Question : What is the sum of all the common terms between the given series $S1$ and $S2$? $\begin{aligned} & S 1=2,9,16, \ldots \ldots, 632 \\ & S 2=7,11,15, \ldots \ldots, 743\end{aligned}$
Option 1: 6974
Option 2: 6750
Option 3: 7140
Option 4: 6860
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Correct Answer: 6974
Solution : Given: The series is $\begin{aligned} & S 1=2,9,16, \ldots \ldots, 632 \\ & S 2=7,11,15, \ldots \ldots, 743\end{aligned}$. From series $S1$ and $S2$, first common term = 23, second common term = 51. ⇒ $d=51–23=28$ Use the formulas, $a_n=a+(n–1)d$, $S_n=\frac{n}{2}[2a+(n–1)d]$, where $a_n$, $n$, $a$, $d$, and $S_n$ are the $n$th term in the sequence, the number of terms, the first term in the sequence, the common difference, and the sum. ⇒ $a_n=a+(n–1)d\leq 632$ ⇒ $23+(n–1)28\leq 632$ ⇒ $(n–1)28\leq 632–23$ ⇒ $(n–1)28\leq 609$ ⇒ $n–1\leq 21.75$ ⇒ $n\leq 22.75$ So, the value of $n=22$. The sum of all the common terms between the given series S1 and S2 = $\frac{22}{2}[2\times 23+(22–1)\times28]$. = $11\times [46+21\times28]$ = $11\times [46+588]$ = $11\times 634$ = $6974$ Hence, the correct answer is 6974.
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Question : What is the sum of the first 20 terms of the following series? $1 \times 2+2 \times 3+3 \times 4+4 \times 5+\ldots \ldots$
Option 1: 3160
Option 2: 2940
Option 3: 3240
Option 4: 3080
Question : Study the given chart and answer the question that follows. The chart shows the quantities of machines (M1, M2, M3) available in different stores (S1, S2, S3, S4).
Which stores have more number of M2 machines than the average number of M2 machines per store?
Option 1: S2 and S4
Option 2: S1 and S3
Option 3: S2 and S3
Option 4: S1 and S4
Question : For the four-sentence (S1 to S4 ) paragraph below, sentences S1 and S4 are given. From the options P, Q,R and S select the appropriate sentences for S2 and S3, respectively. (S1) The men and women took their places after the initial mingling, and immediately a surge of conversation filled the room. (S2) (S3) (S4) One or two of the women were actually bouncing up and down on the sofa cushions. (P) So, the two parties had to lean forward, their elbows on their knees. (Q) At the beginning they mingled awkwardly, clutching their drinks, and walking here and there. (R) Several people made a last-minute dash to the bathroom before the conversation could start. (S) The men's chairs were far enough away from the women's couches.
Option 1: P, R
Option 2: R, Q
Option 3: Q, S
Option 4: S, P
Question : Sparying of DDT on crops causes pollution of_________
Option 1: Air & Soil
Option 2: Crops & Air
Option 3: Soil & Water
Option 4: Air & Water
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the & signs, and to balance the given equation. [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10
Option 1: ×, ÷, ×, ×, −, +, =
Option 2: ×, −, +, ×, ÷, ×, =
Option 3: −, +, ×, ×, ÷, ×, =
Option 4: −, +, ×, ÷, ×, ×, =
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