝐴′ ) is ′

a) Null matrix b)Unit Matrix c)Symmetric d)Skew-Symmetric

𝑎11 𝑎12 𝑎13
5) If ∆= |𝑎21 𝑎22 𝑎23 | and 𝐴𝑖𝑗 is the cofactor of 𝑎𝑖𝑗 then the value of the ∆ is
𝑎31 𝑎32 𝑎33
a) 𝑎11 𝐴31 + 𝑎12 𝐴32+ + 𝑎13 𝐴33 b) 𝑎21 𝐴11 + 𝑎22 𝐴12+ + 𝑎23 𝐴13
c) 𝑎11 𝐴11 + 𝑎12 𝐴21+ + 𝑎13 𝐴31 d) 𝑎11 𝐴11 + 𝑎21 𝐴21+ + 𝑎31 𝐴31
6) The function 𝑓 (𝑥) = |𝑥| , where |𝑥| denotes the modulus function is not differentiable at
a) 0 b)1 c)2.5 d)3
𝑑𝑦
7) If 𝑦 = √𝑠𝑖𝑛𝑥 + 𝑦 then =
𝑑𝑥
𝑐𝑜𝑠𝑥 𝑐𝑜𝑠𝑥 𝑠𝑖𝑛𝑥 𝑠𝑖𝑛𝑥
a) b) c) d)
2𝑦−1 1−2𝑦 1−2𝑦 2𝑦−1
1 𝑥
8) The maximum value of ( ) is
𝑥
1 1 𝑒
a) b) 𝑒 𝑒 c) ( ) d) (𝑒)1/𝑒
𝑒 𝑒
9) ∫ 𝑒 1 + 𝑡𝑎𝑛𝑥 + tan2 𝑥 ) 𝑑𝑥 =
𝑥(

a) 𝑒 𝑥 𝑠𝑒𝑐𝑥 + 𝑐 b)𝑒 𝑥 𝑐𝑜𝑠𝑥 + 𝑐 c)𝑒 𝑥 𝑠𝑖𝑛𝑥 + 𝑐 d)𝑒 𝑥 𝑡𝑎𝑛𝑥 + 𝑐

𝑑𝑥
10) ∫ 2 2
=
sin 𝑥 .cos 𝑥
a) 𝑡𝑎𝑛𝑥 + 𝑐𝑜𝑡𝑥 + 𝑐 b)𝑡𝑎𝑛𝑥 − 𝑐𝑜𝑡𝑥 + 𝑐 c)𝑡𝑎𝑛𝑥. 𝑐𝑜𝑡𝑥 + 𝑐 d)𝑡𝑎𝑛𝑥 − 𝑐𝑜𝑡2𝑥 + 𝑐
11) The angle between two vectors 𝑎 𝑎𝑛𝑑 𝑏⃗ with magnitude √3 𝑎𝑛𝑑 4 respectively and 𝑎 . 𝑏⃗ =
2√3 is
𝜋 𝜋 𝜋 5𝜋
a) b) c) d)
6 3 2 2
12) The value of 𝜆 if the vectors 𝑎 = 2𝑖 − 𝜆𝑗 + 3𝑘 and 𝑏⃗ = 𝑖 + 𝑗 − 2𝑘 are perpendicular
a) 𝜆 = 3 b) 𝜆 = −4 c) 𝜆 = −3 d)𝜆 = 2
13) A line which makes angle 60° with 𝑦 − 𝑎𝑥𝑖𝑠 𝑎𝑛𝑑 𝑧 − 𝑎𝑥𝑖𝑠 , then the angle which it makes with
𝑥 − 𝑎𝑥𝑖𝑠 𝑖𝑠
a)45° b) 60° c) 75° d) 30°
14) The solution set of the inequalities 𝑥 ≥ 0 , 𝑦 ≥ 0 is
a)first quadrant b)second quadrant c) Third quadrant d)Fourth
15) A family has two children the probability that both the children are boys given that at least
one of them is a boy
1 1
a) b) 1/3 c) d)3/4
2 4
****ALL THE BEST***
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST KEY ANSWERS SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 3 DATE: 22.02.2024

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

b b a d d a a d d b b b a a b
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 4 DATE: 22.02.2024

