Solution; Given height of the cylinder, H = 30 cm Radius of the cylinder, r = 7 cm Height of cone, h = 24 cm Radius of cone, r = 7 cm Slant height of the cone, l = √(h2+r2) l = √(242+72) l =...
The correct answer is Option C Consumers. This is because - Primary productivity is determined by the producers that live in a given area. Secondary productivity, on the other hand, is the pace at...
The correct answer is Option C Rocks. This is because - The largest reservoir of phosphorus is in sedimentary rocks..
Given diameter of the cylindrical part of tent, d = 24 m Radius, r = d/2 = 24/2 = 12 m Height of the cylindrical part, H = 11 m Since vertex of cone is 16 m above the ground, height of cone, h =...
The correct answer is Option A Archaebacteria. This is because Archaebacteria are distinguished from other bacteria by the presence of branched chain lipids in their cell membrane, which allows them...
The correct answer is Option C Insertional inactivation of alpha-galactosidase in recombinant bacteria. This is because - Lysozyme breaks down bacterial cell walls. Cellulase is a...
The correct answer is Option C Algae - Methylase. This is because - Bacterial cell walls are destroyed by lysozyme. Cellulase is an enzyme that breaks down cellulose in plant cell walls. In fungus,...
The correct answer is Option C Electrophoresis. This is because - DNA fragments formed by restriction endonucleases in a chemical reaction can be separated by gel electrophoresis using an agarose...
The correct answer is Option A Aspergillus. This is because - Aspergillus niger (a fungus) is a producer of citric acid.
The correct answer is Option B Cotton. This is because - The Bt toxin gene has been cloned from bacteria and expressed in plants in Bt crops to give insect resistance without the use of...
The correct answer is Option D Lack of random mating. This is because - Allele frequencies in a population are stable and constant from generation to generation, hence the gene pool remains...
Given radius of the cone, r = 3.5 cm Radius of hemisphere, r = 3.5 cm Total height of the toy = 15.5 cm Height of the cone = 15.5 – 3.5 = 12 cm Slant height of the cone, l = √(h2+r2) l = √(122+3.52)...
Solution: Given height of the cylinder, h = 10 cm Radius of the cylinder, r = 3.5 cm Radius of the hemisphere = 3.5 cm Total surface area of the article = curved surface area of the cylinder +...
Given edge of the cube, a = 7 cm Diameter of the hemisphere, d = 7 cm Radius, r = d/2 = 7/2 = 3.5 cm Surface area of the hemisphere = 2r2 = 2×(22/7)×3.52 = 44×12.25/7 = 539/7 = 77 cm2 Surface area...
Solution: Dimensions of the cuboid = 15 cm× 10 cm × 3.5 cm Volume of the cuboid = 15×10×3.5 = 525 cm3 Radius of each depression, r = 0.5 cm Depth, h = 1.4 cm Volume of conical depression = (1/3)r2h...
Solution: Given dimensions of the box = 16 cm ×8 cm ×8 cm So volume of the box = lbh = 16×8×8 = 1024 cm3 Radius of the glass sphere, r = 2 cm Volume of the sphere = (4/3)r3 = (4/3)×(22/7)×23 =...
Given dimensions of the block of wood = 20 cm × 10 cm× 10 cm Volume of the block of wood = 20×10×10 = 2000 cm3 [Volume = lbh] Diameter of the cone, d = 10 cm Radius of the cone , r = d/2 = 10/2 = 5...
The correct answer is Option D Lack of random mating. This is because - Allele frequencies in a population are stable and constant from generation to generation, hence the gene pool remains...
Solution: Given side of the cube, a = 28 cm Radius of the cylinder, r = 28/2 = 14 cm Height of the cylinder, h = 28 cm Volume of the cube = a3 = 283 = 28×28×28 = 21952 cm3 Volume of the cylinder =...
Solution: Given diameter of the hole, d = 30 cm radius of the hole, r = d/2 = 30/2 = 15 cm Height of the cylindrical hole, h = 70 cm Volume of the cuboidal block = lbh = 70×30×30 = 63000 cm3 Volume...
Solution: (i)Let the radius of sphere be r. Then height of the cylinder, h = 2r Radius of cylinder = r Volume of cylinder = r2h = ×r2×2r = 2r3 Volume of sphere = (4/3)r3 = (2/3)× 2r3 = (2/3)× Volume...
Solution: Given surface area of the sphere = 1256 cm2 4r2 = 1256 4×3.14×r2 = 1256 r2 = 1256×/3.14×4 r2 = 100 r = 10 cm Total surface area of the hemisphere = 3r2 = 3×3.14×102 = 3×3.14×100 = 942 cm2...
