Question : The 3rd and 8th terms of an Arithmetic progression are –14 and 1, respectively. What is the 11th term?
Option 1: 14
Option 2: 16
Option 3: 20
Option 4: 10
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Correct Answer: 10
Solution : Given: The 3rd and 8th terms of an Arithmetic progression are –14 and 1. Formula for $n^{th}$ term ⇒ $a +(n-1)d$, where $a$ = 1st term, $d$ = common difference and $n$ = number of terms $3^{rd}$ term ⇒ $a +(3-1)d=–14$ ⇒ $a + 2d = – 14$ ---------------------------------(1) $8^{th}$ term ⇒ $a +(8-1)d=1$ ⇒ $a + 7d = 1$ ------------------------------------(2) Subtracting equation (1) from (2), we get, $⇒5d=15$ $\therefore d=3$ Putting this value in equation (1), we get, $a+2×3=-14$ $\therefore a=-20$ So, $11^{th}$ term = $-20 +(11-1)3=10$ Hence, the correct answer is 10.
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Question : If 7 times the 7th term of an arithmetic progression (A.P.) is equal to 11 times its 11th term, then the 18th term of the A.P. will be:
Option 1: 1
Option 2: 0
Option 3: 2
Option 4: –1
Question : The train ticket fare from places A to B in 2nd class AC and 3rd class AC is Rs. 2,500 and Rs. 2,000, respectively. If the fares of 2nd class AC and 3rd class AC are increased by 20% and 10%, respectively, then find the ratio of the new fares of 2nd class AC and 3rd class AC.
Option 1: 15 : 11
Option 2: 12 : 11
Option 3: 13 : 11
Option 4: 15 : 13
Question : What is the simplified form of the expression (1 + x) (1 + x2) (1 + x4) (1 + x8) (1 - x)?
Option 1: 1 – x40
Option 2: 1 – x32
Option 3: 1 – x16
Option 4: 1 – x42
Question : If a3 + b3 = 152 and a + b = 8, then what is the value of ab?
Option 1: 2
Option 2: 11
Option 3: –10
Option 4: 15
Question : Directions: By interchanging the given two signs which of the following equations will be not correct? – and ×
Option 1: 20 × 12 + 6 – 16 ÷ 8 = 20
Option 2: 16 × 91 ÷ 13 + 5 – 3 = 24
Option 3: 20 × 8 – 4 ÷ 2 + 3 = 7
Option 4: 4 × 5 – 36 ÷ 6 + 10 = 10
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