MBA Entrance Exams / #CMAT

April 04, 2017 @ 01:15 PM

Important Quant Questions with solution

MBA aspirants who are appearing in forthcoming CMAT second test from 21st February 2013 to 25th February 2013, may find following Quant questions useful for practice: 

Question 

The equation 2x2 + 2(p + 1) x + p = 0, where p is real, always has roots that are
 
(1)Equal
(2)Equal in magnitude but opposite in sign
(3)Irrational
(4)Real
(5)Complex Conjugates
 
Answer
 
Correct Choice - (4). Correct Answer is - The Roots are Real
 
Explanatory Answer
 
The value of the discriminant of a quadratic equation will determine the nature of the roots of a quadratic equation. 
 
The discriminant of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac.
 
•If the value of the discriminant is positive, i.e. greater than '0', then the roots of the quadratic equation will be real.
•If the value of the discriminant is '0', then the roots of the quadratic equation will be real and equal.
•If the value of the discriminant is negative, i.e. lesser than '0', then the roots of the quadratic equation will be imaginary. The two roots will be complex conjugates of the form p + iq and p - iq.
 
Using this basic information, we can solve this problem as shown below.
In this question, a = 2, b = 2(p + 1) and c = p
Therefore, the disciminant will be (2(p + 1))2 - 4*2*p = 4(p + 1)2 - 8p
= 4[(p + 1)2 - 2p]
= 4[(p2 + 2p + 1) - 2p]
= 4(p2 + 1)
 
For any real value of p, 4(p2 + 1) will always be positive as p2 cannot be negative for real p.
Hence, the discriminant b2 - 4ac will always be positive.
 
When the discriminant is greater than '0' or is positive, the roots of a quadratic equation will be real.
 
Therefore, the answer choice is 4.
 
 
 

Crucial Dates, You Should not Miss

TAPMI, Manipal
Admission Application closes on January 16, 2018 for 2018-20
BIMTECH, Greater Noida
Admissions open for PGDM Programmes at BIMTECH. Apply Now !
Lal Bahadur Shastri Institute of Management
Admissions are Open at LBSIM, Delhi. Apply Now !
FORE School of Management
Apply for PGDM & PGDM-IB Programmes. Application Deadline is December 22, 2017.
Goa Institute of Management
PGDM Admissions Open at GIM. Apply Before January 5, 2018
NIRMA
Last Date to Apply for MBA (Full Time) Programme at NIRMA is January 09, 2018
XAT 2018
Application Last Date 30th November 2017
IMI New Delhi
Application closes 4th December 2017
XIM Bhubaneshwar
Last Date 8th December 2017
SIBM Bengaluru
Apply for SNAP 2017 to be held on Dec 17 and apply for SIBM-Bengaluru through the SNAP Form
Institute of Rural Management Anand
IRMASAT will be conducted on February 4,2018, Apply Before December 31,2017
IBSAT 2017
Last date for IBSAT registration is December 12 , 2017
SSBF
Last date to register for SNAP is 24th November, 2017. Last date for SSBF is 2nd January 2018
SIBM Hyderabad
Apply for SNAP 2017 to be held on Dec 17 and apply for SIBM-Hyderabad through the SNAP Form
K J Somaiya Institute of Management Studies & Research, Mumbai
Last date for Application is 31st Jan, 2018
SDMIMD Mysore
Application for PGDM 2018-20 at SDMIMD is open till February 28, 2018
Institute of Management Technology
Application closes on November 24, 2017
MDI Murshidabad
Application for PGPM 2018-20 at MDI Murshidabad is open till November 24, 2017

Admission Open Now

Following Colleges are accepting applications.

INTERNATIONAL MANAGEMENT INSTITUTE

Admissions open for 2018-20

PGDM, PGDM (HRM), PGDM(B & FS), Executive PGDM

Apply Online