Slide 1 : Welcome Group No. – 3
(class – XI, XII)
First Round : First Round
1. If a set A has 3 elements, then how many subset of set A are? : 1. If a set A has 3 elements, then how many subset of set A are?
Ans. 8 : Ans. 8
2. What is the intersection of two disjoint sets ? : 2. What is the intersection of two disjoint sets ?
Ans. Ф (empty set) : Ans. Ф (empty set)
3. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English? : 3. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
Ans. 50 people : Ans. 50 people
4. What is the domain of the function f(x) = √9 – x2 ? : 4. What is the domain of the function f(x) = √9 – x2 ?
Ans. [ -3, 3] : Ans. [ -3, 3]
5. Find the value of Sin(31π/3) : 5. Find the value of Sin(31π/3)
Ans. √3/2 : Ans. √3/2
6. What is the value of Sin15o ? : 6. What is the value of Sin15o ?
Ans. (√3 – 1)/2√2 : Ans. (√3 – 1)/2√2
7. Find the value of Sin x, if tan x = -5/12, where x lies in II quadrant. : 7. Find the value of Sin x, if tan x = -5/12, where x lies in II quadrant.
Ans. 5/13 : Ans. 5/13
8. In which country the study of trigonometry started first? : 8. In which country the study of trigonometry started first?
Ans. India : Ans. India
Slide 19 : Second Round
1. What is the multiplicative inverse of the complex number (2–3i) ? : 1. What is the multiplicative inverse of the complex number (2–3i) ?
Ans. (2+3i)/13 : Ans. (2+3i)/13
2. Who was the writer of the book ‘Bijaganita’ ? : 2. Who was the writer of the book ‘Bijaganita’ ?
Ans. Bhaskara II : Ans. Bhaskara II
3. How many 3 digit number can be formed by using the digits 1, 2, 3, 4, 5 and 6, if the digit can be repeated? : 3. How many 3 digit number can be formed by using the digits 1, 2, 3, 4, 5 and 6, if the digit can be repeated?
Ans. 216 : Ans. 216
4. How many chords can be drawn by joining the 10 points on a circle? : 4. How many chords can be drawn by joining the 10 points on a circle?
Ans. 45 : Ans. 45
5. A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected. : 5. A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Ans. 5c2 X 6c3 = 200 : Ans. 5c2 X 6c3 = 200
6. What is the middle term of the expansion of (1 + x )2n ? : 6. What is the middle term of the expansion of (1 + x )2n ?
Ans. 2ncnxn : Ans. 2ncnxn
7. What is the sum of first 10 natural number? : 7. What is the sum of first 10 natural number?
Ans. 55 : Ans. 55
8. What is the sum of the series1 + 1/2 + 1/22 + 1/23 + ……..+∞ : 8. What is the sum of the series1 + 1/2 + 1/22 + 1/23 + ……..+∞
Ans. 2 : Ans. 2
Slide 36 : Third Round
1. Find the centre of the circle x2 + y2 + 8x + 10y – 8 = 0. : 1. Find the centre of the circle x2 + y2 + 8x + 10y – 8 = 0.
Ans. ( -4, -5) : Ans. ( -4, -5)
2. What is the length of latus rectum of the parabola y2 = 4ax? : 2. What is the length of latus rectum of the parabola y2 = 4ax?
Ans. 4a : Ans. 4a
3. Who was the father of analytical geometry? : 3. Who was the father of analytical geometry?
Ans. Rene Descarte (1596-1650) : Ans. Rene Descarte (1596-1650)
4. What are the coordinate of the centroid of the triangle, whose vertices are (x1,y1,z1), (x2,y2,z2) and (x3,y3,z3) ? : 4. What are the coordinate of the centroid of the triangle, whose vertices are (x1,y1,z1), (x2,y2,z2) and (x3,y3,z3) ?
