1
Two sets, A and B, are as under:
A = {(a, b) ∈ R × R : |a − 5| < 1 and |b − 5| < 1};
B = {a, b) ∈ R × R : 4 (a − 6)2 + 9(b−5)2 ≤ 36}. Then,
a) A is a subset of B
b) A n B = φ (null set)
c) neither A subset of B nor B is a subset of A
d) B is a subset of A
a) A is a subset of B
The coefficient of x3y4 in (2x+3y2)5 is
a)360
b)720
c)240
d)1080
b)720
Let f: R→ R be defined by f(x)= 1/x, for all x ∈ R, Then f is…..
a) one-one
b) onto
c) bijective
d)not defined
a) one-one
The statement “ for all n, n! < 3n ” is true for:
a) values of n greater than 3
b) values of n greater than 5
c) values of n greater than 7
d) values of n greater than 6
c) values of n greater than 7
If 8 and 2 are the roots of x² + ax + c = 0 and 3,3 are the roots of
x² + dx + b = 0, then the roots of the equation x² + ax + b = 0
a)133.
b)-1,1
c)9,1
d)-1,2
c)9,1
{1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
(a) 1/(n + 1) for all n ∈ N
(b) 1/(n + 1) for all n ∈ Z
(c) n/(n + 1) for all n ∈ N
(d) n/(n + 1) for all n ∈ R
(a) 1/(n + 1) for all n ∈ N
Golden
If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is
(a) 1/x + y
(b) 1/x + 1/y
(b) 1/x + 1/y
What will be the simplified value of (sec A sec B + tan A tan B)2 - ( sec A tan B + tan A sec B)2?
a) 0
b) 1
c) -1
d) 2
b) 1
If α + β = π/4, then the value of (1 + tan α) (1 + tan β) is
a) 1
b) 2
c) –2
d) Not defined
b) 2
Danger
12 people at a party shake hands once with everyone else in the room. How many handshakes took place?
a) 132
b) 66
c) 12! / 2
d) 12!
e) 44
f) 88
b) 66
2X Question
Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total of number of elements in power set of the second test. Then the value of M and N are
a) 7,6
b) 6,4
c) 7,4
d) 6,3
b) 6,4
If A=[1,2],B=[1,2,3,4],C=[5,6] and D=[5,6,7,8] then state which of the following statement is true?
A) (B×D)⊂(A×C)
B) (A×C)⊂(B×D)
C) (A×B)⊂(A×D)
D) (D×A)⊂(B×A)
B) (𝑨×𝑪)⊂(𝑩×𝑫)
2 Answer
Find general solution of the equation cos 4θ = sin 3θ.
A) 𝛳 = (n-1)𝝅/3
B) 𝛳 = 2n𝝅/7
C) 𝛳 = (4n-1)𝝅/2
D) 𝛳 = n𝝅/2
C) 𝛳 = (4n-1)𝝅/2
There are 8 points in a plane and 4 of them are collinear. The number of straight lines joining any 2 points is
a) 39
b) 45
c) 38
d) 23
d) 23
2 Answer
Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, is
(a) 256
(b) 275
(c) 510
(d) 219
(d) 219
In how many ways can 5 students stand in a line if 2 particular students must always stand together?
a) 24
b) 48
c) 120
d) 240
b) 48
In an AP, if a₁ = 5, d = 3, and aₙ = 35, find n.
a) 11
b) 12
c) 10
d) 13
a) 11
2X Question
If f(x)=ax³+bx²+cx+d has zeroes at x=-2,0,3, find a:b:c:d.
a) 1:1:-4:0
b) 1:-1:6:0
c) 1:1:6:0
d) 1:-1:-6:0
d) 1:-1:-6:0
The domain of f(x) = √(x² - 4x + 3) is:
a) [1,3]
b) (-∞,1]∪[3,∞)
c) [3,∞)
d) (-∞,1]
b) (-∞,1]∪[3,∞)
Danger
If the sum of first n terms of a GP is 2ⁿ + 1, find the first term and common ratio.
a) a=2, r=1
b) a=1, r=2
c) a=3, r=2
d) a=2, r=2
e) a=2, r=3
f) a=3, r=3
b) a=1, r=2
2 Answer
How many ways can the letters of the word "MISSISSIPPI" be arranged?
a) 34,650
b) 40,320
c) 50,400
d) 24,800
a) 34,650
In an AP, if a₅ + a₉ = 32 and a₇ + a₁₁ = 40, find the common difference.
a) 2
b) 3
c) 4
d) 5
c) 4
In the expansion of (1+x)50, the sum of the coefficients of odd powers of x is
a)249
b)251
c)250
d)225
a)249
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent then the total number of points of intersection are
a) 40
b) 45
c) 10!
d) 210
b) 45
Golden
A wheel is spinning at 2 radians/seconds. How many seconds will it take to
make 10 complete rotations?
A) 10π seconds
B) 20π seconds
A) 10π seconds