2013 Quantitative Reasoning

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<ul><li><p>Page 79 of 280 </p><p>NUMBER SYSTEM </p><p>Q.1 What is the value of (P+Q)/(P-Q), if P/Q=7/3 ? </p><p>(a) 5/3 (b)3/2 (c)4/2 (d)5/2 </p><p>=</p><p>7</p><p>3</p><p>+</p><p>(a) 5/3 (b)3/2 (c)4/2 (d)5/2 </p><p>Q.2.Which of the following is a proper fraction ? </p><p>(a) 3</p><p>5 (b)</p><p>1</p><p>2 (c)</p><p>7</p><p>3 (d) </p><p>3</p><p>5&amp;</p><p>1</p><p>2</p><p>Q.3. If P=3 +2 2, the value of p + 1/p</p><p>P=3+2 2 P+1</p><p>(a) 8 (b) 6 (c) 8 (d) 83</p><p>Q.4. Which one of the following is not prime number</p><p>a) 1 (b)2 (c)13 (d)11 </p><p>Q.5. Which one of the following number will be terminating </p></li><li><p>Page 80 of 280 </p><p>(a) 129</p><p>225775(b) </p><p>6</p><p>151 (c)</p><p>77</p><p>210(d) </p><p>6</p><p>15</p><p>Q.6.Which of the following number is rational </p><p>a) 13 b) 121 c) 29 d) NONE </p><p>a) 13 b) 121 c) 29 d) </p><p>Q.7. Which is a quadratic equation </p><p>a) X+1</p><p> =2 b)x(x2-1)=7 c) (3x + 2)=4 d) x2</p><p> 1</p><p> =1 </p><p>Q.8. The product of the roots of then quadratic equation 2x2 + 5x 7 = 0 is </p><p>2x2 + 5x 7 = 0 </p><p>(a) 5</p><p>2 b) </p><p>7</p><p>2 c) </p><p>5</p><p>2d) </p><p>7</p><p>2</p><p>Q.9. If one root of the quadratic equation x2 - 4x + 1 = 0 is 2 - 3 . The other root will be </p><p>(a) 2 + 3 (b) 3 (c) 2 - 3(d)None of these </p><p>x2 - 4x + 1 = 0 3</p><p>(a) 2 + 3 (b) 3 (c) 2 - 3 d) </p><p>Q.10. The roots of the equation : 3x2 - 7x + 4 = 0 are </p><p>(a) Rationals (b)Irrationals (c)Positive integers (d)Complex Numbers </p><p>3x2 - 7x + 4 = 0 </p><p>a) b) c) d) </p></li><li><p>Page 81 of 280 </p><p>ANSWERS(NUMBER SYSTEM) </p><p>Q.NO. ANSWERS </p><p>1 d </p><p>2 a </p><p>3 b </p><p>4 a </p><p>5 d </p><p>6 b </p><p>7 a </p><p>8 b </p><p>9 a </p><p>10 a </p></li><li><p>Page 82 of 280 </p><p>AVERAGE </p><p>Q.1. The average of all prime numbers between 30 and 50 is </p><p>(a) 40 (b)39.8 (c)38 (d)41 </p><p> 30</p><p>a) 40 (b) 39.8 (c) 38 (d) 41 </p><p>Q.2. The average of 11 numbers is 60. If the average of first six numbers is 58 and that of last six is 63, </p><p>then the sixth number is </p><p>(a) 66 (b)66.5 (c)62 (d)65 </p><p>(a) 66 (b)66.5 (c)62 (d)65 </p><p>Q.3. Shivani has twice as much money as Adityaand Aditya has 50 % more money than what Sahil has. If </p><p>the average money with them is Rs. 110, then Shivani has Rs. </p><p>(a) 55 (b)60(c)90 (d)180 </p><p>%</p><p>(a) 55 (b)60(c)90 (d)180 </p><p>Q.4. The average weight of 6 boys decreases by 3 kg when one of them weighing 80 kg is replaced by a </p><p>new boy. The weight of new boy is </p><p>(a) 56 kg (b)58 kg (c)62 kg (d)76 kg </p><p>(a) 56 (b)58 (c)62 (d)76 </p><p>Q.5. The average price of three items is Rs. 15000. If their prices are in the ratio 3:5:7, the price of </p><p>cheapest item is </p><p>(a) Rs. 9000 (b)Rs. 15000 (c)Rs. 18000 (d)Rs. 21000 </p></li><li><p>Page 