Solution: Given internal diameter of the hemispherical tank, d = 14 m So radius, r = 14/2 = 7 m Volume of the tank = (2/3)r3 = (2/3)×(22/7)×(7)3 = 718.667 m3 = 718.67 m3 (approx) = 718.67 kilolitre...
Solution: Given radius of the hemispherical bowl, r = 3.5 cm = 7/2 cm Volume of the hemisphere = (2/3)r3 = (2/3)×(22/7)×(7/2)3 = 11×49/6 = 539/6 Hence the volume of the hemispherical bowl is...
Solution: Given surface area of the sphere = 154 cm2 4r2 = 154 4×(22/7)×r2 = 154 r2 = (154×7)/(4×22) r2 = 49/4 r = 7/2 Volume of the sphere = (4/3)r3 = (4/3)×(22/7)×(7/2)3 = 539/3 = 179.666 = 179.67...
Solution: Given side of the cube, a = 4 cm Volume of the cube = a3 = 43 = 4×4×4 = 64 cm3 Diameter of the sphere = 4 cm So radius of the sphere, r = d/2 = 4/2 = 2 cm Volume of the sphere = (4/3)r3 =...
Solution: (i)Let the radii of two spheres be r1 and r2. Given ratio of their radii = 3:7 Volume of sphere = (4/3)r3 Ratio of the volumes = (4/3)r13/(4/3)r23 = r13/ r23 = 33/73 = 27/343 Hence the...
Solution: Let r be the radius of the sphere and a be the side of the cube. Surface area of sphere = 4r2 Surface area of cube = 6a2 Given sphere and cube has same surface area. 4r2 = 6a2 r2/a2 = 6/4...
Solution: Given radius of the spherical balloon, r = 7 cm Radius of the spherical balloon after air is pumped, R = 14 cm Surface area of the sphere = 4r2 Ratio of surface areas of the balloons =...
Solution: Given inner diameter of the brass bowl, d = 10.5 cm Radius, r = d/2 = 10.5/2 = 5.25 cm Curved surface area of the bowl = 2r2 = 2×(22/7)×5.252 = 173.25 cm2 Rate of tin plating = Rs.16 per...
Solution: (i) Given radius of the hemisphere, r = 21 cm Curved surface area of the hemisphere = 2r2 = 2×(22/7)×212 = 2×22×3×21 = 2772 cm2 Hence the curved surface area of the hemisphere is 2772 cm2....
Solution: Given surface area of the sphere = 154 cm2 Surface area of the sphere = 4r2 4×(22/7)×r2 = 154 r2 = 154 ×7/(22×4) = 49/4 r = √49/2 Diameter = 2×r = 2×√49/2 = √49 = 7 Hence the diameter of...
Solution: Given radius of the metallic sphere, r = 4.9 cm Volume of the sphere, V = (4/3)r3 V = (4/3)×(22/7)×4.93 V = 493.005 V = 493 cm3 (approx) Given Density = 7.8 g per cm3 Density = Mass/...
Solution: (i) Given diameter of the sphere, d = 21 cm Radius, r = d/2 = 21/2 = 10.5 Surface area of the sphere = 4r2 = 4×(22/7)×10.52 = 1386 cm2 Hence the surface area of the sphere is 1386 cm2....
Solution: (i) Given radius of the sphere, r = 0.63 m Volume of the sphere, V = (4/3)r3 = (4/3)×(22/7)×0.633 = 1.047 m3 = 1.05 m3 (approx) Hence the volume of the sphere is 1.05 m3. (ii) Given radius...
(i)Given radius of the semi circular lamina, r = 35 cm A cone is formed by folding it. So the slant height of the cone, l = 35 cm Let r1 be radius of cone. Semicircular perimeter of lamina becomes...
Correct option: (4)Decarboxylation Solution: Oxalosuccinate is converted into α-ketoglutarate by oxidative decarboxylation during Kreb’s cycle.
Solution: Given height of the cone, H = 30 cm Let R be the radius of the given cone and r be radius of small cone. Let h be the height of small cone. Volume of the given cone = (1/3)R2H Volume of...
Correct option:(2)Imbibition Solution: Imbibition is an adsorption of water by hydrophilic compounds like cellulose and pectine in root hair cell wall.
So the height of the resulting cone, h = 8 cm Radius, r = 6 cm Slant height, l = 10 cm Volume of the cone, V = (1/3)r2h V = (1/3)×3.14×62×8 V = (1/3)×3.14×36×8 V = 3.14×12×8 V = 301.44 cm3 Hence the...
