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The area bounded by the curve $y=\cos x$ between $x=0$ and $x=\frac{3 \pi}{2}$ is _________ sq. unit.
Find the equation of the line joining $\mathrm{A}(1,3)$ and $\mathrm{B}(0,0)$ using determinants and find $\mathrm{k}$ if $\mathrm{D}(\mathrm{k}, 0)$ is a point such that area of triangle $\mathrm{ABD}$ is $3 \,\mathrm{sq}$ $\mathrm{units}$.
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is,
  1. $\frac{64}{64}$
  2. $\frac{49}{64}$
  3. $\frac{40}{64}$
  4. $\frac{24}{64}$
The number of continuous functions $f:[0,1] \rightarrow(-\infty, \infty)$ satisfying the condition $\int \limits_0^1(f(x))^2 dx =2 \int_0^1 f( x ) dx$ is
Differential coefficient of ${\sin ^{ - 1}}{{1 - x} \over {1 + x}} \,\,,w.r.t$ $\sqrt x $ is
Let $f(x) = \left\{ {\begin{array}{*{20}{c}}
{\,{x^3} - {x^2} + 10x - 5\,\,,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\,\,\,\,\,}\\
{ - 2x + {{\log }_2}({b^2} - 2),\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, > 1\,\,\,\,\,\,\,\,\,\,\,\,}
\end{array}} \right.$ the set of values of $b$ for which $f(x)$ has greatest value at $x = 1$ is given by 
Which of the following equation is non-linear
Consider the system of linear equations ${a_1}x + {b_1}y + {c_1}z + {d_1} = 0$, ${a_2}x + {b_2}y + {c_2}z + {d_2} = 0$ and ${a_3}x + {b_3}y + {c_3}z + {d_3} = 0$. Let us denote by $\Delta (a,b,c)$ the determinant $\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ if $\Delta (a,b,c) \ne 0$, then the value of $x$ in the unique solution of the above equations is
 The solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\frac{2\text{y}}{\text{x}}=0$ with y(1) = 1 is given by.
  1. $\text{y}=\frac{1}{\text{x}^{2}}$
  2. $\text{x}=\frac{1}{\text{y}^{2}}$
  3. $\text{x}=\frac{1}{\text{y}}$
  4. $\text{y}=\frac{1}{\text{x}}$ 
For any $2 \times 2$ matrix $ A$, if $A(adj.\,\,A)$= $\left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$, then $|A|\, = $