1. If the value of p = 9, then what is the value of |5 – p|?
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Correct answer is option - 2
Explanation:
Absolute value of any number is always positive!
Therefore, |5 – p| = |5 – 9| = |-4| = 4.
2. A linepasses through (4, -1) and has a slope of -2. The y-intercept of the line is:
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Correct answer is option - 4
Explanation:
The slope-intercept form of a line is y = mx + b where ‘m’ is the slope and ‘b’ is the y –intercept.
Substitute the given point (x, y) = (4, -1) and the slope to solve for ‘b’.
-1 = -2(4) + b gives -1 = -8 + b.
Therefore, b = 8 – 1 = 7.
3. Two numbers ‘x’ and ‘y’ are added together. What is the correct expression for 5 less than thrice the sum of these numbers?
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Correct answer is option - 5
Explanation:
Since the numbers are first added, it is written as x + y.
Thrice the sum of the numbers gives 3(x + y).
5 less than the sum implies 3(x + y) – 5.
4. What is the least common multiple (LCM) of the numbers 8, 12, and 16?
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Correct answer is option - 5
Explanation:
Prime factorization of 8 = 2 * 2 * 2
Prime factorization of 12 = 2 * 2 * 3
Prime factorization of 16 = 2 * 2 * 2 * 2
Therefore LCM = 2 * 2 * 2 * 2 * 3 = 48.
5. In a particular sequence, the first term is 3, the second term is 7. From the third term onwards, if every term is the arithmetic mean of all the preceding terms, then what is the value of the 30th term of the sequence?
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Correct answer is option - 1
Explanation:
The third term = (3 + 7)/ 2 = 10/2 = 5.
Similarly the fourth term = (3 + 7 + 5)/ 3 = 15/3 = 5
Fifth term = (3 + 7 + 5 + 5)/ 4 = 20/4 = 5.
From the third every term will give ‘5’, hence the 30^{th} term is = 5.
6. If two similar triangles have thesimilarity ratio of the sides as 1: 3, then the ratio of the areas of the similar triangles is?
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Correct answer is option - 3
Explanation:
If two triangles are similar, then the ratio of their areas is square of the similarity ratio of the sides.
Therefore, the ratio of the areas of the similar triangles = 1^{2}: 3^{2} = 1: 9.
7. If (2x + 1) (5x – 3) = mx^{2} + nx + p, then what is the value of m + n – p?
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Correct answer is option - 4
Explanation: Multiplying the given expression we get: (2x + 1) (5x – 3) = 10x^{2} – 6x + 5x – 3
So 10x^{2} – x - 3 = mx^{2} + nx + p implies m = 10, n = -1 and p = -3.
Therefore, m + n – p = 10 + (-1) – (-3) = 9 + 3 = 12.