\[{\text{What is the distance between the points }}\left( {{\text{1,2}}} \right){\text{ and }}\left( {4,6} \right){\text{ under usual or Eucledian metric on }}{R^2}{\text{ ?}}\]

• A) 6
• B) 7
• C) 5
• D) 8

For the distance function \[d(x,y) = \sqrt {\left| {x - y} \right|} \] in R ,\[d(1,\frac{1}{2})\] =-----------.

• A) 1
• B) \[\frac{1}{{\sqrt 2 }}\]
• C) 2
• D) \[\sqrt 2 \]

Let \alpha be a permutation such that {\alpha ^7}\,\, = \,\,I , then order of \alpha is ------------

• A) 5
• B) 6
• C) 8
• D) 7

{\text{What is the distance between the points }}\left( {{\text{1,3}}} \right){\text{ and }}\left( {5,6} \right){\text{ under usual or Eucledian metric on }}{R^2}{\text{ ?}}

• A) 7
• B) 6
• C) 5
• D) 8

\[{\text{In }}{{\text{R}}^5}{\text{, the taxicab distance between points }}\left( {1,2,0,3,4} \right){\text{ and}}\left( {0,4,1,5,6} \right){\text{ is:}}\]

• A) 8
• B) 5
• C) 6
• D) 7

For the distance function d(x,z) = \left| {x - z} \right|in (R,d), d(x,z) \geqslant 0

• A) True
• B) False
• C)
• D)

\[{\text{For points }}\left( {{x_1},{y_1}} \right){\text{and }}\left( {{x_2},{y_2}} \right){\text{, the taxicab distance on }}{R^2}{\text{ is given by:}}\]

• A) \[\mid {x_1} - {x_2}\mid - \mid {y_1} - {y_2}\mid \]
• B) \[\mid {x_1} + {x_2}\mid - \mid {y_1} + {y_2}\mid \]
• C) \[\mid {x_1} + {x_2}\mid + \mid {y_1} + {y_2}\mid \]
• D) \[\mid {x_1} - {x_2}\mid + \mid {y_1} - {y_2}\mid \]

\forall x,y \in \mathbb{R},if\,\,\min \{ \left| x \right|,\left| y \right|\} = 0,then - - - .

• A) x=0 and y=0
• B) y=0
• C) x=0
• D) either x=0 or y=0

If \overrightarrow u = \left( \begin{array}{l} u_1 \\\\ u_2 \\\\ \end{array} \right) and \overrightarrow v = \left( \begin{array}{l} v_1 \\\\ v_2 \\\\ \end{array} \right) , then their dot product is given by;

• A) \sqrt {u_1 ^2 - u_2 ^2 } \sqrt {v_1 ^2 - v_2 ^2 }
• B) u_1 v_1 + u_2 v_2
• C) \sqrt {u_1 ^2 + u_2 ^2 } \sqrt {v_1 ^2 + v_2 ^2 }
• D) u_1 v_2 - u_2 v_1

If x_1 ,x_2 , \cdots ,x_n ,y_1 ,y_2 , \cdots ,y_n \in R , then which of the following is Minkoski’s inequality?

• A) \left( {x_1 y_1 + x_2 y_2 + \cdots + x_n y_n } \right)^2 \le \left( {x_1^2 + x_2^2 + \cdots + x_n^2 } \right)\left( {y_1^2 + y_2^2 + \cdots + y_n^2 } \right)
• B) \sqrt {\left( {x_1 + y_1 } \right)^2 + \left( {x_2 + y_2 } \right)^2 + \cdots + \left( {x_n + y_n } \right)^2 } \le \sqrt {x_1^2 + x_2^2 + \cdots + x_n^2 } \sqrt {y_1^2 + y_2^2 + \cdots + y_n^2 }
• C)
• D)

\forall {x_1},{x_2},{x_3} \in \mathbb{R},if\,\left| {{x_1}} \right| + \left| {{x_2}\,} \right| + \left| {{x_3}\,} \right| = 0,then - - - .

• A) {x_2} = 0
• B) {x_1} = {x_2} = {x_3} = 0
• C) {x_3} = 0
• D) {x_1} = 0

If f(x)=1 and g(x)=2 , then the distance as defined by d(f,g) = \int\limits_0^1 {\left| {f(x) - g(x)} \right|} dx = - - - - .

• A) -1
• B) 1
• C) 0
• D) 2

If\forall x \in \mathbb{R},\left| x \right| > - a, where a > 0, then ----.

• A) - \infty < x < \infty
• B) - \infty < x < a
• C) x < a\,\,\,{\text{and}}\,\,\,x > - a
• D) x < - a\,\,\,{\text{and}}\,\,\,x > a

l^1 :the set of all sequences whose corresponding series: -------- converges.

• A) \sum\limits_{i = 1}^\infty {\frac{1}{{x_i }}}
• B) \sum\limits_{i = 1}^\infty {x_i }
• C) \sum\limits_{i = 1}^\infty {\left| {x_i } \right|}
• D) \sum\limits_{i = 1}^\infty {\frac{1}{{\left| {x_i } \right|}}}

\max \{ {x_1} + {y_1},{x_2} + {y_2}\} - - - \max \{ {x_1} + {x_2}\} + \max \{ {y_1} + {y_2}\}

• A) =
• B) \leqslant
• C) \geqslant
• D) \ne

If{k_1},{k_2},...,{k_n} \geqslant 0 , thenmax\{ {k_i},1 \leqslant i \leqslant n,n \in N\} - - - 0.

• A) \ne
• B) =
• C) \leqslant
• D) \geqslant

If \forall x \in \mathbb{R}, \left| x \right| < - a,where a > 0, then ---.

• A) - a > x > a
• B) - a > x < a
• C) None of these
• D) - a < x < a

Dot product \overrightarrow u \cdot \overrightarrow v of two vectors \overrightarrow u and \overrightarrow v is given by----.

• A) \left| {\overrightarrow u } \right|\left| {\overrightarrow v } \right|\cos \theta
• B) \left| {\overrightarrow u } \right|\left| {\overrightarrow v } \right|\tan \theta
• C) \left| {\overrightarrow u } \right|\left| {\overrightarrow v } \right|\sin \theta
• D) \left| {\overrightarrow u } \right|\left| {\overrightarrow v } \right|\csc \theta

If\[{k_1},{k_2},...,{k_n} \geqslant 0\] , then\[max\{ {k_i},1 \leqslant i \leqslant n,n \in N\} - - - 0.\]

• A) \[ \leqslant \]
• B) =
• C) \[ \geqslant \]
• D) \[ \ne \]

If\forall x \in \mathbb{R},\left| x \right| < - a, where a < 0, then ----.

• A) - a < x < a
• B) - a > x > a
• C) a < x < - a
• D) - a > x < a