# dayanand anglo vedic public school _airoli

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```					             DAYANAND ANGLO VEDIC PUBLIC SCHOOL ,AIROLI
QUESTION BANK
CLASS XI   SUB:MATHEMATICS

Q1.Write the set A= { x: x is a natural number and 4 < x < 8 } in roster form
Q2.Write the set B ={ -4 ,-3 ,-2 } in set builder form.
Q3.Write all subsets of { p, q, r}
Q4.Prove that  A  B  B   .
Q5.Prove that  A  B  B  A   A  B   A  B
Q6.Prove the De Morgan’s laws.
Q7.In a survey of 700 students in a college 180 like coke 275 like Pepsi and 95 like both.
Find how many like neither Pepsi nor coke?
Q8.Find the total number of relations from A to B where A ={1,2} abd B={a,b}
1
Q9.Find the domain and range of f(x)= 2
x 4
1              1  28
Q10.Find the value of a if f(x)=  ax and f            .
x             5 5
x 1                                 1
Q11.If f(x)=       ,then prove that f ( f ( x)) 
x 1                                  x
Q12.Draw the graph of f(x)= x  2
sin 7 A  sin 5 A
Q13.Prove that                          tan A
cos 7 A  cos 5 A
Q14.Prove that sin(A+B)sin(A-B) = sin2A-sin2B
Q15.Prove using mathematical induction that 10 2 n 1  1 is divisible by 11
Q16.Prove by induction that cos  i sin    cos n  i sin n
n

Q17.If p(n)= n 2  n  41 is prime then prove that p(1) ,p(2) ,p(3) is true and p(41) is
false.
Q18.Prove that i n  i n1  i n 2  i n3  0 ,where n is a natural number.
Q19.Solve for x and y 2x+3iy =5 + 6i

Q20.Express in a+ ib form
1  i 3
1 i3
4 n 1
1 i 
Q21.Simplify        
1 i 
Q22.Find the multiplicative inverse of
i  1i  2
i 1
Q23.Plot the complex number on the argand plane (2- i )2
1 i
Q24.Find the modulus and argument of
1 i
Q25.Prove that z  z  z
2

Q26.Express 3  i in polar form.
Q27.Solve x-3 >0 2x-1 < 9
Q28.Solve graphically x-3 > 3
Q29.A carpenter has 10 patterns of chairs and eight patterns of tables .In how many ways
can he make a pair of table and chair ?
Q30.25 buses are running between Delhi and Noida .In how many ways can a person go
from Delhi to Noida and return by a different bus ?
Q31.In how many ways n different books be arranged so that two particular books are
never together.
Q32.In how many ways can the word PENCIL be arranged so that N is always next to E.

Q33.Find the middle term(s)in the expansion of x 2  2y 2   7

9
 x2 1 
Q34.Find the coefficient of x in the expansion of   
4
 2 x
      
Q35.The first three terms of the expansion of ( x  y ) are 1, 56 and 1372 respectively.
n

Find the value of x ,y and n.
Q36.Prove that n C0  nC2  ..... n C1  nC3  ......  2 n1
Q37.Using binomial theorem show that 6 n  5n  1 is divisible by 25.
Q38.How many two digit numbers leave the remainder 1 when divided by 5?
Q39.If a,b,c are in AP then prove that b+c-a , a+c-b and a+b-c are also in Ap.
Q40.Three numbers are in AP and their sum is 15.If 1,3,9 be added to them respectively
they form a GP.Find the numbers.
Q41.The sum of four numbers in a GP is 60 and the arithmetic mean of the first and the
last is 18.Find the numbers.
Q42.Find two numbers whose arithmetic mean is 34 and geometric mean is 16.
Q43.Find the distance of (3,4) from the line 4x +5y =7
Q44.Find the distance between the parallel lines x+2y=5 and 2x+4y=12
Q45.Find the equation of the line passing through the point (1,3) such that intercept on
the y-axis exceeds the intercept on the x-axis by 4.
Q46.Find the value of A for which the lines 2x+3y=7 and Ax+6y=8 are parallel.
Q47.The angle between two lines is 45.If the slope of one of them is ¼ ,find the slope of
the other.
Q48.Find the center and radius of the circle x 2  y 2  4 x  6 y  1  0 .
Q49.Find the equation of the circle concentric with x 2  y 2  2 x  4 y  1  0 and which
touches the x-axis.
Q50.Find equation of the parabola with vetex at origin and directrix y=2.
Q51.Find the equation of the ellipse which passes through the point (-3,1) and has
2
eccentricity       .
5
Q52.Find the equation of the ellipse whose vertices are 0,6 and eccentricity is 1/3 .
x2 y2
Q53.The foci of a hyperbola coincides with the foci of the ellipse         1 .Find the
25 9
equation of the hyperbola if its eccentricity is 2.
Q54.Find the locus of the point equidistant from the points (1,3,2) and (-1,7,1)
Q55.Find the coordinates of the point which divides the line segment joining the points
(2,1,4) and (5,-2,3) in the ration 3:2 internally.
Q56.Two vertices of a triangle are (1,3,5) and (3,2,1) and its centroid is (-1,0,0). Find the
coordinates of the third vertex.
Q57.Find the lengths of the major and minor axes ,vetices ,eccentricity, foci, directrices
and latus rectum of the ellipse 16 x 2  25 y 2  400 .
Q58.Find the axes ,eccentricity and foci of the hyperbola 2 x 2  3 y 2  6 .
Q59.Find n if n C7  n C5 .
Q60.Prove that n C r  nC r 1  n1C r
Q61.Prove that A  ( B  C )  ( A  B)  ( A  C )
Q62.Find the domain and range of
x                                  x
i) f ( x)                      ii) f ( x) 
x                               x 1
2 tan x
Q63.Show that f(x)=                            is a constant function .
(1  tan 2 x) sin 2 x
ax  b
Q64.If y =f(x) =           , then prove that f(y)= x .
cx  a
Q65.Prove using induction that 11n2  12 n1 is divisible by 133.
Q66.Using induction prove that 2  3.2  4.2 2  ....... (n  1).2 n1  n.2 n .

