Description : The x coordinate of the centroid of the area enclosed by the parabolas y = x2 and x = y2 will be a.107 dynes b.0.44 c.0.43 d.0.45 e.0.46
Last Answer : d. 0.45
Description : The y-coordinate of the centroid of the area bounded by the x-axis, the line x = 3 and the parabola y = x2 will be a.2.7 b.2.55 c.107 dynes d.2.6 e.2.65
Last Answer : a. 2.7
Description : Centroid of the are of circle shown in adjacement figure is a.r sin (?/2)/2 ?, 0 b.r sin (?)/?, 0 c.2 r sin (?/2)/?, 0 d.107 dynes e.2r sin (?)/?, 0
Last Answer : c. 2 r sin (?/2)/?, 0
Description : A sphere of radius r is cut from larger sphere of radius R. The distance between their centre is a. The centroid of the remaining valoume lies on the line of centres and the sistanc from the centre of the larger sphere is a.ar2 / (R2 - r2) b.107 dynes c.aR/(R2-r2) d.aR/(R - r) e.ar3 / (R3 - r3)
Last Answer : e. ar3 / (R3 - r3)
Description : What is the point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Last Answer : Equations: y = x+4 and x^2 +y^2 -8x +4y = 30It appears that the given line is a tangent line to the givencircle and the point of contact works out as (-1, 3)
Description : What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?
Last Answer : If: y = 2xThen: y^2 = 4x^2If: x^2 +y^2 -8x -y +5 = 0Then: x^2 +4x^2 -8x -2x +5 = 0Transposing terms: 5x^2 -10x +5 = 0Dividing all terms by 5: x^2 -2x +1 = 0Factorizing the above: (x-1)(x-1) = 0 meaning x = 1By substitution into original equations point of contact is madeat: (1, 2)
Description : The centroid of a triangle is at the inter-section of a.perpendicular bisectors b.107 dynes c.base and perpendicular from opposite vertex d.perpendiculars down from the corners e.medians
Last Answer : e. medians
Description : Center point of circle a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2 b.[x1-x2]/2; [y1-y2]/2; [z1-z2]/2 c.[x1-x2]; [y1-y2]; [z1-z2] d.[x2-x1]; [y2-y1]; [z2-z1]
Last Answer : a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2
Description : What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?
Last Answer : Circle equation: x^2 +y^2 -2x -6y +5 = 0Completing the squares: (x-1)^2 +(y-3)^2 = 5Centre of circle: (1, 3)Tangent line meets the x-axis at: (0, 5)Distance from (0, 5) to (1, 3) = 5 units using the distanceformula
Description : What is the length of a tangent line from the point 7 -2 to a point when it touches the circle x2 plus y2 -10 equals 49?
Last Answer : x² + y² - 10 = 49→ x² + y² = 59= (x - 0)² + (y - 0)² = (√59)²→ circle has centre (0, 0) - the origin - and radius √59The point (7, -2) has a distance from the centre of the circleof:√((7 - 0)² + (-2 - 0)²) = √(7² + (-2)²) = √(49 + 4) = √53
Description : What is the length of the tangent line from the point 9 0 to the circle x2 plus 8x plus y2 -9 equals 0?
Last Answer : Equation of circle: x^2 +8x +y^2 -9 = 0Completing the square: (x+4)^2 +y^2 = 25Radius of circle: 5Center of circle: (-4, 0)Distance from (9, 0) to (-4, 0) = 13 which is ... the length of the tangent line is 12 unitsNote that the tangent line of a circle meets the radius of thecircle at right angles
Description : What is the equation of the tangent line that meets the circle x2 -4x plus y2 -6y equals 4 at the point 6 4?
Last Answer : Circle equation: x^2 -4x +y^2 -6y = 4Completing the squares: (x-2)^2 +(y-3)^2 = 17Point of contact: (6, 4)Center of circle: (2, 3)Slope of radius: 1/4Slope of tangent line: -4Tangent equation: y-4 = -4(x-6) => y = -4x+28Tangent line equation in its general form: 4x+y-28 = 0
Description : What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?
