10 Brain Twisters For CDS 2 2017 Applicants

Applicants of CDS 2 2017 entry aiming for academies like IMA, AFA, NA have to write 3 papers under cds written exam: CDS 2 2017 English Exam, CDS 1 2017 General Ability Exam, CDS 2 2017 Mathematics Exam. All three papers will be conducted simultaneously in one day by UPSC (Union Public Service Commission). Keeping the trend and pattern of the CDS mathematics exam we are sharing 10 Brain Twisters multiple choice question answers For CDS 2 2017 Applicants, try them and plan your preparation strategy accordingly.

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10 Brain Twisters For CDS 2 2017 Applicants

 

1. If the roots of the equation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»lx«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi mathvariant=¨normal¨»mx«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»m«/mi»«moȤnbsp;«/mo»«mo»=«/mo»«moȤnbsp;«/mo»«mn»0«/mn»«/math» are in the ration p:q, then Â«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mfrac»«mi mathvariant=¨normal¨»p«/mi»«mi mathvariant=¨normal¨»q«/mi»«/mfrac»«/msqrt»«mo»+«/mo»«msqrt»«mfrac»«mi mathvariant=¨normal¨»q«/mi»«mi mathvariant=¨normal¨»p«/mi»«/mfrac»«/msqrt»«mo»+«/mo»«msqrt»«mfrac»«mi mathvariant=¨normal¨»m«/mi»«mi mathvariant=¨normal¨»l«/mi»«/mfrac»«/msqrt»«/math» is equal to
a. 0
b. 1
c. 2
d. 3
Answer. a
2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»If«/mi»«mo»§nbsp;«/mo»«msqrt»«mrow»«mn»3«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»7«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»30«/mn»«/mrow»«/msqrt»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msqrt»«mrow»«mn»2«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»7«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»5«/mn»«/mrow»«/msqrt»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»5«/mn»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»has«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»§#945;«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»and«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»§#946;«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»as«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»its«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»roots«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»then«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»value«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»of«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»§#945;§#946;«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«/math»
a. -15
b. -5
c. 0
d. 5
Answer. c
3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»if«/mi»«mo»§nbsp;«/mo»«mfrac»«mi mathvariant=¨normal¨»p«/mi»«mi mathvariant=¨normal¨»x«/mi»«/mfrac»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»q«/mi»«mi mathvariant=¨normal¨»y«/mi»«/mfrac»«mo»=«/mo»«mi mathvariant=¨normal¨»m«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»and«/mi»«mo»§nbsp;«/mo»«mfrac»«mi mathvariant=¨normal¨»q«/mi»«mi mathvariant=¨normal¨»x«/mi»«/mfrac»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»p«/mi»«mi mathvariant=¨normal¨»y«/mi»«/mfrac»«mo»=«/mo»«mi mathvariant=¨normal¨»n«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»then«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»what«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«mo»§nbsp;«/mo»«mfrac»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»y«/mi»«/mfrac»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»equal«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»to«/mi»«mo»?«/mo»«/math»
a. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»n«/mi»«mi mathvariant=¨normal¨»p«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»m«/mi»«mi mathvariant=¨normal¨»q«/mi»«/mrow»«mrow»«mi mathvariant=¨normal¨»m«/mi»«mi mathvariant=¨normal¨»p«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»n«/mi»«mi mathvariant=¨normal¨»q«/mi»«/mrow»«/mfrac»«/math»
b. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»n«/mi»«mi mathvariant=¨normal¨»p«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»m«/mi»«mi mathvariant=¨normal¨»q«/mi»«/mrow»«mrow»«mi mathvariant=¨normal¨»mp«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»nq«/mi»«/mrow»«/mfrac»«/math»
c. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»np«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»mq«/mi»«/mrow»«mrow»«mi mathvariant=¨normal¨»mp«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»nq«/mi»«/mrow»«/mfrac»«/math»
d. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»np«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»mq«/mi»«/mrow»«mrow»«mi mathvariant=¨normal¨»mp«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»nq«/mi»«/mrow»«/mfrac»«/math»
Answer. c