83 of 280 </p><p>(a) Rs. 9000 (b)Rs. 15000 (c)Rs. 18000 (d)Rs. 21000 </p><p>Q.6. Five years ago, the average age of A,B,C,D was 45 years with E joining them now. The average of all </p><p>the five is 49 years. How old is E </p><p>(a) 25 years (b)40 years (c)45 years (d)64 years </p><p>A,B,C,D E E</p><p>E</p><p>(a) 25 (b) 40 (c) 45 (d) 64 </p><p>Q. 7. The average temperature on Monday, Tuesday and Wednesday was 36 degrees C. Average </p><p>temperature on Tuesday, Wednesday and Thursday was 38 deg. C. If the temperature on Thursday was </p><p>37 deg. C, then the temperature on Monday was </p><p>(a) 38 d C (b)31 degree C (c)37 degree C (d)33.5 degree C </p><p>(a) (b) (c) (d) </p><p>Q.8. The average of 5 consecutive numbers is n. If the next two numbers are also included, the average </p><p>will </p><p>(a) increase by 1 (b)remain the same (c)increase by 2 (d)increase by 1.4 </p><p>n</p><p>a) b) </p><p> c) d) </p><p>Q.9. A man goes at the speed of 5 km/hour from P to Q and returns at the speed of 3 km/hour from Q to P. </p><p>The average speed of whole journey is </p><p>(a) 4 km/hour (b)0.25 km/hour(c)4.5 km/hour (d)3.75 km/hour </p></li><li><p>Page 84 of 280 </p><p>P Q / Q P /</p><p>(a) 4 / (b) 0.25 / (c) 4.5 / (d) 3.75 /</p><p>Q.10. Four years ago, at the time of marriage, the average age of a couple was 20 years. Now they have a </p><p>child of age 3 years, then average age of this family is </p><p>(a) 161</p><p>3years (b)</p><p>2</p><p>3 years (c)17 years (d)16 years </p><p>a) 161</p><p>3 (b) </p><p>2</p><p>3(c)17 (d)16 </p></li><li><p>Page 85 of 280 </p><p>ANSWERS(AVERAGE) </p><p>Q.NO. ANSWERS </p><p>1 b </p><p>2 a </p><p>3 d </p><p>4 c </p><p>5 a </p><p>6 c </p><p>7 b </p><p>8 a </p><p>9 d </p><p>10 c </p></li><li><p>Page 86 of 280 </p><p>PASSAGE QUESTIONS Q.1 Q.5:- In the following Pi-chart, peoples of different age group are demonstrated. If the total </p><p>population of the town is 10,000 pick out the right answers based on the given pi- chart: </p><p>Q.1.How many peoples of age group 40-50 less than number of peoples of age group 20-30:- </p><p>(a) 667 (b)567 (c)1333 (d)1667 </p><p>Q.2. What is the ratio of 30-40 group to 10-20 year group </p><p>(a) 2:1 (b)4:3(c)1:2 (d)9:4 </p><p>Q.3. Sum of 10-20 age group people and 40-50 years age group people will be </p><p>(a) 20-30 age group people (b)30-40 age group people(c)upto 10 years age group (d)None of these </p><p>Q.4. What % of upto less than 10 years age group people of the total population </p><p>(a) 36 % (b)10 % (c)25 % (d)72 % </p><p>Q.5. What is difference of people of least age group and greatest age group </p><p>(a) 1500 (b)2000 (c)1000 (d)450 </p><p>Less than1036 degree</p><p>10-20Years48 degree</p><p>20-30 years96 degree</p><p>30-40YEARS108 DEGREE</p><p>40-50 YEARS72 DEGREE</p><p>&lt; 10 BET10-20 20-30 30-40 40-50</p></li><li><p>Page 87 of 280 </p><p>a) 667 b) 567 c) 1333 d)1667 </p><p>2) </p><p>a) 2:1 b) 4:3 c) 1:2 d) 9:4 </p><p>3) 10-20 </p><p>a) b) </p><p>c) d)</p><p> a) 36% b) 10% c) 25% d) 72% </p><p>5) </p><p>a) 1500 b) 2000 c) 1000 d) 450 </p><p>Less than1036 degree</p><p>10-20Years48 degree</p><p>20-30 years96 degree</p><p>30-40YEARS108 DEGREE</p><p>40-50 YEARS72 DEGREE</p><p>&lt; 10 BET10-20 20-30 30-40 40-50</p></li><li><p>Page 88 of 280 </p><p>Eulers formula for convex surface is V + F = E + 2, where V=vertices, F=faces and E= edges </p><p>Q.6. If number of faces in a cuboid are 6, number of vertices are 8, then number of edges will be </p><p>(a) 12 (b)14(c)10 (d)8 </p><p>Q.7. Number of faces in a tetrahedron will be </p><p>(a) 6 (b)4(c)8 (d)None of these </p><p>Q.8. Number of edges in a cone will be according to formula </p><p>(a) formula not applicable (b)1(c)3 (d)2 </p><p>Q.9. Which one of the following is not a convex figure </p><p>(a) cube (b)rectangular prism(c)tetrahedron (d)Sphere </p><p>V+F=E+2 V= F= E=</p><p>a) 12 b) 14 c) 10 d) 8 </p><p>a) 6 b) 4 c) 8 d) </p><p>a) b) 1 c) 3 d) 2 </p><p>a) b) c) d) </p></li><li><p>Page 89 of 280 </p><p>Fundamental Theorem of algebra says that any polynomial equation of degree n has n roots real or </p><p>complex and no more also complex and irrational roots exists in pair contrary to it any trigonometric </p><p>equation has infinite number of roots </p><p>Q.10. Which one of the equation is a polynomial equation:- </p><p>(a) (x2 - 2x + 5 )/(x-1)=0 (b)3x3/2 +5x-1=0 (c)sin x + x=0 (d)x3 2 x2 + 5=0 </p><p>Q.11. Number of zeroes/roots of the polynomial equation x4 + 1 = 0 will be </p><p>(a) 1 (b)2(c)4 (d)3 </p><p>Q.12. If one zero/root of the polynomial equation x2 - 4x + 1=0 is 2 + 3 then the other root will be </p><p>(a) 2 3(b) 3 (c)2 (d)none of these </p><p>Q.13. If the sum and product of roots are -2 and -3 respectively, then the quadratic equation is </p><p>(a) x2 - 2x + 3=0 (b)x2 + 2x - 3=0 (c)x2 - 2x - 3=0 (d)x2 +2x + 3=0 </p><p>Q.14. Number of zeroes of the equation sin x = will be </p><p>(a) 1 (b)Infinite(c)2 (d)3 </p><p>n n n</p><p>a) 22+5</p><p>1 = 0 b) 3x</p><p>3/2+5x-1=0 </p><p> c) sin + = d) 3-22 +5=0 </p><p>11) 4+1=0 /</p><p>a) 1 b) 2 c) 4 d)3 </p><p>12) 2 4 + 1 = 0 / + 3</p></li><li><p>Page 90 of 280 </p><p>a) 2- 3 b) 3 c) 2 d) </p><p>-2 -3 </p><p>a) 2 2 + 3 = 0 b) 2 + 2 3 = 0 </p><p>c) 2 2 3 = 0 d) 2 + 2 + 3 = 0 </p><p>14) sin =1</p><p>2</p><p>a ) 1 b) c) 2 d) 3</p></li><li><p>Page 91 of 280 </p><p>ANSWERS(PASSAGE) </p><p>Q.NO. ANSWERS </p><p>1 a </p><p>2 d </p><p>3 d </p><p>4 b </p><p>5 c </p><p>6 a </p><p>7 b </p><p>8 a </p><p>9 d </p><p>10 d </p><p>11 c </p><p>12 a </p><p>13 b </p><p>14 b </p><p>GEOMETRY </p><p>Qes.1:- In the given figure PQ is a tangent to a circle of radius </p><p> 5cm and PQ = 12 cm, Q is a point of contact, then QP is :- </p><p>PQ,5cm PQ = 12 cm, Q OP </p></li><li><p>Page 92 of 280 </p><p> Q </p><p>P </p><p>O </p><p>(a) 13cm (b)17cm (c) 7 cm (d) 119 cm </p><p>Qes.2:- To draw a line we need atleast </p><p>(a) Only a Point (b) 2 Points (c) 3 Points (d) Infinite points </p><p>2) </p><p>a) (b) (c) (d) </p><p>Qes.3:- If sum of two adjacent angles is 180 the angles will be called </p><p>(a) Complementary angles (b) Supplementary angles </p><p>(b) linear pair of angles (d) vertically opposite angles </p><p>3) </p><p>a) (b) (c) (d) </p><p>Qes.4:- No. of lines passing through a single point is </p><p>(a) One (b) Two (c) Five (d) infinite </p><p>4) </p><p>a) b) c) d) </p><p>Qes.5:- If three or more than three points lie on the same line then the points are </p><p>called </p></li><li><p>Page 93 of 280 </p><p>(a) Non-collinear points (b) Collinear points </p><p>(c) Concurrent points (d) intersecting points </p><p>5) </p><p>a) b) c) d) </p><p>Qes.6:- The sum of two sides of a triangle in comparison to third side is always </p><p>(a) Equal (b) greater (c) less (d) no relation </p><p>6) /</p><p>a) b) c) d) </p><p>Qes.7:- To draw a plane we need atleast points- </p><p>(a) 2 points (b) infinite no. of points (c) 3 points (d) 5 points </p><p>7) </p><p>a) b) c) d) </p><p>Qes.8:- For similarity criterian in triangle which one we have to take as axiam </p><p>(a) SAS (b) ASA (c) AAS (d) RHS </p><p>8)</p><p>a)SAS (b) ASA (c) AAS (d) RHS </p><p>Qes.9:- Let in similar triangles ABC and DEF areas are 64cm2 and 121 cm2 </p><p>respectively if EF = 15.4cmthenBC will be </p><p>(a) 11.2 cm (b) 43.2 cm (c) 15 cm (d) 9.6 cm </p><p>9) ABC ~ DEF EF = </p><p>15.4 BC </p><p>(a) 11.2 (b) 43.2 (c) 15 (d) 9.6 </p></li><li><p>Page 94 of 280 </p><p>ANSWER (GEOMETRY) </p><p>Q1:- a) 13CM </p><p>Q2:- b) 2Points </p><p>Q3:- b) supplementary </p><p>Q4:- d) infinite </p><p>Q5:- b) collinear </p><p>Q6:- b) greater </p><p>Q7:- c) 3points </p><p>Q8:- a) SAS </p><p>Q9:- a) 11.2 cm </p><p>TRIGONOMETRY </p><p>Qes.1:-If x,y,z are the interior angles of a triangle xyz. Then sin</p><p>2cos</p><p>+</p><p>2+ </p><p> cos</p><p>2sin</p><p>+</p><p>2=? </p><p>a) 0 b) c) 1 d) 2 </p><p> xyz x,y z sin</p><p>2cos</p><p>+</p><p>2+cos</p><p>2sin</p><p>+</p><p>2</p><p>b) 0 b) c) 1 d) 2 </p></li><li><p>Page 95 of 280 </p><p>Qes.2:- The value of tan( /2- ) sin( /2 - )cos(/2-) is </p><p>1/tan2 b) tan2 c) (cos3)/sin d) 1/sec2 </p><p> tan </p><p>2 sin </p><p>2 cos </p><p>2 </p><p> a) </p><p>1</p><p> 2b) tan2 c) </p><p>cos 3</p><p>sin d) </p><p>1</p><p>sec 2</p><p> Qes.3:- if p+ 5 cosec2 73 5 tan2 27= 5sec 0 then value of p is </p><p>a) 1 b) 0 d)7 d) 1/7 </p><p>3) p+ 5cosec2 730- 5 tan2 27 = 5 sec 00 p</p><p>a) 1 b) 0 d)7 d) 1</p><p>7 </p><p>Qes.4:- If tan cot =0, 0</p></li><li><p>Page 96 of 280 </p><p>a) 2 b)1</p><p> 2 c) 1 d) </p><p>1</p><p>2 </p><p>Qes.7:- If sin 5 = cos7 then value of 12 is </p><p> 7) sin 5= cos 7 12 </p><p> a)1 b)30 c)60 d)90 </p><p>Qes.8:- If sec =2/3 then value of 9 tan2+ 9 is </p><p>8) sec=2</p><p> 3tan2+ 9</p><p> a)5 b)9 c)4 d)6 </p><p>Qes.9:- If 