Last Answer : Equation of circle: x^2 +y^2 -4x -8y -5 = 0Completing the squares: (x-2)^2 +(y-4)^2 = 25 which is radiussquaredCenter of circle: (2, 4)Tangent line originates from: (8, ... angle triangleUsing Pythagoras theorem: distance^2 minus radius^2 = 15Therefore length of tangent line is the square root of 15
Description : A couple consists of a force P acting at a point A whose coordinates are (-1,2,4) m and force - F acting at a point whose coordinates are (2,3, -2)m. If F = 3i + 2j - 4k in kg units the moment of the couple in kg - m ... .8i - 6j - 3k b.12i - 3j + k c.16i - 12j - 6k d.4i - 3j + k e.8i + 5j + 3k
Last Answer : a. 8i - 6j - 3k
Description : The point (-1,2) divides the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4, then the value of x2 + y2 is : (a) 27 (b) 28 (c) 29 (d) 30
Last Answer : (c) 29
Description : The locus of a point on a thread unwound from a cylinder will be a.A circle b.A cycloid c.A straight line d.A spiral e.An involute
Last Answer : b. A cycloid
Description : A point moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one. The locus of the path traced by the point will be a a.Cycloid b.Hyperbola c.Circle d.Involute e.Ellipsc
Last Answer : d. Involute
Description : What is the length of the circle radius if the circle is x2 plus y2 equals 1?
Last Answer : The center of the circle is at (0, 0) and its radius is thesquare root of 1 which is 1
Description : What is the length of the circles radius for the circle x2 plus y2 169.?
Last Answer : If x^2 plus y^2 = 169 then the center of the circle is at (0, 0)and its radius is the square root of 169 which is 13
Description : What is the center and the radius of the circle x2 plus y2 -4x -6y -3 equals 0?
Last Answer : Equation of circle: x^2 +y^2 -4x -6y -3 = 0Completing the squares: (x-2)^2 +(y-3)^2 = 16 square unitsTherefore center of circle is at (2, 3) and its radius is 4units
Description : What is the center and the radius of the circle x2 plus y2 equals 12x -10y -12?
Last Answer : Equation of circle: x^2 +y^2 = 12x-10y-12Completing the squares: (x-6)^2 +(y+5)^2 = 49So center of circle is at (6, -5) and its radius is 7 units
Description : Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th
Last Answer : NEED ANSWER
Last Answer : According to question find the value of z
Description : Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15 -Maths 9th
Last Answer : Consider the equation x + y + z = 15 From algebraic identities, we know that (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) So, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz) From the question, x2 + y2 + z2 ... y3 + z3 - 3xyz = 15(83 - 71) => x3 + y3 + z3 - 3xyz = 15 12 Or, x3 + y3 + z3 - 3xyz = 180
Description : If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1. -Maths 9th
Last Answer : xsin3θ+ycos3θ=sinθcosθ (xsinθ)sin2θ+(ycosθ)cos2θ=sinθcosθ (xsinθ)sin2θ+(xsinθ)cos2θ=sinθcosθ xsinθ=sinθcosθ x=cosθ Again, ycosθ=xsinθ ycosθ=cosθsinθ y=sinθ Therefore, x2+y2=sin2θ+cos2θ=1.
Description : Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Last Answer : Answer: x = 3/2 or -3 and y = 3 or -3/2.
Description : A solid spherical ball rolls on a table. The momen' of inertia of the ball is given by 3/5 x mass x radius2. The ratio of translational and rotational kinetic energies for ball will be a.2 b.7?16 c.5?3 d.7?8 e.1
Last Answer : c. 5?3
Description : A stone weighing 20 N is whirling in a vertical circle at the extremity of a string 100 cm long. The tension in the string will be zero a.at the highest position b.at the lowest position c.at the midway position d.at none of the above e.107 dynes
Last Answer : a. at the highest position
Description : The shape of a suspended cable under its own weight is a.Catenary b.Elliptical c.Cycloidal d.Semi-circle e.Parabolic
Last Answer : a. Catenary
Description : The centre of gravity of a plane lamina will not be at its geometrical centre if it is a a.Square b.Equilateral triangle c.Circle d.Rectangle e.Right angled triangle
Last Answer : e. Right angled triangle
Description : The moment of inertia of a semi-circle of radius r with respect to a centroidal axis parallel to the diameter is a.0.33 r2 b.0.11 r2 c.0.055 r2 d.0.05 r2 e.0.22 r2
Last Answer : b. 0.11 r2
Description : The satellite moves in a circle around the earth. The radius of this circle is equal to one-half the radius of the moons orbit. The satellite will complete one revolution in a.1 lunar month b.2-3/4 lunar month c.2-2/3 lunar month d.None of the above e.
Last Answer : e. None of the above
Description : Polar moment of inertia is a.Applicable to masses whereas moment of inertia is applicable to area only b.The moment of inertia for an area ralative to a line or axis which is out the plane of area ... The moment of inertia for an area relative to a line or axis perpendicular to the plane of the area
Last Answer : e. The moment of inertia for an area relative to a line or axis perpendicular to the plane of the area
Description : What are the solutions to the simultaneous equations of y equals -2x and x2 plus y2 equals 80?
