Let \(S=\left\{θ∈[0,2π]:8^{2sin^2θ}+8^{2cos^2θ}=16\right\}\) .Then\(n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)\)is equal to :
A zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is __________.
A steel wire of length 3.2 m (Ys = 2.0 × 1011 Nm-2) and a copper wire of length 4.4 m (Yc = 1.1 × 1011 Nm-2), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be:\((Given: π = \frac{22}{7})\)
A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)
Let p and p + 2 be prime numbers and let \(Δ=\begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \\ \end{vmatrix}\)Then the sum of the maximum values of α and β, such that pα and (p + 2)β divide Δ, is _______.
If \(f(x) = \begin{cases} x + a, & x \leq 0 \\ |x - 4|, & x > 0 \end{cases}\) and \(g(x) = \begin{cases} x + 1, & x < 0 \\ (x - 4)^2 + b, & x \geq 0 \end{cases}\) are continuous on R, then (gof) (2) + (fog) (–2) is equal to
If for p ≠ q ≠ 0, the function\(f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}\)is continuous at x = 0, then
Let f(x) = [2x2 + 1] and \(g(x)=\left\{\begin{matrix} 2x-3,\,x<0&\\2x+3, x≥0 &\end{matrix}\right.\)where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.
LetA =\(\begin{pmatrix} 4 & -2 \\ \alpha & \beta \\ \end{pmatrix}\)If A2 + γA + 18I = 0, then det (A) is equal to ______.
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