Mathematics Test 98

Result

Mathematics Test 98

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

A number has four divisors and sum of its divisors excluding 1 & itself is 30, then number of such numbers is -

A
2

B
3

C
4

D
5

Solution

Let number be N number has four divisors

⇒ N = p₁ × p₂ (where p₁ & p₂ are prime numbers)

or number = p₁³

If N = p₁ × p₂

⇒ p₁ + p₂ = 30

possible pairs are (7, 23), (11, 19), (13, 17)

If N = p₁³

⇒ p₁ + p₁² = 30

⇒ p₁ = 5
Question 2
4 / -1

Remainder when 7⁶³⁶ is divided by 19 is equal to-

A
1

B
7

C
12

D
13

Solution

7⁶³⁶ = (343)²¹² = (1 + 19 × 18)²¹²

= 1 + ²¹²C₁(19 × 18) + .....

⇒ Remainder = 1
Question 3
4 / -1

If x is an odd integer and y, z are even integers, satisfying x + y + z = 47 and x, y, z ≥ 0, then number of solutions are

A
100

B
200

C
300

D
400

Solution

x + y + z = 47

⇒ The problem is similar to put 47 identical things in 3 diff. boxes, Let x' = x – 1

⇒ x' + y + z = 2(23)

⇒ ^{23+3 – 1}C_3–1 = ²⁵C₂ = 300
Question 4
4 / -1

Consider the series (1 – x) (1 + x + x²)¹⁰⁰ = a₀x⁰ + a₁x¹ +a₂x²+.......+a₂₀₁x²⁰¹ .

On the basis of above information, answer the following questions :

(a₀a₁ – a₁a₂ + a₂a₃ – ....... + a₂₀₀a₂₀₁) is equal to-

A
a₅₀

B
a₅₁

C
a₁₀₁

D
0