Q67.Prove that 7  77  777  ........ 77.....7 
n
7
81
         
10 n1  9n  10 .(using induction)

Q68.Prove that     2  2  2 cos 4 A  2 cos A .
     9          3       5
Q69.Prove that 2 cos cos         cos        cos    0
13    13          13       13
sec 8 A  1 tan 8 A
Q70.Prove that                        .
sec 4 A  1 tan 2 A
Q71.In triangle ABC ,prove that sin 2 A  sin 2B  sin 2C  4 sin A sin B sin C
Q72.If A+B+C =  ,prove that tan A  tan B  tan C  tan A tan B tan C
Q73.If x  iy3  a  ib ,show that
1                         x y
  4(a 2  b 2 )
a b
Q74.If x =1+2i ,prove that x  7 x  x  16  17  24i
3      2

Q75.If p+iq =
a  i 2   show that p  q
2     2

a1 2

2

2a  i                             4a  1
2

x y3
Q76.Solve graphically x  2 y  4
x, y  0
Q77.Find all pairs of consecutive even natural numbers both of which are larger than 5
and their sum is less than 25.
Q78.The first ,second and the last terms of an AP are a,b,c respectively.Show that the
sum of the AP is
b  c  2a (a  c) .
2(b  a)
1     1     1
Q79.If         , ,           are in AP.Prove that x,y,z are in GP.
x  y 2y y  z
1     1      1
Q80.Find The sum of the series up to n terms                           ........
2.5 5.8 8.11
Q81.Find the sum of all possible products of the first n natural numbers taken 2 at a time.
 1.3.5......2n  1 
Q82.Prove that 2 n C n  2 n                    
        n!         
2n2
Q83.Using binomial theorm show that 3                 8n  9 is divisible by 64.
Q84.Find r if the cooefficient of (2r  4) and r  2 terms in the expansion of
th            th

(1  x)18 are equal.
11
      3
Q85.Find the coefficient of x in the expansion of  x 2   .
6

      x
Q86.Find the equation of the circle concentric with the circle x 2  y 2  2 x  2 y  1  0
and double of its radius.
Q87.Write the contrapositive of the statement “If it rains today then 2+2 =5”.
1  cos 2 x
Q88. Evaluate   lim      2 x 2
x
2

1  sin 2 x                dy             
Q89. If y                then show that     sec 2   x   0
1  sin 2 x                dx         4    
Q90.Two cards are drawn at random from a pack of 52 cards.What is the probability that
both the cards are of the same colour.

HIGHER ORDER THINKING SKILL QUESTIONS

Q91.Find the domain of f(x) =
x  1( x  3)
x2

Q92.IF A-B=   ,then find ( 1+tanA)(1-tanB)
4
Q93.If (1  i)(1  2i)(1  3i)........(  in)  a  ib .Then find 2.5.10….(1+n2)
1
Q94.Find the number of parallelograms that can be formed from a set of three parallel
lines intersecting another set of three parallel lines.
Q95.Find the total number of terms in the expansion of x  a   x  a
100      100

Q96.The sum of the first n terms of 2 APs are 3n+8 and 7n+15.Find the ratio of their 12th
term.
Q97.Find the coordinates if the circumcenter of the triangle whose vetices are A(2,3)
B(3,4) and C(6,8)
Q98.If X = {8 n  7n  1; n  N } and Y = {49(n  1) ; n  N} .Then prove that X is a
subset of Y.
x
Q99.If f(x) =    and c is a real number then find f (c)  f (c)
x
 
Q100.If  and  are different complex numbers with   1 ,then find                  .
1

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