Please be patient as the PDF generation may take upto a minute.

Which of the following fractions lie between $\frac{1}{5}$and$\frac{1}{4}$?
A. $\frac{7}{33}$
B. $\frac{4}{11}$
C. $\frac{13}{57}$
D. $\frac{7}{17}$
1. A and B
2. A and C
3. B, C and D
4. A, B and D

Express $0.\overline{34}$+$0.3\overline{4}$ as a single decimal.
1. $0.67\overline{88}$
2. $0.\overline{689}$
3. $0.68\overline{78}$
4. $0.\stackrel{\rightharpoonup }{687}$

If $\sqrt{5^n}$=125, then $5^{\sqrt[n]{64}}$=_______
1. 25
2. $\frac{1}{125}$
3. 625
4. $\frac{1}{25}$

If $x^4+1=1297$ and $y^4-1=2400$ then $y^2-x^2$=______
1. 10
2. 25
3. 13
4. 43

What is the value of $4^{2x-2}$, if ${\left(16\right)}^{2x+3}$=${\left(64\right)}^{x+3}$ ?
1. 64
2. 256
3. 32
4. 512

Which of the following pairs is having two equal values? (where x $\in$ R)________.
1. $9^{\mathrm{x}/2}, {24}^{\mathrm{x}/3}$
2. ${\left(256\right)}^{4/x}, {\left(4^3\right)}^{4/x}$
3. ${\left(343\right)}^{x/3}, {\left(7^4\right)}^{x/12}$
4. ${\left({36}^2\right)}^{2/7}, {\left(6^3\right)}^{2/7}$

The expression $\left(\sqrt{5}-\sqrt{3}\right) \left(\sqrt{7}-\sqrt{2}\right)$ when simplified becomes a 
1. simple surd
2. mixed surd
3. compound surd
4. binomial surd

If m and n are positive integers, then for a positive number a, ${\left\{\sqrt[m]{\left(\sqrt[n]{a}\right)}\right\}}^{mn}$ =_______
1. $a^{mn}$
2. a
3. $a^{m/n}$
4. 1

If $2^{-m}\times \frac{1}{2^m}=\frac{1}{4}$, then $\frac{1}{14}\left[{\left(4^m\right)}^{1/2}+{\left(\frac{1}{5^m}\right)}^{-1}\right]$=_______
1. $\frac{1}{2}$
2. 2
3. 4
4. $\frac{-1}{4}$

The surds $\sqrt{2}, \sqrt[3]{3}$ and $\sqrt[5]{5}$, in their descending order are
1. $\sqrt[3]{3}, \sqrt[5]{5}, \sqrt{2}$
2. $\sqrt{2}, \sqrt[3]{3}, \sqrt[5]{5}$
3. $\sqrt{2}, \sqrt[5]{5}, \sqrt[3]{3}$
4. $\sqrt[3]{3}, \sqrt{2}, \sqrt[5]{5}$

$2{\left[{\left(16-15\right)}^{-1}+25{\left(13-8\right)}^{-2}\right]}^{-1}+{\left(1024\right)}^0$=______
1. 2
2. 3
3. 1
4. 5

If x=2 and y=4, then ${\left(\frac{x}{y}\right)}^{x-y}+{\left(\frac{y}{x}\right)}^{y-x}$=_________
1. 4
2. 8
3. 12
4. 2

In which of the following pairs of surds are the given two surds similar?
1. $\sqrt{5}, 7\sqrt{5}$
2. $\sqrt[3]{7}, \sqrt[2]{7}$
3. $\sqrt{7}, \sqrt{28}$
4. Both 1 and 3

Which of the following is the greatest?
1. $7^2$
2. ${\left(49\right)}^{3/2}$
3. ${\left(\frac{1}{343}\right)}^{-1/3}$
4. ${\left(2401\right)}^{-1/4}$

$\left(\sqrt[6]{5}\right)\left(\sqrt[3]{2}\right)\left(\sqrt{3}\right)\left(\sqrt[12]{6}\right)$=___________
1. $\sqrt[12]{1749600}$
2. $\sqrt[3]{2}\times \sqrt[12]{109350}$
3. $\sqrt[12]{177960}$
4. Both 1 and 2

If p=3 and q=2, then ${\left(3p-4q\right)}^{q-p}÷{\left(4p-3q\right)}^{2q-p}$=________
1. 1
2. 6
3. $\frac{1}{6}$
4. $\frac{2}{3}$

