Series

Q. If the alphabet series is written in the reverse order, which letter will be fifth to the left of the fourteenth letter from the left?

1. I
2. S
3. R
4. V

Q.

$29,29,27,25,25,21,23,17,$__, __ complete the miscellaneous series.

A.$17,19$

B.$21,13$

C.$21,19$

D.$19,27$

Q.

Subtract :

$\frac{-7}{16}$from $\frac{3}{5}$

Q. Choose the odd numeral group.
(A) 1, 4, 3, 8
(B) 2, 3, 3, 8
(C) 3, 2, 3, 8
(D) 5, 3, 5, 2

Q. If $x+\frac{1}{x}=12$, then find the value of $(x^2+\frac{1}{x^2})$.

Q. Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50$ km/hr and $40$ km/hr respectively. By the time they meet the first train has travelled $100$ km more than second. The distance between $P$ and $Q$ is:

1. $660$ km
2. $900$ km
3. $500$ km
4. $630$ km

Q. On dividing a number by $56$, we get $29$ as remainder. On dividing the same number by $8$, what will be the remainder?

1. $4$
2. $3$
3. $5$
4. None of these

Q. Which number would replace the question mark in series
7, 12, 19, ?, 39

1. 24
2. 31
3. 28
4. 26

Q. The average monthly salary of the workers in a workshop is Rs 8500. if the average monthly salary of 7 technicians is Rs 10, 000 and the average monthly salary of the rest is Rs 7800, the total number of workers in the workshop is

1. 18
2. 20
3. 22
4. 24

Q.

1. 315/99 and 320/99

2. 310/99 and 315/99

3. 310/999 and 313/999

4. 315/999 and 320/999

Q. Solve the following -: $\sqrt{4\frac{1}{6}\times 3\frac{1}{3}\times 5}=$ ?

Q. Say True or False
If $a$=$3\sqrt{5}$ and $b$=$\sqrt{5}$ and $c=2\sqrt{5}$
then does it satisfy the following property $(a-b)-c=(b-c)-a$

1. True
2. False

Q. The value of $1.1!+2.2!+3.3!+..........+n.n!,$ is

1. $(n+1)!$
2. $(n+1)!+1$
3. $(n+1)!-1$
4. None of these

Q. For what value of $p$ does the equation $p{2}^x+2^{-x}=5$ possess a unique solution.

Q. The $n^{th}$ term of the series $4+14+30+52+80+114+.....$ is

1. 5n-1
2. $2n^2+2$
3. $3n^2+n$
4. $2n^2+2n$

Q. $\overrightarrow{r_1}=\hat{i}+\hat{j}+2\hat{k}+\lambda (3\hat{i}-2\hat{j}+4\hat{k})$
$\overrightarrow{r_2}=2\hat{i}+\hat{j}+3\hat{k}+\mu (-6\hat{i}+4\hat{j}-8\hat{k})$

Q. State, which of the following variables are continuous and which are discrete :

1. $0$
2. Can't determine
3. None of these
4. $1$

Q. A village has total population of 2500 people. Out of which 1300 people use brand A soap and 1050 people use brand B soap and 250 people use both brands. Find the percentage of population who use neither of these soaps.

Q. Find the output of the program given below
10 REM Average of ten numbers
20 READ $n_1,n_2,n_3,n_4$............$n_{10}$
30 DATA 2, 4, 14, 8, 22, 32, 44, 58, 74, 92
40 Let Average =
$(n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8+n_9+n_{10})/10$
50 PRINT "Average = "; Average
60 END

1. Average = 38
2. Average = 35
3. Average = 42
4. Average = 30

Q. If $a,b,c,d$ are the roots of the equation $x^4+2x^3+3x^2+4x+5=0$, then $1+a^2+b^2+c^2+d^2$ is equal to

1. $1$`
2. $-1$
3. $2$
4. $-2$

Q. $\frac{3+\sqrt{12}-\sqrt{27}}{7+\sqrt{192}-\sqrt{48}}=a+b\sqrt{3},$then find a and b.

Q. Fill in the blanks.
$(2^{-1}\times 3^{-1}{)}^2\times {\left(\frac{-3}{8}\right)}^{-1}$=________

Q. Find $n$ if ${}^{n-1}{P}_3{:}^n{P}_4=1:9$

Q. If $y=mx+c$; then find the value of $m$, when $y=7,x=5$ and $c=-3$.

Q. The first two terms of G.P. add upto $12$. The sum of $3^{rd}$ and $4^{th}$ term is $48$. If the terms of G.P. are alternating positive and negative then the first terms is

Q. The sum of first n terms of the series $1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+7^2+\cdots$ is $\frac{n{(n+1)}^2}{2}$ when $n$ is even, when $n$ is odd, the sum is

1. $\frac{n{(n+1)}^2}{2}$
2. $\frac{n^2(n+1)}{2}$
3. $\frac{n^2{(n+1)}^2}{4}$
4. $\frac{n^2{(n+1)}^2}{2}$

Q. Find the next terms in the series :

7, 1, 11, 5, 15, 9, __, __

1. 19, 13
2. 12, 18
3. 13, 19
4. 15, 12

Q. Differentiate $y=x^2+\frac{1}{x^2+\frac{1}{x^2+\frac{1}{x^2+......}}}$

1. $\frac{dy}{dx}=\frac{2xy}{2y-x^2}$
2. $\frac{dy}{dx}=\frac{y}{2y-x}$
3. None of these
4. $\frac{dy}{dx}=\frac{y^2}{2y-x}$

Q. Solve $\sqrt[3]{33}x=3^{\frac{1}{3}}$

Q. $121,117,108,92,67,?$

1. $41$
2. $29$
3. $37$
4. $31$