1. If the expression x^{2} + kx – 18 equals ‘0’, then what is the value of ‘k’ when x= 3?
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Correct answer is option - 4
Explanation: If x^{2} + kx – 18 = 0 and x = 3, then substitute ‘x’ value into the given equation.
9 + 3k – 18 = 0 gives 3k – 9 = 0.
This gives 3k = 9 ==> k = 3.
2. The simplified form of (8 + 4i) – (3 – 7i) is:
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Correct answer is option - 3
Explanation: When adding or subtracting complex numbers, we should always combine the real number terms together and the imaginary number terms together.
8 + 4i – 3 + 7i = (8 – 3) + 4i + 7i = 5 + 11i.
3. If a line passes through the origin and is parallel to the line 3x - 2y + 4 = 0, then which of the following gives the equation of the line?
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Correct answer is option - 2
Explanation: The given line can rearranged as 2y = 3x + 4 ==> y = (3/2)x + 2.
This is in the form of y = mx + b, where ‘m’ is the slope of the line and hence slope of the given line is 3/2.
If two lines are parallel, then their slopes are equal. Therefore, slope of the unknown line also as 3/2.
Equation of the line passing through (0, 0) with slope 3/2 is: y – 0 = 3/2(x – 0).
This gives 2y – 3x = 0.
4. The solution of ‘x’ when 10x – 13 ≥ 7 is?
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Correct answer is option - 1
Explanation: Solve the inequality for x by adding 13 on both sides.
10x ≥ 13 + 7 implies 10x ≥ 20.
Dividing 10 on both sides gives x ≥ 2.
5. In an arithmetic sequence, the first term is 3 and the 6^{th} term is 23. What is the 20^{th} term in the sequence?
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Correct answer is option - 5
Explanation: The nth term of an arithmetic sequence = a + (n – 1)d.
The first term, a = 3 and the 6^{th} term is 23.
This gives: 3 + (6 – 1)d = 23 ==> 3 + 5d = 23.
This implies: 5d = 20 ==> common difference, d = 4.
So the 20^{th} term = 3 + (20 – 1)4 = 3 + 76 = 79.
6. If (x + 4)^{2} = 9 and (y + 1)^{2} = 16, then the maximum value of x/y is:
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Correct answer is option - 4
Explanation: (x + 4)^{2 }= 9 implies x + 4 = √9 = ± 3. This gives x = -1 and x = -7.
Similarly, (y + 1)^{2} = 16 implies y + 1 = √16 = ± 4. This gives y = 3 and y = -5.
Therefore the maximum value of x/y is -7/-5 = 7/5.
7. The right angled triangle is shown in the diagram. The value of x is:
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Correct answer is option - 2
Explanation: To find the value of ‘x’, the trigonometric functions can be used.
tan(θ) = (opposite side)/ (adjacent side) where ‘θ’ is an angle.
Hence tan(60°) = 3√3 / x ==> x = (3√3)/ tan(60°).
This gives: x = 3.