Sequence

Q. The local bus service has $2$ lines of buses that start together at $8\text{a.m.}$ Buses on line A leave after every $20$ minutes while Buses on line B leave after every $15$ minutes. In a day, how many times do buses on both line A and B leave together between $7\text{a.m.}$ and $10\text{p.m.}$?​

1. $13$
2. $14$
3. $15$
4. $16$

Q.

The sum of (n+1) terms of $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+..........$ is

1. 

2. 

3. 

4. 

Q. If $a=\sqrt{2}+1$, then find the value of $a-\frac{1}{a}$.

Q. How many congruent pairs of triangles are present in the given square?

1. 8
2. 10
3. 6
4. 4

Q.

By grouping the terms in xyz - xy - z + 1, we get

1. (xy - z)(xy - 1)

2. (z - 1) (xy + 1)

3. (z - 1) (xy - 1)

4. (z + 1) (xy - 1)

Q. $x^2+4y^2+z^2+4xy-2xz-4yz$ = $(x+2y-z{)}^2$

1. False
2. True

Q. Prove that:

(i) $\sqrt{3\times 5^{-3}}÷\sqrt[3]{3^{-1}}\sqrt{5}\times \sqrt[6]{3\times 5^6}=\frac{3}{5}$

(ii) $9^{3/2}-3\times 5^0-{{\left(\frac{1}{81}\right)}^{-}}^{1/2}=15$

(iii) ${\left(\frac{1}{4}\right)}^{-2}-3\times 8^{2/3}\times 4^0+{\left(\frac{9}{16}\right)}^{-1/2}=\frac{16}{3}$

(iv) $\frac{2^{1/2}\times 3^{1/3}\times 4^{1/4}}{{10}^{-1/5}\times 5^{3/5}}÷\frac{3^{4/3}\times 5^{-7/5}}{4^{-3/5}\times 6}=10$

(v) $\sqrt{\frac{1}{4}+(0.01{)}^{-1/2}}-(27{)}^{2/3}=\frac{3}{2}$

(vi) $\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{3}{2}$

(vii) ${\left(\frac{64}{125}\right)}^{-2/3}+\frac{1}{{\left({\displaystyle \frac{256}{625}}\right)}^{1/4}}+\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)=\frac{65}{16}$

(viii) $\frac{3^{-3}\times 6^2\times \sqrt{98}}{5^2\times \sqrt[3]{1/25}\times \left(15\right){-}^{4/3}\times 3^{1/3}}=28\sqrt{2}$

(ix) $\frac{(0.6{)}^0-(0.1)-1}{{\left({\displaystyle \frac{3}{8}}\right)}^{-1}{\left({\displaystyle \frac{3}{2}}\right)}^3+{\left(-{\displaystyle \frac{1}{3}}\right)}^{-1}}=-\frac{3}{2}$

Q.

By grouping the terms in x³ - x² - xy + x + y - 1, we get

1. (x + 1) (x² - y + 1)

2. (x - 1) (x² + y + 1)

3. (x - 1) (x² - y + 1)

4. (y - 1) (x² - y² - 1)

Q.

The expanded form of an expression is $x^2+y^2+z^2+2xy+2yz+2zx$. Which of the following is the expression?

1. ${(x+y+z)}^2$

2. ${(-x+y+z)}^2$

3. ${(x+y-z)}^2$

4. ${(x-y-z)}^2$

Q.

By grouping the terms in a³ + 7a² + ba + 7b - a - 7, we get

1. (a - 7) (a² + b² - 1)

2. (a + 7) (a² + b + 1)

3. (a + 7) (a² + b - 1)

4. (a + 7) (a² - b + 1)

Q. If x³ + 4y³ + 9z³ = 18xyz and x + 2y + 3z = 0 ; evaluate
$\frac{(x+2y{)}^2}{xy}+\frac{(2y+3z{)}^2}{yz}+\frac{(3z+x{)}^2}{zx}$

Q. If $x+\sqrt{15}=4,$then $x+\frac{1}{x}$=

(a) 2
(b) 4
(c) 8
(d) 1

Q. In the given figure, what is the angle subtended by chord AB at the point C on the circle?

1. ${60}^{\circ }$
2. ${65}^{\circ }$
3. ${55}^{\circ }$
4. ${70}^{\circ }$

Q. Raju is married to Sita, who is mother of Piyush. Kajal is daughter of Piyush, who is married to Swati. Pradeep is father of Satyendra, who is the only son. Satyendra is only brother of Swati. How is Piyush related to Pradeep?

1. Son
2. Cannot be determined
3. Uncle
4. Son-in-law

Q. $0.\overline{7}+0.4\overline{7}$=

Q. AAA

1. AA
2. AA
3. AA

Q. If }\sqrt{13-x\sqrt{10}}=\sqrt8+\sqrt5 , then the value of }x

Q. $1+2+3+4+5+\cdots +27=$ ?

1. 378
2. 380
3. 376
4. 372

Q. The n th term of an A.P is 6n+2.Find the common difference

Q.

Factories

1. x³-3x²+3x+7

Q. Which term of the sequence (-8 + 18i), (-6 + 15i), (-4 + 12i), ....is purely imaginary

1. 8^th

2. 6^th
3. 5^th

4. 7^th

Q. The least number divisible by all numbers from 1 to 10(inclusive 1 and 10) is

Q. If x = $\sqrt{5}+2$, then $x-\frac{1}{x}$ equals

(a) $2\sqrt{5}$

(b) 4

(c) 2

(d) $\sqrt{5}$

Q. If m and n are prime numbers, which of the following cannot be the difference between m and n A. 5 B. 7 C. 8 D. 9 E. 11

Q.

By grouping the terms in x⁴ - 2x³ - 6x + 12, we get

1. (x + 2) (x³ - 2)

2. (x - 2)(x³ - 6)

3. (x - 2) (x³ + 6)

4. (x + 2) (x³ - 6)

Q. The digits of a positive integer , having three digits are in AP and sum of the digits is 15. The number obtained by reversing the digits is 594 less than the original number. find the number.

Q.

Find p( 0 ) , p( 1 ) and p( 2 ) of the following polynomials: p ( t ) = t ³ + 5 t² - 3 t - 2

1. 2 , -1 , -20

2. -2, 1, 20

3. 2 , 1 , 20

4. - 2 , 1 , -20

Q. The decimal expansion of the rational number $\frac{14587}{1250}$ is terminating after ___ .

1. five decimal places
2. four decimal places
3. three decimal places
4. two decimal places

Q. p^th term of the series $(3-\frac{1}{n})+(3-\frac{2}{n})+(3-\frac{3}{n})+....$ will be

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

Q. Write the value of ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3.$