Mock Question Paper on Height and Distance for CLAT 2020

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Mock Question Paper on Height and Distance for CLAT 2020What is the maximum area that can be enclosed in a triangle with semi perimeter​​ 12cm?Area of a circle is 81cm2. What is the area of sector whose corresponding arc subtends an angle 2(pi)/9​​ at the centre of the circle?What is the area of a triangle ABC, If AB = 12cm, BC = 14cm and Angle ABC = 30°?On walking 30m towards a pole from A to B, the angle of elevation of top of the pole changes from 30°​​ to 45°. Find the height of the pole.​​ A pool of diameter 25m is dug 15m deep. The mud taken out is uniformly spread around the pool to form an embankment 5m high. What will be the resulting width of embankment?An iron ball of diameter 7inches is dropped into a cup of diameter 1 feet filled with water. Find rise in water level of the cup.The inner radius of a hollow sphere is 7cm, while thickness of the material is 2cm. What is the volume of material used in sphere?A rectangular sheet of dimension 22cm*14cm is rolled in a cylinder. Find the radius of new cylinder.In the previous question, what will be the volume of the cylinder?What will be the curved surface area of cylinder (only sheet area) in question 8?Answer and Solutions:Ans:​​ 163​​ cm2Sol:​​ Given semi perimeter of a triangle, an equilateral triangle encloses maximum areaSide of equilateral triangle = 12*2/3 = 8cm​​ Area (maximum) =​​ 3​​ *8*8/ 4 = 16​​ 3 ​​​​ cm2​​ Ans:​​ 9cm2Sol:​​ Area of the circle = (pi) R2= 81​​ ​​ R2​​ = 81/(pi)Area of the sector = 1 R2θ/2 = ½ * 81 / (pi) * 2(pi) /9 = 9 cm2Ans:​​ 42cm2Sol:​​ Area of triangle= ½ *product of two side * sine of including angleArea of triangle = ½ * 12 * 14 *1/2 = 42 cm2​​ Ans:​​ 40.98cmSol:​​ A triangle with pole as perpendicular (height) and base length from pole foot to point B be xTan 45°​​ = h/x   tan 30​​ °​​ = h/ x+30h=x … eq (1)  1/3 ​​​​  = h/h+30 h3 ​​​​ ​​ = h + 30h*(3 ​​​​ -1 ) = 30 => h = 30/(1.732-1) = 40.98cm​​ Ans:​​ 7.25cmSol:​​ Volume of hollow cylindrical embankment = volume of mud taken out.  (pi) (R2-r2) 15 = (pi) r2*5  (R2​​ –​​ 12.52)15=​​ 12.52​​ *10  R2​​ = 12.5*12.5*15/10 + 156.25 = 390.625  R= 19.75 => Embankment width = R-r = 19.75 – 12.5 =7.25 cm ​​​​ Ans:​​ 1.58 inchesSol:​​ Radius of Cup = ½ =0.5 feet = 6 inchesVolume of water rise [(pi)*R2*h] =Volume of iron ball (4/3 * (pi) * r3)(pi) 62* h = 4/3 * (pi) * 7*7*7/2*2*2 ​​​​ h= 7*7*7*4/6*6*3*8 = 1.58 inches​​ Ans:​​ 1617cm3Sol:​​ Inner Radius, r = 7 cm; Outer Radius, R = 7+2cm = 9 cmVolume of material used= 4/3 * (pi) * (R3​​ –r3) = 4/3 *22/7 * (93​​ -73)    = 1617.5 cm3Ans:​​ 3.5cmSol:​​ Circumference of the cylinder circular end = length of sheet = 22cm 2(pi) r = 22 => r = 22*7/2*22 = 3.5 cmAns: 539cm3Sol:​​ Height of Cylinder = Breadth of cylinder = 14cmVolume of cylinder = (pi) * 14 *3.5*3.5 [as volume of cylinder=(pi)r2h]   = 539cm3Ans: 308cm2​​ Sol:​​ As the area of cylinder will be the same as sheet’s area hence curved surface area of the cylinder = 22*14 = 308cm2​​ (function( $ ) { //footnotes $('.defaultNote').children(":first").css('cursor', 'pointer'); $('.defaultNote').children(":first").click(function(){ var gotoID = '#' + $(this).parent().attr('id'); $('html, body').animate( { scrollTop: $('a[href="' + gotoID + '"]').offset().top - 60, }, 250, 'linear' ) }); }(jQuery)); var numFormat = ",."; (function( $ ) { "use strict"; //do some cleaning on load var sortCells = $('td[data-sorting], th[data-sorting]'); sortCells.each(function(){ var first = $(this).text().trim().charAt(0); if (first == '@'){ var oldHTML = $(this).html(); var newHTML = oldHTML.replace('@', ''); $(this).html(newHTML); } }); function sortingTable(node, pos, ordBy){ var rows = node.children('tbody').children('tr').get(); rows.sort(function(a, b) { var X = $(a).children('td').eq(pos).text().toUpperCase(); var Y = $(b).children('td').eq(pos).text().toUpperCase(); if (numFormat != '.,'){ //we are dealing with a different locale and we need to do some //transformation in numbers X = convert2number(X); Y = convert2number(Y); } else { X = X.replace(/,/g, '').replace(/ /g, ''); Y = Y.replace(/,/g, '').replace(/ /g, ''); } var currencies = ['$', '¥', '£', '€']; var arrayLength = currencies.length; var XX = X; var YY = Y; for (var i = 0; i < arrayLength; i++) { XX = XX.replace(currencies[i], ''); YY = YY.replace(currencies[i], ''); } if (!isNaN(XX) && !isNaN(YY)){ var floatXX = parseFloat(XX); var floatYY = parseFloat(YY); return -(floatYY-floatXX) * ordBy; } else if (!isNaN(XX) && isNaN(YY)){ return -1 * ordBy; } else if (isNaN(XX) && !isNaN(YY)){ return ordBy; } else { if(X < Y) { return -1 * ordBy; } if(X > Y) { return 1 * ordBy; } return 0; } }); $.each(rows, function(index, row) { node.children('tbody').append(row); }); } function removeTableCellDecoration() { $("td[data-sorting], th[data-sorting]").removeClass('sortDecorator'); } //unbind the click event just in case we are loading more than one document $("td[data-sorting], th[data-sorting]").off('click'); $("td[data-sorting], th[data-sorting]").click(function(){ removeTableCellDecoration(); $(this).addClass('sortDecorator'); //get desired ordering var ordering = $(this).attr('data-sortOrdering'); if (ordering == 'ASC'){ var ordBy = -1; $(this).attr('data-sortOrdering', 'DESC'); } else { var ordBy = 1; $(this).attr('data-sortOrdering', 'ASC'); } var cellPosition = $(this).prevAll().length; var table = $(this).parents('table:first'); sortingTable(table, cellPosition, ordBy); }); function convert2number(str) { str = str.trim(); if (str.match(/^\d+/)) { //we have to take special care when the thousand separators are '.' var result_0 = str.replace(/\./g, '_@_'); var result_1 = result_0.replace(window.numFormat[0], '.'); var result = result_1.replace(/_@_/g, ''); result .replace(/ /g, ''); return result; } else { return str; } } }(jQuery));