Maths Rocks Quiz ( Mrq)

15 Questions | By Keshushivang | Last updated: Mar 19, 2022 | Total Attempts: 69

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Maths rocks is facebook page for promoting maths We had organised a quiz on the facebook page. Those who cant give the quiz or want to give quiz again can solve the questions here: 1. There will be 5 easy questions carrying 1 point each There will be 4 average questions carrying 2 points each There will be 6 tough ones carrying 3 points each. 2. Time limit easy 8 mins average 9min hard 10 min Maths rocks www. Facebook. Com/mathsrocks Some Important Instructions 1. NC0 , nC1 , nC2 ,…………. . NCn are represented by C0 , C1 , C2 , …………. Cn. 2. X^y means ‘x’ raise to the power ‘y’. 3. Arc sin

Questions and Answers

1.

EASY QUESTION 1 Find sum of series C0 + C1/2 + C2/3 +………Cn/(n+1).
- A.
  
  2^(n+1) - 1/(n+1)
- B.
  
  4(5+n)+3(2-n)
- C.
  
  2^(n+1)/(n+1)
- D.
  
  4(5-n)+3(2+n)
2.

EASY QUESTION 2 Find the no. of non negative integral solutions of 3x + y + z =24
- A.
  
  438
- B.
  
  351
- C.
  
  117
- D.
  
  108
3.

EASY QUESTION 3 Angle between pair of tangents drawn to the ellipse 3(x)^2 + 2(y)^2 = 5 from the point (1,2) is ?
- A.
  
  90
- B.
  
  180
- C.
  
  Arctan(6)- arctan(1)
- D.
  
  Arctan(12/root5)
4.

EASY QUESTION 4 No. of real roots of the equation e^(sinx) +e^(-sinx) -2 = 0 in the interval [-pi,+pi]
- A.
  
  3
- B.
  
  4
- C.
  
  2
- D.
  
  8
5.

Easy question 5 Find the rank of the word CRICKET in the dictionary which prints only 7 letter words made from CRICKET only.
- A.
  
  117
- B.
  
  554
- C.
  
  531
- D.
  
  553
6.

average question 1 let (xr,yr) (r is subscript) : r={1,2,3,4} be the points of intersection of the parabola y^2=4ax and the circle x^2+y^2+2gx+2fy+c=0. Find y1+y2+y3+y4.
- A.
  
  0
- B.
  
  12.6
- C.
  
  -1
- D.
  
  1
7.

AVERAGE QUESTION 2 Integrate {(arctan(ax) – arctan(x))/x} limit from (0 to infinity).
- A.
  
  Pi/2 ln a
- B.
  
  1
- C.
  
  -1
- D.
  
  Pi/4
8.

AVERAGE QUESTION 3 Sigma(sum)(from n=0 to n=infinty) {1/(3n+1) – 1/(3n+2)}.
- A.
  
  Ln 2/3
- B.
  
  Ln 2
- C.
  
  2e/9 root 5
- D.
  
  pi/3*(root3)
9.

AVERAGE QUESTION 4 Find the area bounded interiorly by graph of |y|=e^(-|x|) – 1/2 .
- A.
  
  1
- B.
  
  6 + ln2
- C.
  
  Ln4 - 2
- D.
  
  Log 2^-3
10.

HARD QUESTION 1 If x^3 + 3px^2 + 3qx +r=0 and x^2 + 2px+q=0 have a common root, then value of 4(p^2-q)(q^2-pr) = ?
- A.
  
  (pq-r)^2
- B.
  
  Pq-r
- C.
  
  0
- D.
  
  1
11.

HARD QUESTION 2 Five ordinary dice are rolled at random and the sum of the numbers shown on them is 16. What is the probability that the numbers shown on each is anyone from 2,3,4 and 5?
- A.
  
  5/81
- B.
  
  1/8
- C.
  
  137/735
- D.
  
  5/648
12.

HARD QUESTION 3 If the area bounded by the curve f(x)=x^3/3 –x^2+a and lines x=0,x=a and y=0 is minimum then find value of ‘a’?
- A.
  
  2/3
- B.
  
  Sqrt 3
- C.
  
  0
- D.
  
  1/3
13.

HARD QUESTION 4 How many 4 letter words can be formed by taking by taking letters from ALLAHABAD
- A.
  
  63
- B.
  
  25840
- C.
  
  287
- D.
  
  2994
14.

HARD QUESTION 5 if (1+x)^n = C0+C1x+C2x^2……..Cnx^n. then find the sum of C1^2+2(C2)^2+3(C3)^2………….n(Cn)^2
- A.
  
  [(2n-1)!]/[(n-1)!]^2
- B.
  
  N(1+x)^(n-1)
- C.
  
  (2n+1)C(n+1)/(n+2)
- D.
  
  2n + 1
15.

HARD QUESTION 6 Sigma(k=1 to k=n) arctan(2k/2+k^2+k^4)
- A.
  
  Pi/4
- B.
  
  (n-2)*pi/8
- C.
  
  Arc tan(n^2 + n +1) - pi/4
- D.
  
  2pie