1. Which of the following numbers can be used an example that not all prime numbers are odd?
Show me the answers!
Correct answer is option - 2
Explanation:In the given options, ‘2’ and ‘4’ are the numbers which are even.
In these two numbers, 2 is the prime number since it is only divisible by 1 and itself.
So even though ‘2’ is not an odd number, it is still a prime number!
2. If the sum of three consecutive integers is 36, then the greatest number of them is?
Show me the answers!
Correct answer is option - 5
Explanation: Let the three consecutive integers be x, x + 1, x + 2.
Sum of the numbers is x + x + 1 + x + 2 = 36. This gives: 3x + 3 = 36.
Solving for ‘x’ gives: 3x = 36 – 3 = 33.
This implies 3x = 33 ==> x = 33/3 = 11
The greatest number among the three numbers is x + 2 = 11 + 2 = 13.
3. What is the expression, (x^{4})^{2} + (y^{3})^{3} equivalent to?
Show me the answers!
Correct answer is option - 4
Explanation: According to the law of exponent, (a^{m})^{n} = a^{m * n}
The expression (x^{4})^{2} + (y^{3})^{3} is (x^{4 * 2}) + (y^{3 * 3}) = x^{8} + y^{9}.
4. If one side of a triangle has a length of 10m and the second side of the triangle has a length of 6m, then which of the given values can be the area of the triangle?
I)35m^{2}
II)30m^{2}
III)6m^{2}
Show me the answers!
Correct answer is option - 4
Explanation: First considering a right angled triangle and taking the given two sides as the base and the height, we get area of the triangle, A = 1/2 * base * height = 1/2 * 10 * 6 = 30m^{2}.
The maximum area is produced by a right angle triangle and the area in an acute triangle or an obtuse angled triangle is less when compared to the right triangle.
Hence the area of the above triangle can be any number less than or equal to ‘30m^{2}’ since 30 is the maximum area produced by the given sides!
5. If a car completely travelled a circular path in 20 seconds, then the angle covered in 4 seconds is:
Show me the answers!
Correct answer is option - 3
Explanation: If the car completed a circle in 20 seconds, then it implies that in 20 seconds the total angle covered by the car is 360°. Angle covered in 4 seconds will be (360° * 4 seconds)/ (20 seconds) = 72°.
6. The expression (sinθ+cosθ)^{2} is equivalent to which of the following expressions?
Show me the answers!
Correct answer is option - 4
Explanation: The given expression can be expanded using one of the algebraic formulas: (a + b)^{2} = a^{2} + 2ab + b^{2}.
So applying the above formula gives: (sinθ + cosθ)^{2} = (sinθ)^{2} + 2 (sinθ) (cosθ) + (cosθ)^{2}.
This can be rearranged: sin^{2}θ + cos^{2}θ + 2 (sinθ) (cosθ).
According to the trigonometric identity: sin^{2}θ + cos^{2}θ = 1.
Hence we get: 1 + 2 (sinθ) (cosθ).
7.
If an isosceles right triangle is inscribed in a circle with center ‘O’ and radius 7√3 m as shown in the figure, then the area of the triangle is:
Show me the answers!
Correct answer is option - 3