Solved maths problems — page 26
1518 problems, newest first. Browse by chapter at NCERT solutions by class.
- Consider the hyperbola (x²)/(a²) - (y²)/(b²) = 1 having one of its foci at P = (-3, 0). If the latus rectum through its other focus subtends a right angle at P
α = 810, β = 1134
- 38. A racing track is build around an elliptical ground whose equation is given by 9x² + 16y² = 144. The width of the track is 3 m as shown below: Based on give
(i) y = ±(3)/(4)√(16 - x²) (ii) (3)/(4)[(x)/(2)√(16 - x²) + 8sin^(-1)((x)/(4))] + C (iii) (a) The area of the region enclosed within the elliptical ground exclu
- OPQ में, जिसका कोण P समकोण है, OP = 7 cm और OQ - PQ = 1 cm, sin Q और cos Q के मान ज्ञात कीजिए।
sin Q = (7)/(25) और cos Q = (24)/(25)
- Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be i + 2 j + k, i + 3 j - 2 k and 2 i + j - k respectively. The altitude from the vert
The position vector of E is (13)/(9) i + 2 j - (11)/(9) k.
- Show that f: N → N, given by f(x)= & x+1, if x is odd, & x-1, if x is even is both one-one and onto. The image of 1 and -1 under f is 1. Fig 1.4 Solution Suppos
The function f: N → N given by f(x)= x+1, & if x is odd x-1, & if x is even is both one-one and onto.
- Find the distance between the points (3, 4) and (-3, -4).
The distance between the points (3, 4) and (-3, -4) is 10 units.
- If ∫_-(π)/(2)^((π)/(2)) (25 x² cos² x)/(2(x + e)²) dx = π (α π² + β), α, β Z, then (α + β)² equals
The problem statement appears to be incorrect or have a typo, as the integral does not simplify to the given form using standard techniques.
- Find the equation of the circle with centre (-3,2) and radius 4.
(x+3)² + (y-2)² = 16
- Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
The value of x is 4.
- If Σ_r=1^(30) r³ (^(30)C_r)²^(30)C_r-1 = α × 2^(29), then α is equal to:
α = 13080
- Let a sample space be S= _1, _2,, _6. Which of the following assignments of probabilities to each outcome are valid? ccccccc Outcomes & _1 & _2 & _3 & _4 & _5 &
Assignments (a) and (b) are valid.
- Roy has saved 40% more in money earned by chores than his brother Anthony. Anthony has saved 10.00 more than their sister Eva. Eva has saved 20.00. How much mon
Roy has 42.00.
- 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 (1)/(e^(x-1)) dx = α - ln 2, then α³ is equal to:
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