4m(cos2- cos3)+ 1-sin2+1-cos2=2cos2sin2+1then value of m is: </p><p>m (cos2-cos3)+1-sin2+1- cos2= 2cos2 sin2+1 </p><p>m</p><p> a)1/2 b)2 c)3 d)1/3 </p><p>ANSWER </p><p>1. c </p><p>2. c </p><p>3. b </p><p>4. d </p><p>5. a </p><p>6. d </p><p>7. d </p><p>8. c </p><p>9. a </p></li><li><p>Page 97 of 280 </p><p> MENSURATION </p><p>Qes.1:-If in a triangle s-a =7cm , s-b=8cm, s-c=6cm then s=? </p><p> Q1) s-a = s-b= s-c= s </p><p>a) 20cm b) 21 cm c)21 cm d)10.5cm </p><p>Qes.2:-Area of an equilateral triangle with side 6cm is </p><p>Q2) </p><p>a) 9 3cm b)6cm c)36 3cm d)6 3cm </p><p>Qes.3:-How much sheet will be required to make a container with lid whose length </p><p>is 13m , breadth is 8 m and height is 4m </p><p>Q3) </p><p> a)3762 b)2562 c)4002 d)4162 </p><p>Qes.4:-If the volume and surface area of a sphere is numerically same then its </p><p>radius is </p><p>Q4) </p><p> a)3 b)2 c)3 d)3.5 </p><p>Qes.5:- One diagonal and perimeter of a rhombus are 24cm and 52cm </p><p>respectively. The other diagonal is </p><p>Q5) </p><p> =22</p><p>7 </p><p> a)15cm b)12cm c)10cm d)13cm </p><p>Qes.6:- If half the circumference of a circle is a 154cm. then diameter of the </p><p>circle is (=22/7) </p></li><li><p>Page 98 of 280 </p><p>Q6) =22</p><p>7 </p><p> a)64cm b)78cm c)86cm d)98cm </p><p>Qes.7:- Find the length of the largest rod that can be placed in a box whose </p><p>dimensions are 30cm, 24cm and 18cm? </p><p>Q7) </p><p>a)30 3cm b)30cm c)30 2 cm d)30 5 cm </p><p>Qes.8:- The curved surface area of a cone is twice the curved surface area of </p><p>other cone and the slant height of latter is twice the slant height of first </p><p>cone. Find the ratio of their radii? </p><p>Q8) </p><p> a)1:4 b)22:41 c)4:1 d) 41:22 </p><p>Qes.9:- If the circumference of edge of a hemisphere is 132cm, find the radius of </p><p>hemisphere: </p><p>Q9) </p><p> a)10.5cm/( ) b)21.2cm/( ) </p><p>c)21.5cm/( ) d)21cm/( ) </p><p>Qes.10:- The volume a cylindrical pipe is 7392cm3. Its length is 21cm and its </p><p>external diameter is 22cm. its thickness is. </p><p>Q10) </p><p>a) 0.5cm( ) b)3cm ( ) </p><p>c)4cm ( ) d)2cm ( ) </p></li><li><p>Page 99 of 280 </p><p>Qes.11:- If the perimeter of a circle is increased by 20%, then area will be </p><p>increased by </p><p> a)44% b)40% c)46% d)48% </p><p>Q11) 20%</p><p>a) 44% b)40% c)46% d)48%</p><p>ANSWER MENSURATION </p><p>1. c </p><p>2. a </p><p>3. a </p><p>4. c </p><p>5. c </p><p>6. d </p><p>7. c </p><p>8. c </p><p>9. d </p><p>10. b </p><p>11. a </p><p>Percentage </p><p>Qes.1:- Increase of 20% in Rs 400 gives a total of </p><p>(a) Rs 480 b)Rs 320 c)Rs 420 d)Rs380 </p><p>Q1) 400 20%</p><p>a) 480 b) 320 c) 420 d) 380</p><p>Qes.2:- Decrease of 25% in Rs 500 will give a total of </p></li><li><p>Page 100 of 280 </p><p>a) Rs375 b)Rs625 c)Rs 525 d)Rs475 </p><p>Q2) 500 25%</p><p>a) 375 b)625...</p></li></ul>


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