permutation and combination Question no. 31 In a plane , there are 10 points out of which 4 are collinear , then the number of triangles that can be formed by joining these points are looks_one 60 looks_two 116 looks_3 120 looks_4 None of these Answer Option looks_two 116 Solution Solution : No. of triangles = n C 3 - p C 3 = 10 C 3 - 4 C 3 = 120 - 4 = 116 Question no. 32 The number of straight lines joining 8 points on a circle is looks_one 8 looks_two 16 looks_3 24 looks_4 28 Answer Option looks_4 28 Solution Solution : No. of straight line = n(n-1)/2 = 8 *7 / 2 = 28 Question no. 33 The number of diagonals in a polygon of m sides is looks_one m(m-5)/2! looks_two m(m-1)/2! looks_3 m(m-3)/2! looks_4 m(m-2)/2! Answer Option looks_3 m(m-3)/2! Solution Solution : The number of diagonals in a polygon of m sides is m(m-3)/2! Question no. 34 How many ...

Permutation and Combination Question no. 16 What is the number of three digit odd numbers formed by using the digits 1,2,3,4,5,6 if repetition of digits is allowed ? looks_one 60 looks_two 108 looks_3 120 looks_4 216 Answer Option looks_two 108 Solution Solution : Number of digits at one's place = 1 , 3 , 5 [Total number is 3] Number of digits at ten's place = 6 [1,2,3,4,5,6] Number of digits at hundred place =6 [ 1, 2 , 3 , 4 , 5 , 6 ] Total number of ways = 3 * 6 * 6 = 108 Question no. 17 What is the number of ways of arranging the letters of the word "BANANA" so that no two N's appear together? looks_one 60 looks_two 40 looks_3 80 looks_4 100 Answer Option looks_two 40 Solution Solution : Total no. of ways = 6!/(3!2!) = 60 Two N's come together = 4!*5 / 3! = 20 No. of ways no two N's appear together = 60 - 20 = 40 Question no. 18 How many times does the ...

Work And time Question no. 1 The H.C.F and L.C.M of two numbers are 21 and 4641 respectively. If one of the numbers lies between 200 and 300, then the two numbers are looks_one 273 , 357 looks_two 273 , 361 looks_3 273 , 359 looks_4 273 , 363 Answer Option looks_one 273 , 357 Solution Solution : HCF = 21 , LCM = 4641 = 13 * 3 * 7 * 17 Each number has 21 as factor First number = 21 * 13 = 273 Second Number = 21 * 17 = 357 Question no. 2 What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24? looks_one 264 looks_two 259 looks_3 269 looks_4 None of these Answer Option looks_two 259 Solution Solution : LCM ( 8 ,11 , 24) = 264 LCM is the smallest number that is divisible by all their factors 264 is the number completely divisible by 8, 11 and 24 Number is increased by 5 = 264 - 5 = 259 Question no. 3 Find the greatest number that will divide 148,246 and 623 le...

Trigonometry Question no. 1 The minimum value of 2sin 2 θ + 3cos 2 θ is looks_one 3 looks_two 2 looks_3 0 looks_4 1 Answer Option looks_two 2 Solution Solution : 2sin 2 θ + 3cos 2 θ = 2sin 2 θ + 2cos 2 θ + cos 2 θ 2(sin 2 θ + cos 2 θ) + cos 2 θ 2 + cos 2 θ -1 ≤ cosθ ≤ 1 0 ≤ cos 2 θ ≤ 1 2 ≤ 2 + cos 2 θ ≤ 3 Question no. 2 The simplest value of sin 2 x + 2tan 2 x–2sec 2 x + cos 2 x is looks_one -1 looks_two 1 looks_3 0 looks_4 2 Answer Option looks_one -1 Solution Solution : sin 2 x + 2tan 2 x–2sec 2 x + cos 2 x sin 2 x + cos 2 x + 2 (tan 2 x - sec 2 x ) = 1 + 2 (-1) = 1 - 2 = -1 Question no. 3 If cos 4 θ– sin 4 θ = 2/3 , then the value of 2cos 2 θ–1 is looks_one 0 looks_two 1 looks_3 2/3 looks_4 3/2 Answer option looks_3 2/3 Solution Solution : Question no. 4 The value of tan4°. tan43°. tan47°. tan86° is looks_one ...

3-D Question no. 1 Co-ordinate of a point equidistant from the points (0,0,0) ,(a,0,0) , (0,b,0) , (0,0,c) is looks_one looks_two looks_3 looks_4 (a,b,c) Answer Option looks_3 Solution Solution : is the point which is equidistant from the (0,0,0) ,(a,0,0) , (0,b,0) , (0,0,c). Question no. 2 Let (3,4,-1) and (-1 ,2 ,3 ) are the end points of a diameter of sphere. then the radius of the sphere is equal to looks_one 1 looks_two 2 looks_3 3 looks_4 9 Answer Option looks_3 3 Solution Solution : where x 1 , y 1 , z 1 and x 2 , y 2 , z 2 are the end points of diameters. Now, put the value in the formula . Question no. 3 The equation of the sphere touching the three co-ordinate planes is looks_one x 2 + y 2 + z 2 + 2a( x + y + z) + 2a 2 = 0 looks_two x 2 + y 2 + z 2 - 2a( x + y + z) + 2a 2 = 0 looks_3 x 2 + y 2 + z 2 ± 2a( x + y + z) + 2a 2 = 0 looks_4 None of t...