$\left[\frac{{\left(32\right)}^{0.2}+{\left(81\right)}^{0.25}}{{\left(256\right)}^{0.5}-{\left(121\right)}^{0.5}}\right]$=_______
1. 2
2. 5
3. 1
4. 11

Which of the following surd is the smallest?
$\sqrt{10}-\sqrt{5}, \sqrt{19}-\sqrt{14}, \sqrt{22}-\sqrt{17}$ and $\sqrt{8}-\sqrt{3}$
1. $\sqrt{10}-\sqrt{5}$
2. $\sqrt{19}-\sqrt{14}$
3. $\sqrt{22}-\sqrt{17}$
4. $\sqrt{8}-\sqrt{3}$

If $\sqrt{m}=\sqrt{a}+\sqrt{c}$ and $\sqrt{m}$, $\sqrt{a}$ and $\sqrt{c}$ are three surds, then
1. $\sqrt{m}$ is dissimilar to $\sqrt{a}$ and $\sqrt{c}$
2. $\sqrt{a}$ and $\sqrt{c}$ are similar to $\sqrt{m}$
3. only $\sqrt{a}$ is similar to $\sqrt{m}$
4. None of these

The surd obtained after rationalizing the numerator of $\frac{4-\sqrt{25-a}}{a-9}$ is equal to
1. $\frac{a-9}{4-\sqrt{25-a}}$
2. $\frac{1}{4-\sqrt{25-a}}$
3. $\frac{1}{\left(a-9\right)\left(4+\sqrt{25-a}\right)}$
4. $\frac{1}{4+\sqrt{25-a}}$

If $\sqrt{13-x\sqrt{10}}=\sqrt{8}+\sqrt{5}$, then what is the value of x?
1. -5
2. -6
3. -4
4. -2

If the surds $\sqrt[4]{4}$, $\sqrt[6]{5}$, $\sqrt[8]{6}$ and $\sqrt[12]{8}$ are arranged in descending order from left to right, then the third surd from the left is 
1. $\sqrt[12]{8}$
2. $\sqrt[4]{4}$
3. $\sqrt[8]{6}$
4. $\sqrt[6]{5}$

$\sqrt{11\sqrt{11\sqrt{11.......4 terms}}} =$
1. $\sqrt[16]{{11}^5}$
2. $\sqrt[16]{11}$
3. $\sqrt[16]{{11}^{14}}$
4. $\sqrt[16]{{11}^{15}}$

If $\frac{5-\sqrt{3}}{2+\sqrt{3}}=x+y\sqrt{3}$, then (x, y) is
1. (13, -7)
2. (-13, 7)
3. (-13, -7)
4. (13, 7)

The simplified form of $\sqrt{125}+\sqrt{125}-\sqrt{845}$ is
1. $\sqrt{15}$
2. $2\sqrt{5}$
3. $-\sqrt{5}$
4. $-2\sqrt{5}$

Which of the following statements is true?
I. If x is a conjugate surd of y, then x can be a RF of y.
II. If x is a RF of y, then x need not be the conjugate of y.
1. Only I
2. Only II
3. Both I and II
4. Neither I nor II

If $\frac{3-2\sqrt{5}}{6-\sqrt{5}}=a+b\sqrt{5}$ hwere and a and b are rational numbers, then what are the values of a and b?
1. $\frac{8}{35}, \frac{-9}{35}$
2. $\frac{8}{31}, \frac{-9}{31}$
3. $\frac{-8}{31}, \frac{9}{31}$
4. $\frac{-8}{35}, \frac{9}{35}$

If $\frac{3^{5x}\times {\left(81\right)}^2\times 6561}{3^{2x}}=3^7$, then x=________
1. 3
2. -3
3. $\frac{1}{3}$
4. $\frac{-1}{3}$

If $\sqrt{2^n}=1024$, then $3^{\left(\frac{n}{4}-4\right)}$=________
1. 3
2. -3
3. 27
4. 81

If  ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-1/3}\right]}^{1/4}$ $=7^m$, then m =________
1. $\frac{-1}{3}$
2. $\frac{1}{4}$
3. -3
4. 2

${\left[{\left\{{\left(\frac{1}{x^{a^2-b^2}}\right)}^{\frac{1}{a-b}}\right\}}^{a+b}\right]}^{\frac{1}{{\left(a+b\right)}^2}}$=____________
1. $x^2$
2. $\frac{1}{x}$
3. $7^3$
4. $\frac{1}{x^2}$

If $\frac{2^{m+n}}{2^{m-n}}=16$ and $a=2^{\frac{1}{10}}$ then $\frac{{\left(a^{2m+n-p}\right)}^2}{{\left(a^{m-2n+2p}\right)}^{-1}}=$_____________
1. 2
2. $\frac{1}{4}$
3. 9
4. $\frac{1}{8}$
 

