Previous Year Solved CTET Math questions - Part1

1.The number of integers less than -3 and greater than -8 is (1) 2 (2) 3 (3) 4 (4) 6 Answer: (3) 4 Explanation: Number of integers greater than -8 and less than -3 are -7,-6,-5,-4. Hence, there are 4 numbers that are less than -3 and greater than -8. 2. The reciprocal of (-3/8)x(-7/13) (1) 104/21 (2) -104/21 (3) 21/104 (4) -21/104 Answer:(1) 104/21 Explanation: Step1: Multiply the given fractions to get (21/104). There are two negative signs            hence the answer has a positive sign. Step2: Invert the fraction to get the reciprocal of the 21/104. It comes out to              be   (104/21). 3.The number of vertices in a polyhedron which has 30 edges and 12 faces is (1) 12 (2) 15 (3) 20 (4) 24 Answer: (3) 20  Solution: Here we will use the Euler's formula,                             V- E + F = 2 Where, V represents the vertices of the polyhedron, E represents Edges and F represents the faces of the polyhedron. Given that, E = 30 and F = 12 , Put these values in the Euler's formula  to get                       V - 30 + 12 = 2            => V = 2 + 30 -12 = 20 4.The distance between two places is 12 Km. A map scale is 1:25000.The distance between the two places on the map, in cm , is (1)24 (2)36 (3)48 (4)60 Answer :(3) 48 Solution: 1 cm on map represents 25000 cm or 0.250 Km Therefore, 0.25 Km is represented by 1 cm or  1Km is represented by 1/0.25  and 12 Km is represented by 1/0.25 X 12 = 48 cm 5. When half of a number is increased by 15, the result is 39. The sum of digits of the original number is (1) 6         (2) 7 (3) 9         (4) 12 Answer:(4) 12 Explanation: Step1:Let the number be X. Then half of this number be X/2. Step2:Then if (X/2) be increased by 15 then we get 39. Writing this in equation                 X/2 + 15 = 39           =>         X/2 = 24           =>            X = 48        the number is 48 Step3: Sum of digits of 48 = 4 + 8 = 12   6. If y = (x-2)/(x + 1), where y is not equal 1, then x equals (1) (y + 2/1- y)     (2) (y +2)/(y -1) (3) (y-2)/(y + 1)    (4) (2-y)/(1-y) Answer:(y + 2/1- y) Solution Step1: Multiplying both the sides by (x+1) to get, (x+1)y = (x-2) Step2: now distributing y,                                    xy + y = x -2 Step3: taking x terms on LHS, on y terms on RHS  x(y-1) = -2 - y Step4: Solving for X to get ,                                        x = (2+y)/(1-y)  7.If for triangle ABC and triangle DEF, the correspondence CAB ~ EDF gives a congruence,  then which of the following is not true ? (1) AC=DE (2) AB=EF (3) angle A= angle D (4) angle B=angle F Answer: (2) AB=EF Explanation: from the congruence CAB ~ EDF , AB should be equal to DF not EF.   8.  40% of (100 - 20% of 300) is equal to (1) 16              (2) 20 (3) 64              (4) 140 Answer:(1) 16  Explanation: Step1: 20% 0f 300 = 0.20x300 = 60 Step2:100 - 60 = 40 Step3:40% of 40 = 0.4x40 = 16 9.  HCF of two numbers is 28 and their LCM is 336. If one number is 112,then the other number is (1) 56 (2) 70 (3) 84 (4) 98 Answer:(3) 84 Explanation: Using the formula HCF X LCM = number1 x number2                      => 28x336 = 112 x number2                      => number2 = 28x336/112 = 28x3 = 84 10. IF 2/3x =0.6 and 0.02y =1, then the value of x + y^-1 is  (1) 0.92 (2) 1.1  (3) 49.1 (4) 50.9 Answer: (1) 0.92 Solution: Step1: 2/3x = 0.6 => x = 0.6x3/2 = 0.9 Step2: 0.02y = 1=> y=1/0.02 = 50 Step3: x + y^-1 = 0.9 + 50^-1 = 0.9 + 1/50 = 0.9 + 0.02 = 0.92

                                                                                    


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