Solved maths problems — page 27
1566 problems, newest first. Browse by chapter at NCERT solutions by class.
- Let A = cosθ & 0 & -sinθ 0 & 1 & 0 sinθ & 0 & cosθ. If for some θ (0,π), A² = A T, then the sum of the diagonal elements of the matrix (A + I)³ + (A - I)³ - 6A
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- Define the real valued function f: R-0 → R defined by f(x)=(1)/(x), x R-0. Complete the Table given below using this definition. What is the domain and range of
The completed table is: |l|c|c|c|c|c|c|c|c|c| x & -2 & -1.5 & -1 & -0.5 & 0.25 & 0.5 & 1 & 1.5 & 2 y=(1)/(x) & -0.5 & -0.67 & -1 & -2 & 4 & 2 & 1 & 0.67 & 0.5 T
- Find all the points of discontinuity of the function f defined by f(x)= rr x+2, & if x<1 0, & if x=1 x-2, & if x>1
The function f(x) is discontinuous at x=1.
- Find the distance between the parallel lines 3x + 4y - 7 = 0 and 3x + 4y + 23 = 0.
The distance between the parallel lines is 6 units.
- Find the radius of curvature for the curve y = e x at the point (0,1).
The radius of curvature for the curve y = e^x at the point (0,1) is 2 √2.
- Let ⌊·⌋ denote the greatest integer function. If ∫_0^e³ Bigl (1)/(e^(x-1)) Bigr dx = α - ln 2, then α³ is equal to:
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