MATHEMATICS QUADRATIC EQUATION AND COMPLEX NUMBER QUIZ-9

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1. Suppose that two persons A and B solve the equation x^2+ax+b=0. While solving A commits a mistake in the coefficient of x was taken as 15 in place of -9 and finds the roots as -7and -2. Then the equation is
•  x2+9x+14=0
•  x2-9x+14=0
•  x2+9x-14=0
•  x2-9x-14=0
Solution

Q2.

•  |z2|<k
•  |z2|=k
•  z2=0
•  |z2|=1
Solution

Q3.  If a>0,b>0,c>0, then both the roots of the equation ax^2+ bx+c=0
•  Are real and negative
•  Have negative real part
•  Are rational numbers
•  None of the above
Solution

Q4. Which of the following statement is true?
(i) The amplitude of the product of the two complex numbers is equal to product of their amplitudes
(ii) For any polynomial f(x) with real coefficients imaginary rosts always occur in conjugate pairs
(iii) Order relation exists in complex numbers whereas it does not exist in real numbers
(iv) The values of Ï‰ used as a cube root of unity and as a fourth root of unity are different
•  (i)and (ii) only
•  (i) and (iv) only
•  (iii) and (ii)only
•  (i),(ii) and (iv) only
Solution
No solution available

Q5.

•  (-∞,-3)
•  (-∞,-3)∪(3,∞)
•  (-∞,-3]∪[-2,0)∪(0,2]∪[3,∞)
•  R
Solution

Q6. Let A,B,C be three collinear points which are such that AB.AC=1 and the points are represented in the Argand plane by the complex numbers 0, z1 and z2 respectively, Then,
•  z1 z2=1
•  z1z ̅2=1
•  |z1 ||z2|=1
•  None of these
Solution
No solution available

Q7.

• a=b
•  a=b/2
•  2a=b
•  a= b/3
Solution

Q8.

• 1/4 (3+9i)
•  1/4 (3-9i)
•  1/2 (3+2i)
•  No point
Solution

Q9.If P,P' represent the complex number z_1 and its additive inverse respectively, then the equation of the circle with PP' as a diameter is
•  z/z1 =z ̅1/z
•  zz ̅=z1 z ̅1=0
•  zz ̅11+z ̅z11=0
•  None of these
Solution

Q10. The expression y=ax2+bx+c has always the same sign as, c if
•  4 ac < b2
•  4 ac > b2
•  ac < b2
•  ac > b2
Solution

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