Start the test Question no. 1 Suppose, ω and ω 2 are two distinct cube roots of unity different from 1. Then, what is (ω 1 - ω 2 ) 2 equal to? 3   1   -1   -3 Question no. 2 What is the argument of the complex number (−1 − i) , where i = √(−1)?   5π/4   -5π/4   3π/4 None of these Question no. 3 What is one of the square roots of 3 + 4i, where i = √(−1)? 2+i   2-i   -2 + i   -3 - i Question no. 4 Consider the following statements I. ( ω 10 +1) 7 + ω = 0 II. ( ω 105 +1) 10 = p 10 for some prime number p, where, ω ≠ 1 is a cubic root of unity. Which of the above statement(s) is/are correct? Only I   Only II   Both I and II   Neither I nor II Question no. 5 The origin and the roots of the equation z 2 + pz + q = 0 form an equilateral triangle, if p 2 = q ...

Practice question For Complex Number 1.If w is a complex cube root of unity and x 2 = w 2 - w -2 , then what is the value of x 2 + 4x + 7 ? 2. If z is complex number such that z + z -1 = 1 , then what is the of z 99 + z -99 ? 3. If the point z 1 = 1 + i is the reflection of the point z 2 in the line i z - iz = 5 , what is the point z 2 ? 4. What is the real part of (sinx + icosx) 3 ? 5. If x = a + b , y = aα + bβ , z = aβ + bα , where α and β are complex cube root of unity , then show that xyz = a 3 + b 3 . 6. Let z be the complex number such that |z| + z = 3 + i , what is the value of |z| ? 7. Find the condition for which the complex number sinx + icos2x and cosx - isin2x are conjugate to each other ? 8. For all complex number z 1 , z 2 , satisfying |z 1 | = 12 and |z 2 - 3- 4i | = 5 , what is the minimum value of |z 1 - z 2 | ? 9. If iz 3 + z 2 -z + i = 0 , then show that |z| = 1. 10. If z 1 and z 2 are two non...

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 ...

Boat and stream Question no. 1 A person can swim in still water at 4 km/h. If the speed of water is 2 km/h, how many hours will the man take to swim back against the current for 6 km. looks_one 3 looks_two 4 looks_3 4.5 looks_4 None of these Answer Option looks_one 3 Solution Solution : Speed of swim = 4 km/hr Speed of water = 2 km/ hr against the water speed of swim = 2 km/hr Time taken by man = distance/ speed = 6 / 2 = 3 hr Question no. 2 A man can swim in still water at 4.5 km/h, buttakes thrice as long to swim upstream than downstream. The speed of the stream is looks_one 2.25 looks_two 2 looks_3 3 looks_4 None of these Answer Option looks_one 2.25 Solution Solution : speed of swim = 4.5 km/hr Time taken to downstream = x hr Time taken to upstream = 3x hr Speed of stream = z distance of upstream = distance of downstream (4.5 - z) * 3x = (4.5 + z )* x ( 4.5 - z )* 3 = 4.5 + z 4.5 + z = 13.5 - 3...

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 ...