Simplify
$\left[\left(p^{-1}+q^{-1}\right)\left(p^{-1}-q^{-1}\right)÷\left(\frac{1}{p^{-1}}-\frac{1}{q^{-1}}\right)\left(\frac{1}{p^{-1}}+\frac{1}{q^{-1}}\right)\right]{\left(pq\right)}^2$
1. ${\left(pq\right)}^2$
2. -1
3. $-{\left(pq\right)}^{-2}$
4. 1

If x= $\frac{2}{\sqrt{10}-\sqrt{8}}, y=\frac{2}{\sqrt{10}+2\sqrt{2}}$, then ${\left(x-y\right)}^2$=
1. $4\sqrt{2}$
2. 32
3. $8\sqrt{2}$
4. 64

If $a=\sqrt{6}-\sqrt{3}, b=\sqrt{3}-\sqrt{2}$and $c=\sqrt{2}-\sqrt{6}$, then find the value of $a^3+b^3+c^3-2abc$.
1. $3\sqrt{2}-5\sqrt{3}-\sqrt{6}$
2. $3\sqrt{2}-5\sqrt{3}-\sqrt{6}$
3. $3\sqrt{2}-4\sqrt{3}+\sqrt{6}$
4. $3\sqrt{2}+4\sqrt{3}+\sqrt{6}$

$\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}}}}....\infty }$=
1. $\frac{81}{64}$
2. $\frac{9}{8}$
3. $\frac{3}{2}$
4. $\frac{3}{2\sqrt{2}}$

If $a^p=b^q=c^r=abc$, then pqr=_____
1. $p^{2}q+q^{2}r$
2. pq+qr+pr
3. ${\left(pq+qr+rp\right)}^2$
4. pq(qr+rp)

The value of ${\left[{\left(23+2^2\right)}^{2/3}+{\left(140-29\right)}^{1/2}\right]}^2$ is _______
1. 196
2. 289
3. 324
4. 400

If $x=\sqrt{6}+\sqrt{5}$, then $x^2+\frac{1}{x^2}-2=$
1. $2\sqrt{6}$
2. $2\sqrt{5}$
3. 24
4. 20

$\sqrt{6+\sqrt{6+\sqrt{6+.....\infty }}}$ is equal to______
1. -3
2. 3
3. 6
4. 2

Simplify
$\frac{1}{\sqrt{19-\sqrt{360}}}-\frac{1}{\sqrt{21-\sqrt{440}}}+\frac{2}{\sqrt{20+\sqrt{396}}}$=___________
1. 1
2. 2
3. 0
4. None of these 

If $a=\sqrt{17}-\sqrt{16}$ and b=$\sqrt{16}-\sqrt{15}$ then
1. a<b
2. a>b
3. a=b
4. None of these

$\left(\sqrt[6]{15-2\sqrt{56}}\right) . \left(\sqrt[3]{\sqrt{7}+2\sqrt{2}}\right)$=_________
1. 0
2. 1
3. -1
4. 2

$\sqrt{\sqrt{63}+\sqrt{56}}=$
1. $\sqrt[4]{7}\left(\sqrt{3}+\sqrt{5}\right)$
2. $\sqrt[4]{7}\left(\sqrt{3}+1\right)$
3. $\sqrt[4]{7}\left(\sqrt{3}+\sqrt{5}\right)$
4. $\sqrt[4]{7}\left(\sqrt{2}+1\right)$

If $\frac{\sqrt{7}+2\sqrt{3}}{2\sqrt{7}-\sqrt{5}}=\frac{c+\sqrt{p}+\sqrt{q}+\sqrt{r}}{23}$ (p<q<r), where p, q, r are rational numbers, then q+r-p=
1. 361
2. 302
3. 418
4. 426

The following are the steps involved in finding the value of x - y from  $\frac{8 - \sqrt{5}}{8 + \sqrt{5}}= x -y\sqrt{50}$ . Arrange them in sequential order.
(A) $\frac{13 - 2\sqrt{40}}{8 - 5} = x - y\sqrt{40}$
(B) $\frac{{\left(\sqrt{8}\right)}^2 + {\left(\sqrt{5}\right)}^2 - 2\left(\sqrt{8}\right)\left(\sqrt{5}\right)}{{\left(\sqrt{8}\right)}^2 - {\left(\sqrt{5}\right)}^2} = x -y\sqrt{40}$
(C) $x -y = \frac{11}{3}$
(D) $x = \frac{13}{3} and y = \frac{2}{3}$
(E) $\frac{(\sqrt{8 } - \sqrt{5})(\sqrt{8} - \sqrt{5})}{(\sqrt{8 } + \sqrt{5})(\sqrt{8} - \sqrt{5})} = x -y\sqrt{40}$
1. EABDC
2. EBADC
3. ABDEC
4. DEBAC