Ans.{(x1+y1+z1)/3,(x2+y2+z2)/3,(x3+y3+z3)/3} : Ans.{(x1+y1+z1)/3,(x2+y2+z2)/3,(x3+y3+z3)/3}
5. What is the projection of the vector ( i + j+ k) along the vector (i – j + k)? : 5. What is the projection of the vector ( i + j+ k) along the vector (i – j + k)?
Ans. 1/√3 : Ans. 1/√3
6. What is the distance of the plane 2x – 3y + 4z – 6 = 0 from the origin? : 6. What is the distance of the plane 2x – 3y + 4z – 6 = 0 from the origin?
Ans. 6/√29 : Ans. 6/√29
7. If p(A) = 3/5 and p(B) = 1/5, find p(A ∩ B), if A and B are independent event. : 7. If p(A) = 3/5 and p(B) = 1/5, find p(A ∩ B), if A and B are independent event.
Ans. 3/25 : Ans. 3/25
8. Two cards are drwan successively with replacement from a well shuffled deck of 52 cards. Find the probability of getting two aces. : 8. Two cards are drwan successively with replacement from a well shuffled deck of 52 cards. Find the probability of getting two aces.
Ans. 1/169 : Ans. 1/169
Slide 53 : Fourth Round
1. What is the value of lim x→0(xn – an)/(x – a) : 1. What is the value of lim x→0(xn – an)/(x – a)
Ans. nan-1 : Ans. nan-1
2. ∫[1/(ex+e-x )]dx is equal to- : 2. ∫[1/(ex+e-x )]dx is equal to- a. tan-1(ex) + c b. tan-1(e-x) + c
c. tan-1(e-x+ex) + c d. tan-1(2ex) + c
Ans. . tan-1(ex) + c : Ans. . tan-1(ex) + c
3. What is the limit of lim x→0 (sinax/sinbx) : 3. What is the limit of lim x→0 (sinax/sinbx)
Ans. b/a : Ans. b/a
4. ∫ cos 2x/(sin x + cos x)2dx = : 4. ∫ cos 2x/(sin x + cos x)2dx = -1/(sin x + cos x) + c
log(sin x + cos x) + c
log(sin x – cos x) + c
1/(sin x + cos x)2 + c
Ans. B. log(sin x + cos x) + c : Ans. B. log(sin x + cos x) + c
5. ∫1/(√x2 – a2)dx : 5. ∫1/(√x2 – a2)dx (1/2a)log|(x-a)/(x+a)|+ c
(1/2a)log|(x+a)/(x-a)| + c
log|x+√(x2-a2)| + c
(1/2a) sin-1(x/a) + c
Ans. C. log|x+√(x2-a2)| + c : Ans. C. log|x+√(x2-a2)| + c
6. ∫ex secx( 1+tanx)dx = : 6. ∫ex secx( 1+tanx)dx = ex cosx + c
ex secx + c
ex sinx + c
ex tanx + c
Ans. B. ex secx + c : Ans. B. ex secx + c
7. What is the area of ellipse x2/a2 + y2/b2 = 1? : 7. What is the area of ellipse x2/a2 + y2/b2 = 1?
Ans. Πab square unit. : Ans. Πab square unit.
8. What is the integrating factor for the differential equation x(dy/dx) + 2y = x2 : 8. What is the integrating factor for the differential equation x(dy/dx) + 2y = x2
Ans. I. F. = e∫pdx = elogx = x : Ans. I. F. = e∫pdx = elogx = x
Program organisers : Program organisers Power point By – Sh. H. P. PATEL and Sh. K. TIWARI
Questions prepared By – Sh. D. S. Sengar, Sh. H. P. Patel and Sh. B. V. Gupta.
ACKNOWLEDGEMENT : ACKNOWLEDGEMENT We are highly thankful to our Principal Ms. Kavita Singh to cooperate and motivate us for making a nice quiz program. We are also thankful to all the staff and students, they are help us directly or indirectly. THANKS