1) Which of the following relation in the set {1,2,3} is symmetric and transitive but not reflexive
a) {(1,2)(2,1)(1,1)} b) {(1,2)(2,1} c) {(1,2)(2,1)(1,1)(2,2)} d)Both (a) and (c)
2) Find the number of all one-one functions from set {1,2,3} to itself
a) 8 b)4 c)6 d)3
3) The set of values of 𝑥 , if 𝑠𝑖𝑛−1 [2𝑥√1 − 𝑥 2 ] = 2𝑐𝑜𝑠 −1 𝑥 , holds is
1 1 1 1 1
a) ≤𝑥≤1 b) − ≤ 𝑥 ≤ c) −1 ≤ 𝑥 ≤ 1 d)− ≤ 𝑥 ≤
√2 √2 √2 2 2
𝑥+2 𝑦−3
4) If [ ] is scalar matrix then
0 4
a) 𝑥 = 2 , 𝑦 = 0 b)𝑥 = −2 , 𝑦 = 3 c)𝑥 = 2 , 𝑦 = 3 d)𝑥 = −2 , 𝑦 = −3
1 2
5) If 𝐴 = [ ] then |2𝐴| is equal to
4 2
a) 2|𝐴| b) 3|𝐴| c) 4|𝐴| d) |𝐴|
𝑑𝑦
6) If 𝑦 = 𝑠𝑖𝑛𝑥 2 , then =
𝑑𝑥
a) 2𝑠𝑖𝑛𝑥 b)2𝑠𝑖𝑛𝑥𝑐𝑜𝑠𝑥 c)2𝑥𝑐𝑜𝑠𝑥 2 d)−2𝑥𝑐𝑜𝑠𝑥 2
7) The derivative of sin−1 𝑥 exists in the interval
𝜋 𝜋
a) [−1,1] b) (−1,1) c)𝑅 d) (− , )
2 2
8) The rate of change of the area of a circle per second with respect to its radius 𝑟 when 𝑟 = 5 𝑐𝑚
is
a) 10 𝜋 𝑐𝑚2 /𝑠𝑒𝑐 b) 12 𝜋 𝑐𝑚2 /𝑠𝑒𝑐 c) 8 𝜋 𝑐𝑚2 /𝑠𝑒𝑐 d) 11 𝜋 𝑐𝑚2 /𝑠𝑒𝑐
1−𝑥
9) ∫ 𝑑𝑥 =
√𝑥
3𝑥 3/2 2𝑥 3/2 3𝑥 3/2 3𝑥 3/2
a) 2√𝑥 + +𝑐 b) 2√𝑥 − + 𝑐 c) √𝑥 + +𝑐 d) 2√𝑥 − +𝑐
2 3 2 2
1 𝑥
10) ∫0 𝑑𝑥 =
𝑥 2 +1
1 1
a) 𝑙𝑜𝑔√2 b) − 𝑙𝑜𝑔2 c) 𝑙𝑜𝑔√2 d) 𝑙𝑜𝑔2
2 2
11) If 𝜃 is the angle between two vectors 𝑎 𝑎𝑛𝑑 𝑏⃗ , then 𝑎 . 𝑏⃗ ≥ 0 only when
𝜋 𝜋
a) 0 < 𝜃 < b) 0 ≤ 𝜃 ≤ c) 0 < 𝜃 < 𝜋 d) 0 ≤ 𝜃 ≤ 𝜋
2 2
12) If the vectors 2𝑖 + 3𝑗 − 6𝑘 and 4𝑖 + 𝑚𝑗 − 12𝑘 are parallel then the value of 𝑚 is
a) 3 b)6 c)4 d)2
13) If a line makes an angle 90° , 135° , 45° with the + ve direction of 𝑥, 𝑦 𝑎𝑛𝑑 𝑧 axes respectively
then the direction cosines are
1 1 1 1 1 1 −1 1
a) 1, , b) 1, , c) 0, , d) 0, ,
√2 √2 2 √2 √2 √2 √2 √2
14) Corner points of 𝑍 = 200𝑥 + 500𝑦 are (0,5), (4,3) 𝑎𝑛𝑑 (0,6) then the minimum value of 𝑍 is
a) 2400 b) 3000 c) 2000 d) 2300
7 9 4 𝐵
15) If 𝑃(𝐴) = , 𝑃 (𝐵 ) = and 𝑃(𝐴 ∩ 𝐵) = then 𝑃 ( ) =
13 13 13 𝐴
2 7 4 1
a) b) c) d)
7 8 7 4

***ALL THE BEST***

 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST KEY ANSWERS SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 4 DATE: 22.02.2024