Last Answer : If: y = -2x then y ^2 = 4x^2If: x^2 + y^2 = 80 then x^2 +4x^2 = 80So: 5x^2 = 80Divide all terms by 5: x^2 = 16Square root both sides: x = -4 or +4By substitution into the original equation solutions are: (-4,8) and (4, -8)
Description : If z equals yf x2 - y2 show that ydz divided by dx plus xdz divided by dy equals xz divided by y?
Last Answer : 4
Description : A particle is of wieght 8 kg. When it is allowed to fall under the force of gravity its momentum at the time t = 2 sec would be a.8 kg sec b.32 kg sec c.2 kg sec d.16 kg sec e.48 kg sec
Last Answer : d. 16 kg sec
Description : Power required for a train weighing 200 Mg to move at a uniform speed of 60 Kmph up an incline of 1 in 200 is (Resistance due to friction is negligible) a.16.67 KW b.163.5 KW c.1000 KW d.9810 KW e.Tapered bearing
Last Answer : b. 163.5 KW
Description : A body of weight 100 kg is placed on a horizontal plane. A horizontal force of 30 kg is applied and the block is just on the point of motion. The angle of friction is a.About 16? b.30? c.45? d.60? e.None of the above
Last Answer : a. About 16?
Description : The piston of a steam engine moves in S.H.M. The crank rotates at 180 r.p.m. and the stroke length is 2 metres. The linear velocity of the piston when it is at a distance of 1 metre from the centre is a.8.88 m/sec b.16.32 m/sec c.5.88 m/sec d.8.16 m/sec e.Zero
Last Answer : e. Zero
Description : A flywheel weighs 400 kg and has a radius of gyration of 30 cm about its axis of rotation. It is mounted on a shaft subjected to a moment of 40 kgm. If the flywheel starts from restits speed after 3 seconds wil be a.10.9 rad/sec b.19.0 rad/sec c.51.2 rad/sec d.3.33 rad/sec e.16.35 rad/sec
Last Answer : d. 3.33 rad/sec
Description : A crate weighing 40 kg rests on a cart moving with an acceleration W. The coefficient of friction between the cart and the crate is a.2.45 m/sec2 b.4.00 m/sec2 c.0.25 m/sec2 d.4.16 m/sec2 e.1.25 m/sec2
Last Answer : a. 2.45 m/sec2
Description : The ratio of moment of inertia of a circular body about x axis to that about y axis is a.? b.? c.1?4 d.1 e.
Last Answer : e. 1
Description : M.I. of sphere of 0.5 m radius about a mutually perpendicular axis (Z-axis) when its M.I. about X-axis and Y-axis are 50 kgm2 and 50 kgm2 is a.50 Kgm2 b.Tapered bearing c.100 Kgm2 d.25 Kgm2 e.12.5 Kgm2
Last Answer : a. 50 Kgm2
Description : A stone of wight 100 kg is thrown vertically upwards by a man of height y = 1.8 m with an initial velocity of 20 m/sec. The maximum height to which it will rise would be a.22.2 m b.26 m c.15.1 m d.20.2 m e.10 m
Last Answer : a. 22.2 m
Description : A particle starts from rest and moves in a straight line whose equation of motion is given by S = 2t3 - t2 - 1. The acceleration of the particle after one sec will be a.6 m/sec2 b.4 m/sec2 c.12 m/sec2 d.10 m/sec2 e.8 m/sec2
Last Answer : d. 10 m/sec2
Description : At a roller support the line of reaction and the roller base must be at an angle of a.60? b.90? c.not less than 60? d.not more than 60? e.107 dynes
Last Answer : b. 90?
Description : According to principle of transmissiblity of forces, when a force acts upon a body, its effect is a.maximum when it acts at C.G. of the body b.minimum when it acts at C.G. of the body c.different at different points of the body d.107 dynes e.same at every point in its line of action
Last Answer : e. same at every point in its line of action
Description : The locus of instantaneous centre of a moving rigid body a.Epicycloid b.Straight line c.Involute d.Cycloid e.Centrode
Last Answer : e. Centrode
Description : The resultant of coplaner parallel forces is found by load line diagram, while the position is found by a.link polygen b.funicular polygon c.string polygon d.any of the above e.107 dynes
Last Answer : d. any of the above
Description : According to the principle of transmissibility of forces, when a force acts upon a body ; its effect is a.Minimum when it acts at C.G. of the body b.Maximum when it acts at C.G. of the body c.Different at different points of body d.Same at every point in its line of action e.None of the above
Last Answer : d. Same at every point in its line of action