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Previous Year Question Papers

The dimensional formula for electric field intensity is :
A $\left[\mathrm{MLT}^{-3} \mathrm{~A}^{-1}\right]$
B $\left[\mathrm{MLT}^{-1} \mathrm{~A}^{-3}\right]$
C $\left[\mathrm{MLT}^{3} \mathrm{~A}^{-1}\right]$
D $\left[\mathrm{MLT}^{-3} \mathrm{~A}^{1}\right]$

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Correct option is A $\left[\mathrm{MLT}^{-3} \mathrm{~A}^{-1}\right]$ The unit of electric field intensity is newton per coulomb i.e. N/C. Newton is the unit of force and has dimensions...

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The correct expression for Lorentz force is
A $\quad \mathrm{q}[\overrightarrow{\mathrm{E}}+(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{V}})]$
B $\quad \mathrm{q}[\overrightarrow{\mathrm{E}}+(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})]$
(C) $\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$
D $\mathrm{q} \overrightarrow{\mathrm{E}}$

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Correct option is (B) $\mathrm{q}[\overrightarrow{\mathrm{E}}+(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})]$ In electromagnetic field both electric and magnetic forces are...

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Answer in brief: The optical path ray of light of a given wavelength travelling a distance of $3 \mathrm{~cm}$ in flint glass having refractive index $1.6$ is same as that on travelling a distance $\mathrm{x} \mathrm{cm}$ through a medium having refractive index $1.25 .$ Determine the value of $x .$

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Given: The distance travelled by wavelength in flint glass is $3 \mathrm{~cm}$ The refractive index of Flint glass is $1.6$ The refractive index of another medium is $1.25$ $$...

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Which of the following homologous series has incorrect general formula?
A Alkyne $\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}$
B Alkanol $\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}+2} \mathrm{O}$
C Alkanal $\mathrm{C}_{\mathrm{m}} \mathrm{H}_{2 \mathrm{n}+1} \mathrm{O}$
D Carboxylic acid $\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{~m}} \mathrm{O}_{2}$

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Correct option is (C) Alkanal $\mathrm{C}_{\mathrm{u}} \mathrm{H}_{2}+1 \mathrm{O}$ General formula of Alkanal, $\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}} \mathrm{O}$ Therefore, option...

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Solve the following linear programming problem graphically: Maximise $\mathrm{Z}=4 \mathrm{x}+\mathrm{y} \ldots(1)$ subject to the constraints: $\mathrm{x}+\mathrm{y} \leq 50 \ldots(2)$ $$ \begin{array}{l} 3 \mathrm{x}+\mathrm{y} \leq 90 \ldots(3) \\ \mathrm{x} \geq 0, \mathrm{y} \geq 0 \ldots(4) \end{array} $$

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The shaded region in fig. is the feasible region determined by the system of constraints (2) to (4). We observe that the feasible region $\mathrm{OABC}$ is bounded. So,we now use Corner Point Method...

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Evaluate

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$$ \begin{array}{l} \int \frac{2 x^{3}-1}{x^{4}+x} d x \\ \Rightarrow \int \frac{\left(4 x^{3}+1\right)-\left(2 x^{3}+2\right)}{x^{4}+x} d x \\ \Rightarrow \int \frac{4 x^{3}+1}{x^{4}+x} d x-2 \int...

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Find the minimum value of $\mathrm{Z}=3 \mathrm{x}+5 \mathrm{y}$, subject to the constraints $-2 \mathrm{x}+\mathrm{y} \leq$ $4, \mathrm{x}+\mathrm{y} \geq 3, \mathrm{x}-2 \mathrm{y} \leq 2, \mathrm{x} \geq 0$ and $\mathrm{y} \geq 0$ $Z=3 x+5 y$, subject to the constraints $-2 x+y \leq 4, x+y \geq 3, x-2 y \leq 2, x \geq 0$ and $y \geq 0$

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$Z=3 x+5 y$, subject to the constraints $-2 x+y \leq 4, x+y \geq 3, x-2 y \leq 2, x \geq 0$ and $y \geq 0$ Draw the line $-2 x+y=4, x+y=3$ and $x-2 y=2$ and shaded region which is satisfied by above...

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If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P, then the determinant $\left|\begin{array}{lll}\mathrm{x}+2 & \mathrm{x}+3 & \mathrm{x}+2 \mathrm{a} \\ \mathrm{x}+3 & \mathrm{x}+4 & \mathrm{x}+2 \mathrm{~b} \\ \mathrm{x}+4 & \mathrm{x}+5 & \mathrm{x}+2 \mathrm{c}\end{array}\right|$ is
A 0
B 1
C $\mathrm{x}$
D $2 \mathrm{x}$

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Correct option is (A)0 Given $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. $$ \Rightarrow 2 \mathrm{~b}=\mathrm{a}+\mathrm{c} $$ $$ \left|\begin{array}{lll} \mathrm{x}+2 & \mathrm{x}+3 &...

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