If $c$ denotes the contradiction then dual of the compounds statement $\backsim p\wedge (q\vee c)$ is

If $A=\left[\begin{array}{cc}2& 3\\ -3& 2\end{array}\right], B=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ then ${\left(B^{-1}{A}^{-1}\right)}^{-1}=$

If \(A=\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]\), adj \(A=\left[\begin{array}{ccc}5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y\end{array}\right]\), then value of \(\mathrm{x}+\mathrm{y}\) is

Let \(\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \quad\) and \(\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\), where \(\alpha, \beta \in \mathbb{R}\), be three vectors. If the projection at \(\overline{\mathrm{a}}\) on \(\overline{\mathrm{c}}\) is \(\frac{10}{3}\) and \(\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\), then the value of \(\alpha^2+\beta^2-\alpha \beta\) is equal to

If the equation \(\mathrm{k} x y+10 x+8 \mathrm{y}+16=0\) represents a pair of lines, then

The inverse of the statement
"If the surface area increase, then the pressure decreases.", is

Which of the following is NOT equivalent to $p\to q?$

Considering mode of asexual reproduction, match the Column I with II and select the correct option:

	Column I		Column II
i.	Yeast	a.	fragmentation
ii.	Penicillium	b.	zoospores
iii.	Filamentous algae	c.	budding
iv.	Chlamydomonas	d.	conidia

A metal sphere of radius \(R\), density \(\rho_1\) moves with terminal velocity \(V_1\) through a liquid of density \(\sigma\). Another sphere of same radius but density \(\rho_2\) - moves through same liquid. Its terminal velocity is \(\mathrm{V}_2\). The ratio \(\mathrm{V}_1: \mathrm{V}_2\) is

Derivative of $\log \left(\sec \theta +\tan \theta \right)$ with respect to $\sec \theta$ at $\theta =\frac{\pi }{4}$ is _______

A particle \(P\) starts from the point \(Z_0=1+2 i\) where \(i=\sqrt{-1}\). It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive \(y\)-axis by 3 units to reach a point \(Z_1\). From \(Z_1\) the particle moves \(\sqrt{2}\) units in the direction of vector \(\hat{i}+\hat{j}\) and then it moves through an angle \(\frac{\pi}{2}\) in anticlockwise direction on a circle with centre at origin to reach at point \(Z_2\), then \(Z_2=\)

Two circular loops \(\mathrm{P}\) and \(\mathrm{Q}\) are made from a uniform wire. The radii of \(P\) and \(Q\) are \(R_1\) and \(R_2\) respectively. The moments of inertia about their own axis are \(\mathrm{I}_{\mathrm{P}}\) and \(\mathrm{I}_{\mathrm{Q}}\) respectively. If \(\frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=\frac{1}{8}\) then \(\frac{\mathrm{R}_2}{\mathrm{R}_1}\) is

Graph shows the variation of de-Broglie wavelength \((\lambda)\) versus \(\frac{1}{\sqrt{V}}\) where ' \(V\) ' is the accelerating potential for four particles A, B, C, \(\mathrm{D}\) carrying same charge but of masses \(\mathrm{m}_1, \mathrm{~m}_2\), \(\mathrm{m}_3, \mathrm{~m}_4\). Which on represents a particle of largest mass?