Practice question For Quadratic Equation 1. How many real solutions of the equation x 2 − 3 |x| + 2 = 0 exist ? 2. Find the value of ‘a’ for which one root of the quadratic equation (a 2 − 5a + 3) x 2 + (3a − 1) x + 2 = 0 is twice as large as the other. 3. If the roots of the quadratic equation x 2 + px + q = 0 are tan30° and tan15°, respectively then what is the value of 2 + q − p ? 4. The quadratic equations x 2 – 6x + a = 0 and x 2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. what is the common root ? 5. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation , what is the quadratic equation ? 6. If (1 – p) is a root of quadratic equation x 2 + px + (1− p) = 0 , what are its roots ? 7. If roots of the equation x 2 – bx + c = 0 be two consecutive integers, then What is the value b 2 – 4c ? 8. If both the...

Start the test Question no. 1 Let z, w be complex numbers such that z + i w =0 and arg zw =π . Then arg z equals   π/4   5π/4   3π/4   π/2 Question no. 2 If z and w are two non-zero complex number such that |zw|=1, and Arg (z)-Arg(w)=π/2 , then z¯w is equal to   1   -1   -i   i Question no. 3 If |z+4|<= 3, then the maximum value of |z+1| is   4   10   6   0 Question no. 4 The conjugate of complex number is 1/(i-1), then that complex number is   1/(i+1)   -1/(i+1)   1/(i-1)   -1/(i-1) Question no. 5 What are the square roots of -2i ?   ∓(1+i)   ∓(1-i)   ∓i   ∓1 Question no. 6 What is the value of the sum of   i   2i   -2i   1+i Question no. 7 What is the number of distinct solution of the equation z 2 + |z| = 0 (where z i...

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...