Ntse Maths Sample Paper
Sample Questions in Mathematics 1. If a and b are positive integers such that a b = 125, then (a − b) a + b − 4 is equal to
1. 16 2.
5 5
2. 25
3. 28
4. 30
× 53 ÷ 5 −3/ 2 = 5 a+ 2 then the value of a is equal to
1. 4 3.
2. 5
3. 6
4. 8
An electric contractor purchases a certain amount of wire. 10% of which is stolen. After using 85% of the remainder, he had 54 m of the wire left. How much wire did he purchase? 1. 300 m 2. 350 m 3. 375 m 4. 400 m
4.
×, y and z are three sums of money such that y is the simple interest on ×. z is the simple interest on y for the same time and the same rate of interest. Then we have
1. x 2 = yz 5.
2. z 2 = xy
3. y 2 = xz
4. xyz = 1
A rectangular plank 2 meters wide is placed on a square lawn parallel to its diagonal as shown in the figure. What is the area of the plank?
1. 14 sq m
2. 12 sq m
3. 7 2 sq m
4. 14 2 sq m
21
6.
Two circular wheels of same radius ‘ r ’ centimeter are their central hubs at a distance of ‘a’ centimeter from one another. The minimum length (in cm) of the fan belt which will pass around both the wheels is
1. a +
7.
π r
2
2.
(a + π r ) / 2
3. 2 a + π r
4. 2 ( a + π r)
From a rectangular sheet of cardboard measuring 8 cm x 4 cm , two largest circular discs of same radius touching each other were cut off. What is the area (in cm2) of the remaining cardboard sheet?. 1. 32 - 8 π
2. 32 - 4 π 3. 32 - π 4. 32 - 2 π
8.
In which of the following cases a triangle ABC, with base BC given, can be constructed? 1. ∠ B 2. ∠ B 3. ∠ B and ∠ C and ∠ C and ∠ C acute angles right angles obtuse angles
4. ∠ B obtuse and ∠ C right angles 9. In the figure A F, BG, C H, D I, E J are straight lines. What is the sum of ∠ A, ∠ B, ∠ C,……..∠ J
1. 6000
2. 7200
3. 9000
4. 3600
22
Solution/Rationale for Mathematics Questions
Q. No.
Answer
Solution/Rationale
Q1.
1
ab = 125 ⇒ 53 = 125 Then ( a − b ) a + b −
1. 16 2.
5 5
2. 25
3. 28
4. 30
× 53 ÷ 5 −3/ 2 = 5 a+ 2 then the value of a is equal to
1. 4 3.
2. 5
3. 6
4. 8
An electric contractor purchases a certain amount of wire. 10% of which is stolen. After using 85% of the remainder, he had 54 m of the wire left. How much wire did he purchase? 1. 300 m 2. 350 m 3. 375 m 4. 400 m
4.
×, y and z are three sums of money such that y is the simple interest on ×. z is the simple interest on y for the same time and the same rate of interest. Then we have
1. x 2 = yz 5.
2. z 2 = xy
3. y 2 = xz
4. xyz = 1
A rectangular plank 2 meters wide is placed on a square lawn parallel to its diagonal as shown in the figure. What is the area of the plank?
1. 14 sq m
2. 12 sq m
3. 7 2 sq m
4. 14 2 sq m
21
6.
Two circular wheels of same radius ‘ r ’ centimeter are their central hubs at a distance of ‘a’ centimeter from one another. The minimum length (in cm) of the fan belt which will pass around both the wheels is
1. a +
7.
π r
2
2.
(a + π r ) / 2
3. 2 a + π r
4. 2 ( a + π r)
From a rectangular sheet of cardboard measuring 8 cm x 4 cm , two largest circular discs of same radius touching each other were cut off. What is the area (in cm2) of the remaining cardboard sheet?. 1. 32 - 8 π
2. 32 - 4 π 3. 32 - π 4. 32 - 2 π
8.
In which of the following cases a triangle ABC, with base BC given, can be constructed? 1. ∠ B 2. ∠ B 3. ∠ B and ∠ C and ∠ C and ∠ C acute angles right angles obtuse angles
4. ∠ B obtuse and ∠ C right angles 9. In the figure A F, BG, C H, D I, E J are straight lines. What is the sum of ∠ A, ∠ B, ∠ C,……..∠ J
1. 6000
2. 7200
3. 9000
4. 3600
22
Solution/Rationale for Mathematics Questions
Q. No.
Answer
Solution/Rationale
Q1.
1
ab = 125 ⇒ 53 = 125 Then ( a − b ) a + b −