Correct option :(A)(1) Leaf curl and chilli mosaic virus Solution: ‘Pusa Sadabhar’ is resistance to disease leaf curl and chilli mosaic virus of chilli. Himgiri of wheat is resistance to leaf and...
Correct option: (4)Hyaluronic acid Solultion: Hyaluronic acid is a hetropolysaccharide. It is made up of glucuronic acid and N acetyl-D-glucosamine disaccharide units.
Correct option:(1)Cambia of both stock and scion fuse together Solution: Cambium is essential for grafting in plants because cambia is consists of meristematic cells of stock and scion fuse...
Solution: Given perimeter of the base of a cone = 44 cm 2r = 44 2×22/7×r = 44 r = 44×7/(2×22) r = 7 cm Slant height, l = 25 height, h = √(l2-r2) h = √(252-72) h = √(625-49) h = √576 h = 24 cm Volume...
Solution: Given perimeter of the base of a cone = 44 cm 2r = 44 2×22/7×r = 44 r = 44×7/(2×22) r = 7 cm Slant height, l = 25 height, h = √(l2-r2) h = √(252-72) h = √(625-49) h = √576 h = 24 cm Volume...
Solution: Given diameter of the conical tent, d = 20 m radius, r = d/2 = 20/2 = 10 m Slant height, l = 42 m Curved surface area of the conical tent = rl = (22/7)×10×42 = 22×10×6 = 1320 m2 So the...
Solution: (a) Let r1 and r2 be the radius of the given cones and h be their height. Ratio of radii, r1:r2 = 3:4 Volume of cone, V1 = (1/3)r12h Volume of cone, V2 = (1/3)r22h V1 /V1 = (1/3)r12h/...
Solution: Given height of the cone, h = 24 cm Radius, r = 7 cm We know that l2 = h2+r2 l2 = 242+72 l2 = 576+49 l2 = 625 l = √625 l = 25 Curved surface area = rl = (22/7)×7×25 = 22×25 = 550 cm2 So...
Solution: Given slant height of conical tomb, l = 25 m Base diameter, d = 14 m So radius, r = 14/2 = 7 m Curved surface area = rl = (22/7)×7×25 = 550 m2 Hence the curved surface area of the cone is...
Solution: Given height of a cone, h = 15 cm Volume of the cone = 1570 cm3 (1/3)r2h = 1570 (1/3)3.14 ×r2×15 = 1570 5 ×3.14×r2 = 1570 r2 = 1570/5×3.14 = 314/3.14 = 100 r = 10 Hence the radius of the...
Solution: Given diameter, d = 3.5 m So radius, r = 3.5/2 = 1.75 Depth, h = 12 m Volume of the cone = (1/3)r2h =(1/3)×(22/7)×1.752×12 = (22/7)× 1.752×4 = 38.5 m3 = 38.5 kilolitres [1 kilolitre = 1m3]...
Solution: Given radius, r = 7 cm Slant height, l = 25 cm We know that l2 = h2+r2 Height of the conical vessel, h = √(l2-r2) = √(252-72) = √(625-49) = √576 = 24 cm Volume of the cone = (1/3)r2h...
Solution: (i)Given radius, r = 6 cm Height, h = 7 cm Volume of the cone = (1/3)r2h =(1/3)×(22/7)×62×7 = 22×12 = 264 cm3 Hence the volume of the cone is 264 cm3. (ii) Given radius, r = 3.5 cm Height,...
Solution: (i) Given curved surface area of the cone = 308 cm2 Slant height of the cone, l = 14 cm rl = 308 (22/7)×r×14 = 308 r = 308×7/(22×14) = 7 Hence the radius of the cone is 7 cm. (ii)Total...
Solution: Given diameter of the cone = 10.5 cm Radius, r = d/2 = 10.5/2 = 5.25 cm Slant height of the cone, l = 10 cm Curved surface area of the cone = rl = (22/7)×5.25×10 = 165 cm2 Hence the curved...
Solution: (i)Volume of cone = (1/3)r2h If radius is halved and height is doubled, then volume = (1/3)(r/2)2 2h = (1/3)r2h/2 If the radius of a right circular cone is halved and its height is...
Solution: (i) Length of the can, l = 5 cm Width, b = 4 cm Height, h = 15 cm Volume of the can = lbh = 5×4×15 = 300 cm3 (ii) Diameter of the cylinder, d = 7 cm Radius, r = d/2 = 7/2 = 3.5 cm Height,...
Solution: Given length of the pencil, h = 14 cm Diameter of the pencil = 7 mm radius, R = 7/2 mm = 7/20 cm Diameter of the graphite = 1 mm Radius of graphite, r = ½ mm = 1/20cm Volume of graphite =...
