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...

Vector Question no. 1 For any vector a and b , ( a ✕ b ) 2 looks_one a 2 - b 2 looks_two a 2 + b 2 looks_3 a 2 b 2 -( a.b ) 2 looks_4 none of these Answer Option looks_3 a 2 b 2 -( a.b ) 2 Solution Solution : ( a ✕ b ) = | a || b |sinθ n ( a ✕ b ) 2 = | a | 2 | b | 2 sin 2 θ = | a | 2 | b | 2 ( 1 - cos 2 θ) = | a | 2 | b | 2 - | a | 2 | b | 2 cos 2 θ = | a | 2 | b | 2 -( a.b ) 2 Question no. 2 A unit vector prependicular to 3 i + 2 j - k and 12 i + 5 j -5 k , is looks_one (5 i - 3 j -9 k )/√ 115 looks_two (5 i + 3 j -9 k )/√ 115 looks_3 (-5 i + 3 j -9 k )/√ 115 looks_4 (5 i + 3 j +9 k )/√ 115 Answer option looks_3 (-5 i + 3 j -9 k )/√ 115 solution Solution : Question no. 3 For any vector a and b ,if a ✕ b =0 , then looks_one a=0 looks_two b=0 looks_3 not parallel looks_4 n...

COMPLEX NUMBER Question no. 31 If z ≠1 and z 2 /(z-1) is real , then the point represented by complex number z lies looks_one Either on the real axis or on circle not passing through the origin looks_two On circle with center at the origin looks_3 Either on real circle or on a circle passing through the origin looks_4 On the imaginary axis Answer Option looks_one Either on the real axis or on circle not passing through the origin Solution Solution : Question no. 32 If ω (≠1) is cube root of unity and (1+ω) 7 = A+ Bω. then (A,B) equals looks_one (1,0) looks_two (0,1) looks_3 (-1,1) looks_4 (1,1) Answer Option looks_4 (1,1) Solution Solution : (1+ω) 7 = A+ Bω (-ω 2 ) 7 = A + Bω -ω 14 = A + Bω -(ω 3 ) 4 .ω 2 = A + Bω - ω 2 = A+ Bω 1 + ω = A + Bω A = 1 , B = 1 Question no. 33 Let ...

COMPLEX NUMBER Question no. 16 what is the square root of i, where i=&#8730-1 looks_one (1+i)/2 looks_two (1-i)/2 looks_3 (1+i)/√2 looks_4 none of these Answer Option looks_one (1+i)/2 Solution Solution : Question no. 17 If z= ,then what is the argument of z is looks_one 3&#x03C0/4 looks_two &#x03C0/4 looks_3 5&#x03C0/6 looks_4 -3&#x03C0/4 Answer Option looks_4 -3&#x03C0/4 Solution Solution : Question no. 18 what is ? looks_one 1 looks_two -1 looks_3 i looks_4 -i Answer option looks_3 i Solution Solution : Question no. 19 If A+iB= (4+2i)/(1-2i), then what is the value of A looks_one -8 looks_two 0 looks_3 4 looks_4 8 Answer Option looks_two 0 Solution Solution : Question no. 20 what is the argument of (1-sinΘ) + icosΘ looks_one π/2 -Θ/2 looks_two π/2 +Θ/2 looks_3 π/4 -Θ/2 look...

quadratic equations Question no. 16 If P(x)= ax 2 +bx+c=0 and Q(x)= -ax 2 +bx+c=0, where ac≠0 then P(x).Q(x)=0 has at least looks_one four real roots looks_two two real roots looks_3 four imaginary roots looks_4 none of these Answer Option looks_two two real roots Solution ax 2 +bx+c=0 has D = b 2 -4ac , D can be less than 0 or greater than 0 , there is a possibility of having complex roots or real roots. -ax 2 +bx+c=0 has D = b 2 + 4ac , D is always greater than or equal to 0 , so it has 2 reals roots , So P(x)Q(x) = 0 has atleast 2 real roots Question no. 17 If the roots of the given equation 2x 2 +3(λ-2)x+ λ+4=0 be equal in magnitude but opposite in sign, then λ = looks_one 1 looks_two 2 looks_3 3 looks_4 2/3 Answer option looks_two 2 solution let A and B are two roots of given quadratic equation A + B = 0 3 (λ -2)/ 2 = 0 λ = 2 Question no. 18 If a+b+c=0, then the roots of ...