Question : If $x=-1$, then the value of $\frac{1}{x^{99}}+\frac{1}{x^{98}}+\frac{1}{x^{97}}+\frac{1}{x^{96}}+\frac{1}{x^{95}}+\frac{1}{x^{94}}+\frac{1}{x}-1$ is:
Option 1: 1
Option 2: 0
Option 3: –2
Option 4: –1
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Correct Answer: –2
Solution : We have, $\frac{1}{x^{99}}+\frac{1}{x^{98}}+\frac{1}{x^{97}}+\frac{1}{x^{96}}+\frac{1}{x^{95}}+\frac{1}{x^{94}}+\frac{1}{x}-1$ Substituting value of $x=–1$ in the given expression, $=\frac{1}{(–1)^{99}}+\frac{1}{(–1)^{98}}+\frac{1}{(–1)^{97}}+\frac{1}{(–1)^{96}}+\frac{1}{(–1)^{95}}+\frac{1}{(–1)^{94}}+\frac{1}{(–1)}-1$ $=-1+1-1+1-1+1-1-1$ $=–2$ Hence, the correct answer is –2.
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Question : If $\frac{2 x+3}{18 \div 3 \times 4+2}=\frac{12 \times 3+5}{2 \times 4 \div 2}$, then what is the value of $x$?
Option 1: 132.25
Option 2: 131.75
Option 3: 134.35
Option 4: 120.5
Question : What is the value of $\frac{44–13+17–21+45–24}{12 \text { of } 4–3 \times 4–6 \times 2}$?
Option 2: 2
Question : If x : y = 3 : 4, then the value of $\frac{5x-2y}{7x+2y}$ is:
Option 1: $\frac{7}{25}$
Option 2: $\frac{7}{23}$
Option 3: $\frac{7}{29}$
Option 4: $\frac{7}{17}$
Question : The value of $\lambda$ for which the expression $x^3 + x^2 - 5x + \lambda$ will be divisible by $(x-2)$ is:
Option 1: 2
Option 2: – 2
Option 3: – 3
Option 4: 4
Question : What is the value of $\frac{49}{8} \times \frac{2}{3} \div \frac{98}{16} \times \frac{12}{4}$?
Option 1: 7
Option 3: 1
Option 4: 9
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