1. An organization awarded 48 medals in event ' 𝐴 ', 25 in event ' 𝐵 ' and 18 in event
' 𝐶 '. If these medals went to total 60 men and only five men got medals in all the
three events, then, how many received medals in exactly two of three events?
A) 10
B) 15
C )21
D) 9
1+𝑖cos⁡𝜃
2. The sum of all possible values of 𝜃 ∈ [−𝜋, 2𝜋], for which 1−2𝑖cos⁡𝜃 is purely
imaginary, is equal to:
A) 4𝜋
B) 3𝜋
C) 2𝜋
D)5𝜋
2
2|
|𝑧
3. If 𝑧 = 𝑥 + 𝑖𝑦, 𝑥𝑦 ≠ 0, satisfies the equation 𝑧 + 𝑖𝑧‾ = 0, then
is equal to :
1
A)9
B) 4
C) 4
D) 1
4. Let 3, 𝑎, 𝑏, 𝑐 be in A.P. and 3, 𝑎 − 1, 𝑏 + 1, 𝑐 + 9 be in G.P. Then, the arithmetic
mean of 𝑎, 𝑏 and 𝑐 is :
A) -4
B) -1
C) 13
D) 11
5. The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ⋯ is :
A) 3420
B) 3450
C) 3250
D) 3520
6. The number of ways in which 21 identical apples can be distributed among three
children such that each child gets at least 2 apples, is
A) 130
B) 136
C) 142
D) 406
7. The coordinates of a point dividing the line segment joining (1,2) and (4,5)
internally in the ratio 2: 1 is ____
a) (3,4)
b) (4,3)
c) (5,4)
d) (5,3)
8. Find the equation of line parallel to 4𝑥 + 𝑦 = 2 and pass through (2,5).
a) 4𝑥 + 𝑦 − 13 = 0
b) 4𝑥 + 𝑦 + 13 = 0
c) 4𝑥 − 𝑦 − 13 = 0
d) 4𝑥 − 𝑦 + 13 = 0
9. If a circle pass through (4,0) and (0,2) and center at 𝑦-axis then find the radius of
the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units
10. If length of transverse axis is 8 and conjugate axis is 10 and transverse axis is
along 𝑥-axis then find the equation of hyperbola.
𝑥 2
𝑦 2
𝑥 2
𝑦 2
𝑥 2
𝑦 2
a) (4) − (5 ) = 1
b) (5) − (4 ) = 1
c) (10) − (8 ) = 1
𝑥 2
𝑦 2
d) (8) − (10) = 1
11. Find the distance of point ( 2,3,5 ) from X-Z plane.
a) 2 units
b) 3 units
c) 5 units
12. If lim𝑥→0
A) 0
d) 1 unit
cos⁡(2𝑥)+𝑎cos⁡(4𝑥)−𝑏
is finite, then (𝑎 + 𝑏) is equal to :
𝑥4
3
B) 4
C) -1
1
D) 2
13. If 𝐴 and 𝐵 are two events such that 𝑃(𝐴) = 0.7, 𝑃(𝐵) = 0.4 and 𝑃(𝐴 ∩ 𝐵‾) = 0.5,
where 𝐵‾ denotes the complement of 𝐵, then 𝑃(𝐵 ∣ (𝐴 ∪ 𝐵‾)) is equal to
1
1
1
1
(A) 3
(B) 2
(C) 4
(D) 6
2
7
14. Let Ajay will not appear in JEE exam with probability p = , while both Ajay and
1
Vijay will appear in the exam with probability q = 5. Then the probability, that
Ajay will appear in the exam and Vijay will not appear is :
9
A) 35
3
B) 35
24
18
(C) 35
D) 35
15. The mean of two samples of the sizes 250 and 320 were found to be 20,12
respectively. Their standard deviations were 2 & 5, respectively. Find the variance
of combined sample of size 650.
a) 10.23
b) 32.5
c) 65
d) 26.17
1
10
16. If the term independent of 𝑥 in the expansion of (√a𝑥 2 + 2𝑥3 )
equal to:
A) 6
B) 4
C) 2
is 105, then a2 is
D) 9
17. A solution is to be kept between 77∘ F and 86∘ 𝐹. What is the range in temperature
in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given
by F = 9/5C + 32∘ ?
a) [15∘ , 20∘ ]
b) [20∘ , 25∘ ]
c) [25∘ , 30∘ ]
d) [30∘ , 35∘ ]
18. The value of (sin⁡70∘ )(cot⁡10∘ cot⁡70∘ − 1) is
A) 0
B) 2/3
19. The value of
2𝜋
4𝜋
6𝜋
cos⁡( 7 ) + cos⁡( 7 ) + cos⁡( 7 ) is equal to :
C) 1
D)3/2
1
A) -1
1
B) − 2
1
C) − 3
D) − 4
20. The value of sin⁡10∘ sin⁡30∘ sin⁡50∘ sin⁡70∘ is :A)
1
36
B)
1
16
C)
1
32
D)
1
18
𝑥 2 −1
21. 𝑓(𝑥) = 𝑥 2 +1 , for every real number, then what is the minimum value of 𝑓 ?
1+𝑖√3
𝑛
22. The least positive integer n for which (1−𝑖 3) = 1, is:
√
23. Set 𝐴 has 𝑚 elements and set 𝐵 has 𝑛 elements. If the total number of subsets of 𝐴
is 112 more than the total number of subsets of 𝐵, then the value of 𝑚. 𝑛 is ____ .
24. What is the value of lim𝑥→4
𝑥 2 −2𝑥−8
?
𝑥−4
1
1
1016
25. The number of integral terms in the expansion of (52 + 78 )
is: