# Live Mtouch

1.

50%

16.67%

16.67%

16.67%

2. $\frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

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

$\frac{1}{7}=0.\overline{142857}$

$(\frac{1}{2})^2 \$

$\implies$

$\neq$

$\ a_1 + a_5 \$

$\overline{A}$

$c^20$

$18*\tfrac{\pi }{180^{\circ}}$

$\frac{Pl}{2}$

$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

n * βn)

$t\frac{\partial x}{\partial t} + x = t \text{ is }$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

$​A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

16.67%

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

33.33%

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with }
y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

This is test
nice

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with }
y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

This is test
nice

33.33%

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

16.67%

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

$​A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha$

3. testing

$frac{partialx}{partialt} + x = text{ is }$

$IF = e^{int Pdt} = e^{int frac{1}{t}dt} = e^{int e} = t$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

33.33%

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

16.67%

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

16.67%

$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

n * βn)

$t\frac{\partial x}{\partial t} + x = t \text{ is }$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

n * βn)

$t\frac{\partial x}{\partial t} + x = t \text{ is }$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

33.33%

hems testing

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

hems testing

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

0%

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

$\frac{1}{7}=0.\overline{142857}$

$(\frac{1}{2})^2 \$

$\implies$

$\neq$

$\ a_1 + a_5 \$

$\overline{A}$

$c^20$

$18*\tfrac{\pi }{180^{\circ}}$

$\frac{Pl}{2}$

$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

4.

Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
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Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
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Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
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16.67%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
16.67%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
16.67%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
16.67%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
33.33%

Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium

5. $frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$frac{1}{2}$

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

$x^2$

$frac{1}{2}$

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

$frac{1}{7}=0.overline{142857}$

$(frac{1}{2})^2$

$implies$

$neq$

$a_1 + a_5$

$overline{A}$

$c^20$

$18*tfrac{pi }{180^{circ}}$

$frac{Pl}{2}$

$frac{alpha ^{n}+beta ^{n}}{frac{1}{alpha ^{n}}+frac{1}{beta ^{n}}}$

n * βn)

$tfrac{partial x}{partial t} + x = t text{ is }$

$IF = e^{int Pdt} = e^{int frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{itfrac{pi }{2}})^{x}$

$A−left ( forall x p(x)Rightarrow forall x q(x) right )Rightarrow left ( exists x neg p(x) vee forall x q(x) right )$

$frac{1}{2pi j}oint_{C} f(z)dz$

$frac{partial^2y(t) }{partial t^2} + 2frac{partial y(t)}{partial t} + y(t) = delta (t) text{ with } y(t)|_{t=0^{-}} = -2 text{ and } frac{partial y}{partial t}mid _{t = 0^{-}} = 0$

$iint_{s} 5vec{r}cdot hat{n}dS text{ is}$

To write Augmented matrix:

${left[begin{array}{ccc|c}1 & 1 & 1 & 1 \a & -a & 3 & 5 \5 & -3 & a & 6 \end{array}right]}$

$begin{vmatrix}1& 1& 1& :& 6\1& 4& 6& :& 20\1& 4& lambda & :& mu \end{vmatrix}$

$=L^{−1}left ( begin{bmatrix}S& 0\S& 0end{bmatrix}−begin{bmatrix}0& 1\ −2& −3end{bmatrix} right )^{−1}$

$L^{−1}left ( begin{bmatrix}frac{s+3}{(s+1)(s+2)}& frac{1}{(s+1)(s+2)}\ frac{−2}{(s+1)(s+2)}& frac{s}{(s+1)(s+2)}end{bmatrix} right )$

$=left [ x^{4}+32x^{5} right ]^{1}_{0}=33$

$iiint bigtriangledowncdot Pdv$

$​A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0alpha$

1

1

25%

2

2

25%

3

3

25%

4

4

25%

Currently there is no PrepInsta Explanation.

6. UPDATED
$\int 12\sum_{1}^{5} \left ( 123 \right )$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

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

$\frac{1}{7}=0.\overline{142857}$

$(\frac{1}{2})^2 \$

$\implies$

$\neq$

$\ a_1 + a_5 \$

$\overline{A}$

$c^20$

$18*\tfrac{\pi }{180^{\circ}}$

$\frac{Pl}{2}$

$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

n * βn)

$t\frac{\partial x}{\partial t} + x = t \text{ is }$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

$​A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha$

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

40%

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

20%

$\int 12\sum_{1}^{5} \left ( 123 \right )$

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

$\int 12\sum_{1}^{5} \left ( 123 \right )$

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

40%

$\int 12\sum_{1}^{5} \left ( 123 \right )$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$

$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$

$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$

$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$

$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$

$\iiint \bigtriangledown\cdot Pdv$

$​A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha$

7.

20%

$\frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

$\frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

20%

$\frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

$\frac{1}{2}$

$Calculate (144^{-312}) ?$

$144^(-312)^1/6$

$\frac{1}{2} \$

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

$x^2$

$\frac{1}{2} \$

60%

$t\frac{\partial x}{\partial t} + x = t \text{ is }$

$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$

$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$

$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$

$\frac{1}{2\pi j}\oint_{C} f(z)dz$

$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$

$\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}$

8.

Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
40%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
20%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
20%
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium
20%

Infosys Aptitude Questions Topics No. of questions in test Suggested Avg. Time Difficulty Other
Data Interpretation 0 - 3 2 mins Medium Medium
Percentages 0 - 3 2 mins Medium Medium
Profit and Loss 0 - 3 2 mins Medium Medium
Probability 0 - 3 2 mins Medium Medium
Area, Shape and Parameter 0 - 3 2 mins Medium Medium

9. The solution to the recurrence equation   is: <latex>T(2^{k}) = 3 T(2^{k-1}) + 1, T (1) = 1</latex>

<latex>(3^{k+1} – 1)/2</latex>

<latex>(3^{k+1} – 1)/2</latex>

66.67%

2*T(n) =     2n + 4(n-1) + 8(n-2) + 16(n-3) + 2n

2*T(n) =     2n + 4(n-1) + 8(n-2) + 16(n-3) + 2n

33.33%

T (2k) = 3  T (2k-1) + 1

= 32  T (2k-2) + 1 + 3
= 33  T (2k-3) + 1 + 3 + 9
. . . (k steps of recursion (recursion depth))
= 3k  T (2k-k) + (1 + 3 + 9 + 27 + … + 3k-1)
= 3k + ( ( 3k – 1 ) / 2 )
= ( (2 * 3k) + 3k – 1 )/2
= ( (3 * 3k) – 1 ) / 2
= (3k+1 – 1) / 2

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