Two aliphatic aldehyde P and Q react in the presence of aqueous K2CO3 to give compound R, which upon treatment with HCN provides compound S. on acidification and heating , S gives the product shown below The compound S is
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The value of (((log)29)2)(log)2((log)29)1×(7)(log)471is ________.
Consider the circle x2+y2=9 and the parabola y2=8x. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.
A solution curve of the differential equation (x2+xy+4x+2y+4)(dxdy)−y2=0 passes through the point (1,3) Then the solution curve is
If g(x)=∫sinxsin(2x)sin−1(t)dt,then: (a)gprime(2π)=−2π (b) gprime(−2π)=−2π (c)gprime(−2π)=2π (d) gprime(2π)=2π
A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the parabola y2=16x 0≤y≤6 at the point art F(x0,y0). The tangent to the parabola at F(X0,Y0) intersects the y-axis at G(0,y). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum P) m= Q) = Maximum area of △EFG is (R) y0= (S) y1=
The area enclosed by the curvesy=sinx+cosxandy=∣cosx−sinx∣ over the interval [0,2π]
For a real number α, if the system ⎣⎡1αα2α1αα2α1⎦⎤⎣⎡xyz⎦⎤=⎣⎡1−11⎦⎤ of linear equations, has infinitely many solutions, then 1+α+α2=
The value of the integral ∫021((x+1)2(1−x)6)411+3dxis ______.