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# Bhaskara Contest (NMTC Junior 2018 - IX and X Grades) - Stage I- Problems and Solution

#### Part A

The value of is
(A)
(B)
(C)
(D)

###### Problem 2

A train moving with a constant speed crosses a stationary pole in 4 seconds and a platform long in 9 seconds. The length of the train is (in meters)
(A) 56
(B) 58
(C) 60
(D) 62

###### Problem 3

One of the factors of is

(A)
(B)
(C)
(D)

###### Problem 4

The natural number which is subtracted from each of the four numbers to give four numbers in proportion is
(A) 1
(B) 2
(C*) 3
(D) 4

###### Problem 5

The solution to the equation is

(A) 2
(B) 4
(C) 5
(D) No solution

###### Problem 6

If , the value of is
(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 7

There are two values of for which the equation has only one solution for . The sum of these two value of is

(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 8

The number of zeros in the product of the first 100 natural numbers is
(A) 12
(B) 15
(C) 18
(D) 24

###### Problem 9

The length of each side of a triangle in increased by then the percentage increase of area is
(A)
(B)
(C)
(D)

###### Problem 10

The number of pairs of relatively prime positive integers such that is an integer is
(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 11

The four digit number is a perfect square. The value of is
(A) 52
(B) 62
(C) 54
(D) 68

###### Problem 12

are positive real numbers such that . The smallest value of is
(A) 15
(B) 16
(C) 17
(D) 18

###### Problem 13

real numbers. The least value of is
(A) 1
(B) 0
(C) -1
(D) 2

###### Problem 14

I is the incenter of a triangle in which
(A)
(B)
(C)
(D)

###### Problem 15

In the adjoining figure is a square and DFEB is a rhombus

(A)
(B)
(C)
(D)

#### Part B

###### Problem 16

is a square are point on respectively and . The value of is

###### Problem 17

The average of 5 consecutive natural numbers is 10 . The sum of the second and fourth of these numbers is

###### Problem 18

The number of natural number for which is a perfect square is

###### Problem 19

is an integer and is also an integer. The sum of all such is

###### Problem 20

is a fraction where have no common factors other 1 . b exceeds a by 3 . If the numerator is increased by 7 , the fraction is increased by unity. The value of

###### Problem 21

If then the value of is

###### Problem 22

The angle of a heptagon are . The value of is

###### Problem 23

is a triangle and is its altitude. If , then the value of is

###### Problem 24

As sphere is inscribed in a cube that has surface area of . A second cube is then inscribed within the sphere. The surface area of the inner cube in is

###### Problem 25

A positive integer is multiple of 7 . If lies between 15 and 16 , the number of possible values (s) of n is

###### Problem 26

The value of which satisfies the equation is

###### Problem 27

man do a work in days. If there had been men more, the work would have been finished days earlier, then the value of is

###### Problem 28

The sum of the digit of a two number is 15 . If the digits of the given number are reversed, the number is increased by the square of 3 . The original number is

###### Problem 29

When expanded the units place of is

If and , then is

#### Part A

The value of is
(A)
(B)
(C)
(D)

###### Problem 2

A train moving with a constant speed crosses a stationary pole in 4 seconds and a platform long in 9 seconds. The length of the train is (in meters)
(A) 56
(B) 58
(C) 60
(D) 62

###### Problem 3

One of the factors of is

(A)
(B)
(C)
(D)

###### Problem 4

The natural number which is subtracted from each of the four numbers to give four numbers in proportion is
(A) 1
(B) 2
(C*) 3
(D) 4

###### Problem 5

The solution to the equation is

(A) 2
(B) 4
(C) 5
(D) No solution

###### Problem 6

If , the value of is
(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 7

There are two values of for which the equation has only one solution for . The sum of these two value of is

(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 8

The number of zeros in the product of the first 100 natural numbers is
(A) 12
(B) 15
(C) 18
(D) 24

###### Problem 9

The length of each side of a triangle in increased by then the percentage increase of area is
(A)
(B)
(C)
(D)

###### Problem 10

The number of pairs of relatively prime positive integers such that is an integer is
(A) 1
(B) 2
(C) 3
(D) 4

###### Problem 11

The four digit number is a perfect square. The value of is
(A) 52
(B) 62
(C) 54
(D) 68

###### Problem 12

are positive real numbers such that . The smallest value of is
(A) 15
(B) 16
(C) 17
(D) 18

###### Problem 13

real numbers. The least value of is
(A) 1
(B) 0
(C) -1
(D) 2

###### Problem 14

I is the incenter of a triangle in which
(A)
(B)
(C)
(D)

###### Problem 15

In the adjoining figure is a square and DFEB is a rhombus

(A)
(B)
(C)
(D)

#### Part B

###### Problem 16

is a square are point on respectively and . The value of is

###### Problem 17

The average of 5 consecutive natural numbers is 10 . The sum of the second and fourth of these numbers is

###### Problem 18

The number of natural number for which is a perfect square is

###### Problem 19

is an integer and is also an integer. The sum of all such is

###### Problem 20

is a fraction where have no common factors other 1 . b exceeds a by 3 . If the numerator is increased by 7 , the fraction is increased by unity. The value of

###### Problem 21

If then the value of is

###### Problem 22

The angle of a heptagon are . The value of is

###### Problem 23

is a triangle and is its altitude. If , then the value of is

###### Problem 24

As sphere is inscribed in a cube that has surface area of . A second cube is then inscribed within the sphere. The surface area of the inner cube in is

###### Problem 25

A positive integer is multiple of 7 . If lies between 15 and 16 , the number of possible values (s) of n is

###### Problem 26

The value of which satisfies the equation is

###### Problem 27

man do a work in days. If there had been men more, the work would have been finished days earlier, then the value of is

###### Problem 28

The sum of the digit of a two number is 15 . If the digits of the given number are reversed, the number is increased by the square of 3 . The original number is

###### Problem 29

When expanded the units place of is

###### Problem 30

If and , then is

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