Mathematics Test

Result

Mathematics Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

It is given that n arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b ∈ R. If the m^th mean between these two sets of numbers is the same, then a : b equals

A
n - m + 1 : m

B
n + m + 1 : m

C
m : n - m + 1

D
n : n - m + 1

Solution
Question 2
1 / -0

If p^th, q^th and r^th terms of an AP, respectively are a, b and c, then a(q - r) + b(r - p) + c(p - q) is equal to

A
1

B
0

C
a + b + c

D
-1

Solution
Question 3
1 / -0

Suppose a, b, and c are distinct real numbers such that a, 2b, 3c are in AP and a, b, c are in GP. Then, which of the following can be the common ratio of the GP

A
2

B
1/2

C
1/3

D
3

Solution
Question 4
1 / -0

Let S₁, S₂, … be squares such that for each n≥ 1, the length of a side of S_n equals the length of a diagonal of S_{n + 1}. If the length of a side of S₁ is 10 cm, then the smallest value of n for which Area (S_n) < 1 is

A
7

B
8

C
9

D
10

Solution
Question 5
1 / -0

If A and B are two matrices such that AB = B and BA = A, then A² + B² is equal to

A
2AB

B
2BA

C
A + B

D
AB

Solution
Question 6
1 / -0

A
2

B
-1

C
0

D
12

Solution
Question 7
1 / -0

A

B

C

D

Solution
Question 8
1 / -0

A
B is symmetric

B
B is invertible

C
A is periodic

D
All of the above

Solution
Question 9
1 / -0

A
3

B
5

C
9

D
11

Solution
Question 10
1 / -0

Let S = (x – 1)¹⁰ + (x – 1)⁹ (x + 1) + (x – 1)⁸ (x + 1)²+ …….+ (x + 1)¹⁰

Which of the following is a constant term in the expansion of S?

A
2

B
11_C₁

C
11_C₁₀

D
1

Solution
Question 11
1 / -0

The terms independent of x in the expansion of E are in

A
A.P.

B
G.P.

C
A.G.P.

D
None of these

Solution
Question 12
1 / -0

The coefficient of x^k in the expansion of E = 1 + (1 + x) + (1 + x)² + … + (1 + x)ⁿ is

A
ⁿC_k

B
^{n +1}C_k

C
^{n +1}C_{k +1}

D
None of these

Solution
Question 13
1 / -0

Let S = (x – 1)¹⁰ + (x – 1)⁹ (x + 1) + (x – 1)⁸ (x + 1)² + ……. + (x + 1)¹⁰

If O is the sum of coefficients of odd powers of x and E is the sum of the coefficients of even powers of x, which of the following statements is correct?

A
E = 2¹¹

B
E = O

C
O = 2¹¹

D
E = 2¹⁰

Solution
Question 14
1 / -0

A
0

B
1

C
e

D
e/√3

Solution
Question 15
1 / -0

If ⁿC₄, ⁿC₅and ⁿC₆ are in AP, then the value of n can be

A
6

B
7

C
8

D
9

Solution