The following are the steps involved in finding the least among $\sqrt{3}, \sqrt[3]{4} and \sqrt[6]{15} .$ Arrange them in sequential order.
(A) $\therefore \sqrt[6]{15} \mathrm{is} \mathrm{the} \mathrm{smallest}$
(B) $\therefore 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} = 3^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} , 4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} = 4^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} , {15}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} = {15}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$
(C) The LCM of the denominators of the exponents is 6.
(D) $\sqrt{3} = 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} , \sqrt[3]{4} =4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} , \sqrt[6]{15} = {15}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$
(E) $\therefore \sqrt{3} = \sqrt[6]{27} , \sqrt[3]{4} = \sqrt[6]{16} , \sqrt[6]{15} = \sqrt[6]{15}$
1. DCABE
2. DABEB
3. DCBEA
4. DBCAE

If $y = 3- \sqrt{8}$ , then ${\left(y - \frac{1}{y}\right)}^2 = \_\_\_\_\_\_\_\_\_$
1. 9
2. 81
3. 4
4. 32

The following are the steps involved in finding the value of a + b from $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = a + b\sqrt{3}$ . Arrange them in sequential order.
(A) $\frac{2^2 + {\left(\sqrt{3}\right)}^2 + 2 x 2 x \sqrt{3}}{2^2 - {\left(\sqrt{3}\right)}^2} = a + b\sqrt{3}$
(B) a + b = 7 + 4 = 11
(C) $\frac{(2 + \sqrt{3})(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})} = a + b\sqrt{3}$
(D) $\frac{7 + 4\sqrt{3}}{4 - 3} = a + b\sqrt{3}$
(E) a = 7 and b = 4
1. CDAEB
2. CAEBD
3. CADEB
4. CEDAB

The following are the steps involved in finding the greatest among $\sqrt[3]{2} ,\sqrt[6]{3} and \sqrt{6}$. Arrange them in sequential order.
$$\begin{gathered} \left(A\right) The LCM of the denominators of the exponents is 6. \\ \left(B\right) \therefore \sqrt[6]{216} i.e., \sqrt{6} . is the greatest. \\ \left(C\right) \sqrt[3]{2} = 2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} , \sqrt[6]{3 }= 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} , \sqrt{6} = 6^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \\ \left(D\right) 2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} = 2^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} , 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} = 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} , 6^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} = 6^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$6$}\right.} \\ \left(E\right) \sqrt[3]{2} = \sqrt[6]{4}, \sqrt[6]{3} = \sqrt[6]{3} , \sqrt{6} = \sqrt[6]{216} \end{gathered}$$
1. CDAEB
2. CDABE
3. DCAEB
4. DACBE 

If $x = \frac{1}{\sqrt{3} + 2}$ , then ${\left(x + \frac{1}{x}\right)}^2 = \_\_\_\_\_\_\_\_\_\_\_\_ .$
1.  16
2.  3
3.  12
4.  6

If $\sqrt[x]{3} x \sqrt[y]{5} = 10125, then 12xy = \_\_\_\_\_\_\_\_\_\_$.
1.  1
2. $\frac{1}{3}$
3. 2
4. $\frac{1}{2}$

If $x = \frac{1}{5 + 2\sqrt{6}} , then x^2 - 10x + 1 = \_\_\_\_\_\_\_\_\_$
1.  1
2.  -1
3.  0 
4.  6

If $x = \frac{2}{\sqrt{3} - \sqrt{5}} and y = \frac{2}{\sqrt{3} + \sqrt{5}} , then x + y = \_\_\_\_\_\_\_\_\_\_$ . 
1.  3
2.  4$\sqrt{3}$
3.  -2$\sqrt{3}$
4.  6

$\frac{3}{7}$lies between the fraction _________ .
1.  $\frac{4}{9},\frac{5}{9}$
2.  $\frac{43}{99}, \frac{4}{9}$
3.  $\frac{42}{99}, \frac{4}{9}$
4.  $\frac{41}{99}, \frac{42}{99}$

