Free Quantitative Reasoning MCQs with Answers

491. The identity element of N. w-r-t "+" is?

• A. 1
• B. 0
• C. 2
• D. None

Explanation: In the context of the natural numbers (N) and the addition operation (+), there is no identity element with respect to addition. The identity element for addition is an element e such that for any element a, a+e=e+a=a.However, in the set of natural numbers under addition, there is no natural number that, when added to any other natural number, leaves the other number unchanged. The natural numbers start from 1 to infinity, and "0" is not included in this set.

492. If tanθ is 1/7 then csc²θ-sec²θ/csc²θ-sec²θ=?

• A. 4/3
• B. 5/7
• C. 3/4
• D. 1/2

Explanation: We know that 60 mins= 60×60 secs=3600 seconds Hence , Using above calculations, The answer is 3600"

493. sin 3Θ/sinΘ- cos 3Θ/cosΘ=?

• A. 0
• B. sin2Θ
• C. 2 tanΘ
• D. 2

Explanation: Correct answer is "2" or "D option".It can be solved as:Hence correct option is "2".

494. The sign of tan2140 is

• A. +ive
• B. -ive
• C. may be any
• D. none

Explanation: 2140⁰ = 5×360⁰ +140⁰As tan 140 is in 2nd quadrant and tan is -ve in 2nd quad.Hence the answer is -ve

495. Q34. (cos20+isin20)5 ÷ (cos 30+ isin30)3=?

• A. cos 20+ i sin 20
• B. cos 30 + i sin30
• C. cos 10 + i sin 10
• D. cos20 - i sin 20

Explanation: Answer: b (x=1, y=0)Solution: [1-1+ii]100= 1-i1 +i ×1-i1-i100= 1-i(1-i)(1+i)(1-i)100=(1-i)212- i2100=12 -21i+ i212 - i2 100=1-2i+(-1)1-(-1)100 =1-2i-11+1100= -2i 2100= -i100=-i250=-(-1)50= 1 In x+iy form 1+0i

496. For what value of 'm' and 'n' - 1 and 2 are the roots of the polynomialx3+mx2+nx+6 ?

• A. 1,3
• B. -4 , 9
• C. 2, 7
• D. -4, 1

Explanation: Solution: This question can be solved by putting the value of roots individually in the equation, this will generate two separate equations which are to be solved using the elimination method.The roots are -1 and 2.x=2 x=-1(2)3+m(2)2+n2+6=0 (-1)3+m(-1)2+n-1+6=08+4m+2n+6=0 -1+m-n+6=014+4m+2n=0 5+m-n=027+2m+n=07+2m+n=0Now we will solve these two equations simultaneously. 2m+n=-7 m-n=-5 3m = -12 m = -123= -4Put the value of m in any of the above equations to find value of n.5+m-n=05+(-4)-n=05-4-n=0-n+1=0-n=-1n=1

497. If sec²Φ+cosec²Φ= sec²Φcosec²Φ then state the domain

• A. Φ≠n pi/2, n€Z
• B. Φ≠n pi/6, n€Z
• C. Φ≠n pi/3, n€Z
• D. Φ≠n pi, n€Z

Explanation: We know that 60 mins= 60×60 secs=3600 seconds Hence , Using above calculations, The answer is 3600"

498. sin [409 pi/2]=?

• A. 0
• B. 1
• C. -1
• D. infinity

Explanation: Here we will use the concept of coterminal angles,

499. (tan θ - θ / 2) = ?

• A. sin (θ - θ / 2)
• B. cos (θ - θ / 2)
• C. -tan (θ - θ / 2)
• D. 2sin (θ - θ) cos (θ - θ)

Explanation: Correct answer is "C option" or " -tan (θ - θ / 2) ''It is a basic question and answer can be found by taking - common from the question.

500. If cosθ=12/13 then tanθ?

• A. 5/12
• B. -5/12
• C. 12/5
• D. both a and b

Explanation: We know that 60 mins= 60×60 secs=3600 seconds Hence , Using above calculations, The answer is 3600"