The sum of the squares of two consecutive natural numbers is 145. Find those numbers. A. 6, 7 B. 10, 11 C. 8, 9 D. 10, 9
Solution x² + (x + 1)² = 145⇒2x² + 2x + 1 = 145⇒2x² + 2x – 144 = 0⇒x²+ x – 72 = 0⇒x(x + 9) – 8(x + 9) = 0⇒x = -9, 8
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Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h.The former arrives half an hour before the latter. Find the distance.
(1) 8km (2)7km (3) 6 km (4)9km Solution: If the required distance be x km,then x/3-x/4=1/2 ⇒ 4x-3x/12=1/2 ⇒ x/12=1/2 ⇒ x= 6km Then the option is (3) 6km
Find the surface area of a rectangular prism with dimensions: length = 10 units, width = 6 units, and height = 8 units.
Solution Surface Area = 2 × (Length × Width + Width × Height + Height × Length)Surface Area = 2 × (10 units × 6 units + 6 units × 8 units + 8 units × 10 units)Surface Area = 2 × (60 + 48 + 80) square unitsSurface Area = 376 square units.
Using identity (a-b)²=a²-2ab+b² find the value of (98)².
Solution (98)² can be further written as (100 – 2)²By comparing the above equation with the identity, we geta = 100 and b = 2(98)²=(100)²−2(100)(2)+(2)²=10000−400+4=9604
Using identity (a-b)²=a²-2ab+b² find the value of (98)². Read More »
If 5√x+12√x=13√x, then x is equal to :
(1) 25/4 (2) 4 (3)9 (4) 16 Solution: 5√x+12√x=13√x We know that 52+122=132 [PythagoreanTriplet) :. √x =2 ⇒ x = 22 =4 Then the option is (2) 4
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A particular football team won 10 matches out of all the total number of matches they played. If their winning percentage was 40 %, how many matches did they play?
Solution Let the total number of matches played be x.The team won around 10 matches, and the team’s winning percentage was 40%.40/100 × x = 1040x = 10 × 10040x = 1000x = 1000/40= 100/4= 2Hence, the team played 25 matches.
The missing number in the sequence 5,6,15,…?…. 89,170,291 is:
(1) 50 (2) 40 (3) 42 (4) 32 Solution: The pattern of the given number series is : 5 + 12 = 6 6 + 32 = 15 15 +52= 40 40+72= 89 89+92= 170 Then the missing number is 40.
The missing number in the sequence 5,6,15,…?…. 89,170,291 is: Read More »
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Solution Since every polyhedron satisfies Euler’s formula, therefore checking if polyhedron can have 10 faces, 20 edges and 15 vertices.No. of Faces (F) = 10No. of Vertices (V) = 15No. of Edges (E) = 20By Using Euler’s formula: F + V – E = 2 and Substituting the values, we get⇒ 10 + 15 –
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A goods train 158 metres long and travelling at the speed of 32 km per hr. leaves Delhi at 6 am. Another mail train 130 metres long and travelling at the average speed of80 km per hr. leaves Delhi at 12 noon and follows the goods train. At what time will the mail train completely cross the goods train?
(1)4hours (2)4 hours 21.6 sec. (3)5 hours 21.6 sec. (4) None of these Solution: The goods train leaves Delhi at 6 am and mail train at 12 noon, hence after 6 hours The distance covered by the goods train in 6 hours at 32 km per hr. = 32*6= 192 kms The relative velocity of
Find the probability that a leap year has 52 Sundays.
Solution A leap year can have 52 Sundays or 53 Sundays. In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days. Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed) (Wed, Thur) (Thur, Friday) (Friday, Sat).So there are total 7
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