If $\sum _{k = 4}^{143} \frac{1}{\sqrt{k} + \sqrt{k + 1} } = a - \sqrt{b},$ then a and b respectively are
1.  10 and 0
2.  -10 and 4
3.  10 and 4
4.  -10 and 0

The surd $\frac{12}{3 + \sqrt{5} + 2\sqrt{2}},$ after rationalizing the denominator becomes
1.  $\sqrt{5} - \sqrt{2} + \sqrt{10} + 1$
2.  $\sqrt{5} + \sqrt{10} + \sqrt{2} + 1$
3. $\sqrt{10} + \sqrt{2} +\sqrt{5} + 1$
4.  $\sqrt{5} - \sqrt{10} - \sqrt{2} - 1$

If $A^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$A$}\right.} = B^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$B$}\right.} = C^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$C$}\right.} , A^{BC} + B^{AC} + C^{AB} = 729.$ Which of the following equals $A^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}$ ?
1.  $\sqrt[ABC]{81}$
2.  $\sqrt{2}$
3.  $\sqrt[ABC]{27}$
4. $\sqrt[ABC]{9}$

If $x = \frac{1}{2 - \sqrt{3}} ,$ then the value of $x^2 - 2x^2 - 7x + 10$ is equal to 
1.  $2 + \sqrt{3}$
2.  $10$
3.  $7 + 2\sqrt{3}$
4.  8

If x = $1 + 5^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} + 5^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} ,$then find the value of $x^3 - 3x^2 - 12x + 6.$
1.  22
2.  20
3.  16
4.  14

$\frac{4}{ \sqrt{10 - 2\sqrt{21}}} = \_\_\_\_\_\_\_\_ .$
1.   $\frac{1}{4}\left(\sqrt{7} + \sqrt{3}\right)$
2.  $\frac{1}{4}\left(\sqrt{7} - \sqrt{3}\right)$
3.  $\sqrt{7} + \sqrt{3}$
4.  $\sqrt{7} - \sqrt{3}$

If $y = 3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right. } + 3 , then y^3 - 9y^2 + 27y = \_\_\_\_\_\_\_\_ .$
1.  27
2.  -27
3.  -30
4.  30

$\frac{1}{\sqrt{8 + 2 + \sqrt{15}}} = \_\_\_\_\_\_\_\_\_ .$
1.  $\frac{1}{2}\left(\sqrt{5} + \sqrt{3}\right)$
2.  $\frac{1}{2 }\left(\sqrt{5} - \sqrt{3}\right)$
3.  $\frac{1}{2}\left(\sqrt{5} + 1\right)$
4.  $\frac{1}{2}\left(\sqrt{5} - 1\right)$

If $x = 2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} - 2 , then x^3 + 6x^2 + 12x = \_\_\_\_\_\_\_\_ .$
1.  6
2.  -6
3.  8
4.  -8

$\frac{3}{\sqrt{19 - 2\sqrt{88}}} - \frac{8}{\sqrt{14 + 2\sqrt{33}}} = \_\_\_\_\_\_\_\_\_\_.$
$$
1.  $\sqrt{19 + 2\sqrt{33}}$
2.  $\sqrt{14 - 2\sqrt{88}}$
3.  $\sqrt{11 +2 \sqrt{24}}$
4.  $\sqrt{11 -2\sqrt{55}}$

$\sqrt{\sqrt[x]{2^x\sqrt[x^2]{3^{x^3}\sqrt[x^3]{6^{x^6}\sqrt[x^4]{9^{x^{10}}}}}}} =$
1.  18
2.  54
3.  24 
4.  36

$\sqrt{7 + 2\sqrt{6}} + \sqrt{7 - 2\sqrt{6}} = \_\_\_\_\_\_\_\_\_ .$
1.  14
2.  $\sqrt{6}$
3.  $2\sqrt{6}$
4.  7

$\sqrt{3^2\sqrt{9^2 \sqrt{{\left(81\right)}^2 \sqrt{{16}^{16}}}}} = \_\_\_\_\_\_\_\_\_\_\_ .$
$$
1.  $6 x 2^4$
2.  $3^{ 3} x 2$
3.  $6^3 x 2^3$
4.  $6^3 x 2$

$\sqrt[6]{15 - 2\sqrt{56}} \sqrt[3]{\sqrt{7} + 2\sqrt{2}} =$
1.  0
2.  $\sqrt{2}$
3.  1
4.  $\sqrt[6]{2}$

If p = $7 - 4\sqrt{3 } , then \frac{p^2 + 1}{7_p} = \_\_\_\_\_\_\_\_\_ .$
1.  2
2.  1
3.  7
4.  $\sqrt{3}$