Sum of n Terms

Q.

${6_C}_2=\_\_$

Q.

If $S_1=a_2+a_4+a_6+...$ upto $100$ terms and $S_2=a_1+a_3+a_5+...$ upto $100$ terms of a certain A.P., then its common difference is

1. $S_1-S_2$

2. $S_2-S_1$

3. $\frac{\left(S_1-S_2\right)}{2}$

4. None of these

Q.

Liam deposits $\mathrm{\$}3,500$ in a saving account that pays $7\frac{1}{2}\mathrm{\%}$ interest, compounded quarterly.
$a$. Find the first quarter’s interest.
$b$. Find the first quarter’s ending balance.
$c$. Find the second quarter’s interest.
$d$. Find the second quarter’s ending balance.
$e$. Find the third quarter’s interest.
$f$. Find the third quarter’s ending balance.
$g$. Find the fourth quarter’s interest.
$h$. What is the balance at the end of one year?
$i$. How much interest does the account earn in the first year?

Q.

The ratio of sum of n terms of 2 AP's is (7n+1):(4n+27).

Find the ratio of their m^th term.

Q.

$\frac{5+9+13+.......upton.terms}{If7+9+11+.....upto(n+1)terms}=\frac{17}{16}$ then n is equal to

1. 7
2. 6
3. none of these
4. 9

Q. Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{...\text{to}\infty }}}}}$

1. $1$
2. $2$
3. $4$
4. $3$

Q.

$1+2^1+2^2+2^3.........{.2}^{1999}$ =

1. 

2. 

3. 

4. 

Q. One side of an equilateral triangle is 24 cm. The mid points of its sides are joined to form another triangle whose mid points are in term joined to form still another triangle. This process continues indefinitely. Find the sum of the perimetres (in cm) of all such triangles.

Q. ∆ABC is an isosceles triangle in which AB=AC. One angle is twice the other angles. Find ∠A and ∠B

1. ${90}^{o}and{45}^o$
2. ${60}^{o}and{30}^o$
3. ${45}^{o}and{30}^o$
4. ${30}^{o}and{60}^o$

Q. If $\sqrt{\frac{6+2\sqrt{3}}{33-19\sqrt{3}}}=a+b\sqrt{3},$ then $a+b=$

1. 6
2. 10
3. 8
4. 12

Q. What will be the unit digit of the squares of the following number ?
$55555$

Q.

A sequence $\log a$, $\log \frac{a^2}{b}$, $\log \frac{a^3}{b^2}$ is ...where $a\ne b$

1. $AP$

2. $GP$

3. $HP$

4. $noneofthese$

Q.

If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+...+10(11{)}^9=k(10{)}^9,$ then k is equals to:
(IIT JEE Main 2014)

1. $\frac{441}{100}$

2. $\frac{121}{10}$

3. 100

4. 110

Q. The value of $\sum _{r=1}^{n}log\left(\frac{a^r}{b^{r-1}}\right)$ is

1. 
2. 
3. 
4. 

Q. Given log₁₀ a = b, express 10^2b-3 in terms of a.

Q.

Mr. Richard has a recurring deposit account in a post office for $3$ years at $7.5\%\mathrm{p}.\mathrm{a}.$ simple interest. If he gets $\mathrm{Rs}8,325$ as interest at the time of maturity, find: (i) the monthly installment. (ii) the amount of maturity.

Q. If $\left|a\right|<1$ & $\left|b\right|<1$, then the sum of the series $1+\left(1+a\right)b+\left(1+a+a^2\right)b^2+\left(1+a+a^2+a^3\right)b^3+....$ is

1. $\frac{1}{(1-a)(1-b)}$
2. $\frac{1}{(1-b)(1-ab)}$
3. $\frac{1}{(1-a)(1-ab)}$
4. $\frac{1}{(1-a)(1-b)(1-ab)}$

Q. The expression $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equivalent to :

1. $4$
2. $8$
3. $\sqrt{2}$
4. $2$

Q. Out of the following, has the highest number of terms.

1. a monomial
2. a binomial
3. a trinomial

Q. Solve the following problems and verify the data in each case by drawing Venn diagrams. In a class, $50$ students offered Mathematics, $42$ offered Biology and $24$ offered both the subjects. Find the total number of students in the class.

Q. If $b=6-\left[\frac{4b+3}{2a-5}\right]$, express a in terms of b.

1. $a=\frac{33-b}{2(6-b)}$
2. $a=\frac{b-33}{2(6-b)}$
3. $a=\frac{33-b}{2(b-6)}$
4. none of the above

Q. Let $a_0=0$ and $a_n=3a_{n-1}+1$ for $n\ge 1$ then the remainder obtained on dividing $a_{2010}$ by11 is

1. $4$
2. $7$
3. $3$
4. $0$

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : $9^{\frac{3}{4}}.{\text{9}}^{\frac{1}{4}}$ equals 9.

A : $9^{\frac{3}{4}}.{\text{9}}^{\frac{1}{4}}$ का मान 9 के बराबर है।

R : If x > 0 be real number and p and q be rational numbers, then x^p·x^q = x^p+q.

R : यदि x > 0 वास्तविक संख्या है तथा p व q परिमेय संख्याएँ हैं, तब x^p·x^q = x^p+q

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q.

$\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+...nterms=?$

1. $\frac{6n^2}{(n+1)}$

2. $\frac{6n}{(n+1)}$

3. $\frac{6(2n-1)}{(n+1)}$

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

Q. If $1\le a\le 2$, then $\sqrt{a-2\sqrt{a-1}}-\sqrt{a+2\sqrt{a-1}}=$.......

1. $2\sqrt{a-1}$
2. $2$
3. $-2$
4. $1$

Q. Find the solution of $\log (x^3-3)=0$ and write the solutions in roster form of set.

Q. Find the value of $\sin 2x+\cos 2x$ if $0\le x\le \frac{\pi }{2}$, ${\sin }^{2}x=a$ and ${\cos }^{2}x=b$.

1. $2\sqrt{ab}+b-a$
2. $2ab+a^2-b^2$
3. $2\sqrt{ab}+2a-1$
4. $2ab+2a-1$
5. $2\sqrt{ab}-2b+1$

Q. If ${\log }_{10}8=0.90$, then the value of ${\log }_{10}0.125$ is

1. $0.9$
2. $1$
3. $0$
4. $-0.9$

Q. If the sum of the series 54, 51, 48, 45.......$T_n$ is 513, then the number of terms are

1. 17
2. 20
3. 18
4. None of these

Q. Find the sum of first 6 terms of an AP whose first term is 1 and sixth term is 6.

1. 18
2. 19
3. 21
4. 20