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Calculate the volume of a prism which has a base of square of side 9 cm and has a height of 27 cm.
Volume of a prism = Area of the base × height
= 81× 27
= 2187
Each edge of a regular tetrahedron is 6cm.Find the total surface area of the tetrahedron in (sq.cm)?
Total surface area of a regular tetrahedron = area of 4 equilateral triangles
Sin 22.5 + cos 112.5 =?
Sin 22.5 + cos (90 + 22.5)
∵Cos (90 + θ) = - sin θ
Sin 22.5 - sin22.5 = 0
If p/q + q/p = 1, then p3+ q3 = ?
O is the circumcentre of triangle ABC. Find the value of x if angle BAC = 60° and angle BOC = 4x+52
If O is the circumcentre then BOC = 2BAC= 120
Then 4x + 52 = 120
4x = 68
x = 17
What is the mean of the marks scored by students in a science exam?
42, 40, 53, 49, 55
Mean = (42 + 40 + 53 + 49 + 55) ÷ 5 = 47.8
Directions For Questions
The following table represents the percentage marks of five students in six subjects. Consider the table and answer the following questions.
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The average marks obtained by the students in English and Hindi respectively
Average in English = (72 + 70 + 71 + 75 + 67)/5 = 71
Average in Hindi = (65 + 70 + 71 + 70 + 74)/5 = 70
Who has the highest total marks?
Binod = 75 + 80 + 65 + 68 + 72 + 65 = 425
Bindu = 80 + 85 + 75 + 65 + 70 + 70 = 445
Baibhav = 82 + 88 + 70 + 69 + 71 + 71 = 451
Bimal = 78 + 87 + 65 + 70 + 75 + 70 = 445
Binu = 76 + 82 + 55 + 72 + 67 + 74 = 426
∵ Baibhav secured the highest total with 451 marks.
Find the difference of average marks obtained by all the students in Science and History
Total marks obtained by all the students in Science = 80 + 85 + 88 + 87 + 82 = 422
Average = 422 ÷ 5 = 83.4
Total marks obtained by all the students in History = 65 + 75 + 70 + 65 + 55 = 330
Average = 330 ÷ 5 = 66
Difference of average of science and history = 83.4 – 66 = 17.4
If b = (2a+3)/(3a – 2) , find a when b = 5
b = (2a+3)/(3a-2)
b = 5
5 = (2a+3)/(3a-2)
5(3a – 2) = 2a + 3
15a – 10 = 2a + 3
15a – 2a = 3 + 10
13a = 13
a = 1
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