Solution: Given height of the metal pipe = 77 cm Inner diameter = 4 cm Inner radius, r = d/2 = 4/2 = 2 cm Outer diameter = 4.4 cm Outer radius, R = d/2 = 4.4/2 = 2.2 cm (i)Inner curved surface area...
Solution: Given internal diameter of the tube = 11.2 cm Internal radius, r = d/2 = 11.2/2 = 5.6 cm Length of the tube, h = 21 cm Thickness = 0.4 cm Outer radius, R= 5.6+0.4 = 6 cm Volume of the...
Solution: Let r1 and r2 be the radius of the two cylinders and h1 and h2 be their heights. Given ratio of the diameter = 3:4 Then the ratio of radius r1:r2 = 3:4 Given volume of both jars are same....
Solution: Given the ratio of curved surface area and the total surface area = 1:2 Total surface area = 616 cm2 Curved surface area = 616/2 = 308 cm2 2rh = 308 rh = 308/2 = 308×7/2×22 rh = 49 …(i)...
Solution: (i) Let r be the radius and h be the height of the cylinder. Given the sum of radius and height of the cylinder, r+h = 37 cm Total surface area of the cylinder = 1628 cm2 2r(r+h) = 1628...
Solution: Let the radius of the base of a right circular cylinder be r and height be h. Volume of the cylinder, V1 = r2h The radius of the base of a right circular cylinder is halved and the height...
Solution: Given radius of the cylinder, r = 3.5 cm Height of the cylinder, h = 7.5 cm Total surface area = 2r(r+h) Curved surface area = 2rh Ratio of Total surface area to curved surface area =...
Answer correct to the nearest. 100 words. Solution: Height of the barrel of a pen, h = 7 cm Diameter, d = 5mm = 0.5 cm Radius, r = d/2 = 0.5/2 = 0.25 cm Volume of the barrel of pen, V = r2h =...
Solution: (i) Given diameter of the cylinder, d = 20 cm Radius, r = d/2 = 20/2 = 10 cm Curved surface area = 1000 cm2 2rh = 1000 2×3.14×10×h = 1000 62.8h = 1000 h = 1000/62.8 = 15.9 cm Hence the...
Solution: Given curved surface area of a cylinder = 4400 cm2 Circumference of its base = 110 cm 2r = 110 r = 110/2 = (110×7)/2×22 = 17.5 cm (i) Curved surface area of a cylinder, 2rh = 4400...
Solution: Given height of the pole, h = 7 m Diameter of the pole, d = 20 cm radius, r = d/2 = 20/2 = 10 cm = 0.1m Volume of the pole = r2h = (22/7)×0.12×7 = 0.22 m3 Weight of wood per m3 = 225 kg...
Solution: Given Height of the cylinder, h = 7 cm Volume of the cylinder, V = 448 cm3 r2h = 448 ×r2×7 = 448 r2 = 448/7 = 64 r = 8 Lateral surface area = 2rh = 2××8×7 = 112 cm2 Total surface area =...
Solution: Given diameter of the road roller, d = 0.7 m Radius, r = d/2 = 0.7/2 = 0.35 m Width, h = 1.2 m Curved surface area of the road roller = 2rh =2 ×(22/7)×0.35×1.2 = 2.64 m2 Area of the play...
Solution: (i) Given diameter of the well, d = 2 m Radius, r = d/2 = 2/2 = 1 m Depth of the well, h = 20 m Volume of the well, V = r2h = (22/7)×12×20 = 62.85 m3 Hence the amount of soil dug out to...
Solution: Given height of the cylinder, h = 16 cm When rectangular foil of length 22 cm is folded to form cylinder, the base circumference of the cylinder is 22cm 2r = 22 r = 22/2 = 3.5 cm Volume of...
Solution: Given diameter of the cylindrical glass, d = 7 cm Radius, r = d/2 = 7/2 = 3.5 cm Height of the cylindrical glass, h = 12 cm Volume of the cylindrical glass, V = r2h = (22/7)×3.52×12 = 462...
Solution: Given diameter of the cylinder, d = 35 cm radius, r = d/2 = 35/2 = 17.5 cm Height of the cylinder, h = 1.2 m = 120 cm (i)Outer lateral surface area = 2rh = 2×(22/7)×17.5×120 = 13200 cm2...
Solution: Given radius of the cylinder, r = 5 cm Height of the cylinder, h = 10 cm Total surface area = 2r(r+h) = 2×5(5+10) = 2×5×15 = 150 cm2 Hence the total surface area of the solid cylinder is...