4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi mathvariant=¨normal¨»If«/mi»«mo»§nbsp;«/mo»«msup»«mi mathvariant=¨normal¨»a«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi mathvariant=¨normal¨»by«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»cz«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«mo»,«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»ax«/mi»«mo»-«/mo»«msup»«mi mathvariant=¨normal¨»b«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi mathvariant=¨normal¨»cz«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»and«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»ax«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»by«/mi»«mo»-«/mo»«msup»«mi mathvariant=¨normal¨»c«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«mo»,«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»then«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»value«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»of«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mi mathvariant=¨normal¨»x«/mi»«mrow»«mi mathvariant=¨normal¨»a«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»y«/mi»«mrow»«mi mathvariant=¨normal¨»b«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»y«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»z«/mi»«mrow»«mi mathvariant=¨normal¨»c«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»z«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»will«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»be«/mi»«/mtd»«/mtr»«/mtable»«/math»
a. a+b+c
b. 3
c. 1
d. 0
Answer. c
5. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi mathvariant=¨normal¨»If«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»equations«/mi»«mo»§nbsp;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi mathvariant=¨normal¨»px«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»q«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»and«/mi»«mo»§nbsp;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi mathvariant=¨normal¨»qx«/mi»«mo»-«/mo»«mi mathvariant=¨normal¨»p«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»have«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»common«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»root«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨normal¨»then«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»which«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»one«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»of«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»following«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»correct«/mi»«mo»?«/mo»«/mtd»«/mtr»«/mtable»«/math»
a. p-q = 0
b. p+q-2 = 0
c. p+q-1 = 0
d. p-q-1 = 0
Answer. d
6. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»If«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mn»2«/mn»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/msup»«mo»+«/mo»«msup»«mn»2«/mn»«mrow»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/mrow»«/msup»«mo»,«/mo»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»then«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»value«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»of«/mi»«mo»§nbsp;«/mo»«mn»2«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»6«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»5«/mn»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»equal«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»to«/mi»«/math»
a. 0
b. 1
c. 2
d. 3
Answer. a
7. The sum and difference of two expression are «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»9«/mn»«mi»x«/mi»«mo»-«/mo»«mn»10«/mn»«/math» respectively. The HCF of two expressions will be
a. (x+1)
b. (x-1)
c. (3x+7)
d. (2x-3)
Answer. b
8. If (s-a)+(s-b)+(s-c) = s, then the value of Â«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»(«/mo»«mi»s«/mi»«mo»-«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mi»s«/mi»«mo»-«/mo»«mi»b«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mi»s«/mi»«mo»-«/mo»«mi»c«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»s«/mi»«mn»2«/mn»«/msup»«/mrow»«mrow»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/math» will be
a. 3
b. 1
c. 0
d. -1
Answer. b
9.  Â«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi mathvariant=¨normal¨»if«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»polynomial«/mi»«moȤnbsp;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»6«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»px«/mi»«mn»5«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»qx«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»3«/mn»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»divisible«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»by«/mi»«moȤnbsp;«/mo»«mo»(«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»,«/mo»«moȤnbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨normal¨»th«/mi»«mi mathvariant=¨normal¨»en«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»the«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»value«/mi»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»of«/mi»«moȤnbsp;«/mo»«msup»«mi mathvariant=¨normal¨»p«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»q«/mi»«mn»2«/mn»«/msup»«moȤnbsp;«/mo»«mi mathvariant=¨normal¨»is«/mi»«/mtd»«/mtr»«/mtable»«/math»
a. 1
b. 9
c. 10
d. 13
Answer. c
10. Let p and q be non-zero integers. Consider the polynomial A(x) = x^2 + px+q It is given that (x – m) and (x – km) are simple factors of A(x), where m is a non-zero integer and k is a positive integer, k ≥ 2. Which one of the following is correct?
a.
b.
c.
d.
Answer. b

 

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