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

d c a c c c b a b c b b d d c
 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 5 DATE: 22.02.2024
1) A relation 𝑅 in the set 𝐴 = {1,2,3} given by {(1,2), (2,1)} is
a) reflexive b)symmetric c)transitive d)equivalence
𝑥
2) Let 𝑦 = , 𝑥 ∈ 𝑅 , 𝑦 ∈ (−1,1) is
1+|𝑥|
a) one-one and onto b) onto but not one-one
c) one-one but not onto d) neither one-one nor onto
2
3) The principal value of 𝑠𝑒𝑐 −1 (− ) is
√3
𝜋 𝜋 5𝜋 5𝜋
a) b) c) d)
6 3 3 6
4) If 𝐴 = [𝑎𝑖𝑗 ] is a square matrix of order 2 × 2 , where 𝑎𝑖𝑗 = |−2𝑖 + 𝑗| , then
1 3 1 0 2 0 1 1
a) [ ] b) [ ] c) [ ] d) [ ]
0 2 3 2 3 1 3 2
3 𝑥 3 2
5) If | |=| | then 𝑥 =
𝑥 1 4 1
a) 2 b)4 c)8 d)±2√2
6) ( ) [ ]
𝑓 𝑥 = 𝑥 is continuous at 𝑥 =
a)0 b)2.7 c)−2 d)2
𝑑𝑦 2
7) If 𝑦 = 𝑎𝑠𝑖𝑛𝑥 + 𝑏𝑐𝑜𝑠𝑥 , then 𝑦 2 + ( ) is a
𝑑𝑥
a) function of 𝑥 and 𝑦 b)constant c)function of 𝑥 d)function of 𝑦
8) The function 𝑓 (𝑥) = 𝑠𝑖𝑛𝑥 is increasing in the interval
𝜋 𝜋
a) (0, 𝜋) b) ( , 𝜋) c) (0, ) d) None
2 2
𝑑 3
9) If [𝑓 (𝑥)] = 4𝑥 3 − ( 4 ) such that 𝑓 (2) = 0 , then 𝑓(𝑥) is
𝑑𝑥 𝑥
3 1 129 1 129 1 129 1 129
a) 𝑥 + + b) 𝑥 3 + − c) 𝑥 4 + + d) 𝑥 4 + −
𝑥4 8 𝑥4 8 𝑥3 8 𝑥3 8
10) ∫ √1 − 𝑠𝑖𝑛2𝑥 𝑑𝑥 =
a) −𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 + 𝑐 b) 𝑠𝑖𝑛𝑥 − 𝑐𝑜𝑠𝑥 + 𝑐 c) 𝑡𝑎𝑛𝑥 + 𝑠𝑒𝑐𝑥 + 𝑐 d) 𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 + 𝑐
11) If 𝑎 𝑎𝑛𝑑 𝑏⃗ are two non-zero vectors such that |𝑎 . 𝑏⃗| = |𝑎 × 𝑏⃗| then 𝑠𝑒𝑐𝜃 =
𝜋 𝜋
a) 2 b) c)√2 d)
4 2
12) 𝑖. (𝑗 × 𝑘 ) + 𝑗. (𝑖 × 𝑘 ) + 𝑘. (𝑖 × 𝑗) is
a) 0 b)−1 c)1 d)3
13) If a line has the direction ratios 2, −1, −2 , then its direction cosines
2 1 2 2 1 2 2 1 2
a) −2,1,2 b) − , , c) , − , − d)− , − , −
3 3 3 3 3 3 3 3 3
14) In a linear programming problem , the objective function is always
a) a quadratic function b) a constant function
c) a linear function d) non-simultaneous function
15) Two events 𝐴 𝑎𝑛𝑑 𝐵 will be independent , if
a) 𝐴 𝑎𝑛𝑑 𝐵 are mutually exclusive b)𝑝(𝐴′ ∩ 𝐵′ ) = [1 − 𝑝(𝐴)][1 − 𝑃(𝐵)]
c)𝑃(𝐴) = 𝑃(𝐵) d) 𝑃(𝐴) + 𝑃(𝐵) = 1

***ALL THE BEST***

 DR R. B. PATIL MAHESH P U COLLEGE
PRIYADARSHINI COLONY, GOKUL ROAD, HUBBALLI
KCET/JEE TEST KEY ANSWERS SUB: MATHEMATICS
CLASS: PU – II THEORY MCQ TEST - 5 DATE: 22.02.2024

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

b c d b d b b c d d c c c c b