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CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 7 - MCQExams.com

The value of the sum 1.2.3+2.3.4+3.4.5+....... upto n terms=
  • 16n2(2n2+1)
  • 16n2(n21)(2n1)(2n+3)
  • 18(n2+1)(n2+5)
  • 14(n)(n+1)(n+2)(n+3)
If the coefficients of x9,x10,x11 in the expansion of (1+x)n are in arithmetic progression then n241n=
  • 398
  • 298
  • 398
  • 198
The value of 1(2n1)!0!+1(2n3)!2!+1(2n5)!4!+....+11!(2n2)! equal to
  • 22n1
  • 22n2
  • 22n3
  • 22n2(2n1)!
If xR, find the minimum value of the expression 3x+31x.
  • 32
  • 23
  • 33
  • none of these
Sum of the series
(100C1)2+2(100C2)2+3(100C3)2+.....100(100C100)2 equals:
  • 299[1.3.5.....(199)](99)!
  • 100.100C100
  • 50.200C100
  • 100.199C99
The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+ ...... is  n(n+1)22  when n is even.When n is odd the sum is -
  • 3n(n+1)2
  • 8n3+6n2+n3
  • n(n+1)24
  • [n(n+1)4]2
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12+2.22+32+2.42+52+2.62+..... If B2A=100λ, then λ is equal to
  • 464
  • 496
  • 232
  • 248
If z22z+4=0 then the value of (z2+2z)2+(z24+4z2)2+(z38+8z3)2+........+(z24224+224Z24)2 is equal to.
  • 24
  • 32
  • 48
  • None of these
The odd natural numbers have been divided in groups as (1,3);(5,7,9,11);(13,15,17,19,21,23);..... Then the sum of numbers in the 10th group is
  • 4000
  • 4003
  • 4007
  • 4008
If 9@3=12,15@4=22,16@14=4, then what is the value of 6@2=?
  • 26
  • 1
  • 30
  • 8
 5 2 7
 ? 3 1
 4 5 2
 -15 7 13
Select the missing number from the given alternatives.
  • 1
  • 5
  • 9
  • 7
Select the missing number from the given alternatives.
34214
65444
527?
  • 58
  • 14
  • 49
  • 4
If 12×16=188 and 14×18=248, then find the value of 16×20=?
  • 320
  • 360
  • 316
  • 318
Select the missing number from the given alternatives.
908224_58dcb79bac6e47e4a5a056e98ecf5ebf.png
  • 110
  • 115
  • 121
  • 54
If 28÷11=8,39÷21=7,45÷27=4, then 95÷25=?
  • 11
  • 9
  • 16
  • 5
In a row of girls, Mridula is 18th from the right and Sanjana is 18th from the left. If both of them interchange their position, Sanjana becomes 25th from the left, how many girls are there in the row?
  • 40
  • 41
  • 42
  • 35
Choose the correct answer from the alternatives given :
The sum of 12+1+13+2+14+3+.....+1100+99 is
  • 9
  • 10
  • 11
  • None of these
Choose the correct answer alternatives given.
Select the missing number from the given alternatives.

908756_fd63ade1fdca4c419eb6d7cc3bd855da.png
  • 18
  • 21
  • 5
  • 17
If 13+23+....+103=3025, then the value of 23+43+.....+203 is
  • 7590
  • 5060
  • 24200
  • 12100
In our number system the base is ten. If the base were changed to four you would count as follows: 1,2,3,10,11,12,13,20,21,22,23,30,.... The twentieth number would be:
  • 20
  • 38
  • 44
  • 104
  • 110
The value of the product 
612×614×618×6116×.. up to infinite terms is
  • 6
  • 36
  • 216
  • 512
If a and b are two unequal positive numbers, the:
  • 2aba+b>ab>a+b2
  • ab>2aba+b>a+b2
  • 2aba+b>a+b2>ab
  • a+b2>2aba+b>ab
  • a+b2>ab>2aba+b
If y=x+x2+x3+... up to infinite terms, where x<1, then which one of the following is correct?
  • x=y1+y
  • x=y1y
  • x=1+yy
  • x=1yy
If 1.3+2.32+3.33+...+n.3n= (2n1)3a+b4 then a and b are respectively 
  • n,2
  • n,3
  • n+1,2
  • n+1,3
The value of 1log3e+1log3e2+1log3e4+...  up to infinite terms is
  • loge9
  • 0
  • 1
  • loge3
If x=1y+y2y3+... upto infinite terms, where |y| < 1, then which one of the following is correct?
  • x=11+y
  • x=11y
  • x=y1+y
  • x=y1y
6k=1[sin2kπ7icos2kπ7]=

  • 1
  • 0
  • i
  • i
Arrange these numbers in ascending order. 
756,567,657,676 
  • 657,567,756,676
  • 567,657,676,756
  • 756,676,657,567
  • 676,756,567,657
For some natural N , the number of positive integral x satisfying the equation, 
1!+2!+3!+......+(x)!=(N)2 is :
  • None
  • One
  • Two
  • Infinite
State True or False.
1+15+352+553+..... = 138
  • True
  • False
State true or false.
199.1+197.3+195.5+.....3.197+1.397=666700
  • True
  • False
The sum of the given series 1+3+5+7+9+......+53 is 729.
  • True
  • False
If Sn=nr=12r+1r4+2r3+r2 then S20 =
  • 220221
  • 420441
  • 439221
  • 440441
The sum to 50 terms of the series 12+34+78+1516+.... is equal to
  • 25051
  • 1250
  • 250+49
  • 2501
50r=1[149+r12r(2r1)]=
  • 150
  • 199
  • 1100
  • 1101
The value of x satisfying the equation 5050(12+23+34+......+50495050)1+12+13+......+15050=x5050 is 
  • 1
  • 5049
  • 5050
  • 5051
If 1+x2=3x, then 24n=1(xn+1xn) is equal to 
  • 48
  • 48
  • ±48(ωω2)
  • none of these
If |a|<1 and |b|<1 then s=1+(1+a)b+(1+a+a2)b2+(1+a+a2+a3)b3+...is.
  • 1(1b)(1ab)
  • 1(1+b)(1ab)
  • 1(1b)(1+ab)
  • 1(1+b)(1+ab)
The sum of the series 1(1×2)+1(2×3)+1(3×4)+.......+1(100×101) is equal to

  • 200101
  • 100101
  • 50101
  • 25101
If |a|<1 and |b|<1 then S=1+(1+a)b+(1+a+a2)b2+...=
  • 1(1b)(1ab)
  • 1(1+b)(1ab)
  • 1(1b)(1+ab)
  • 1(1+b)(1+ab)
If (1+3+5+....+p)+(1+3+5+....+q)=(1+3+5+.....+r), where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of p+q+r, (where P>6 ) is :
  • 12
  • 21
  • 27
  • 24
Let Tn=nr=1nr22r.n+2n2,Sn=n1r=0nr22r.n+2n2, then
  • Tn>SnnϵN
  • Tn>π4
  • Sn<π4
  • limnSn=π4
If Sn=32+3322+33322+.... upto n terms =an+1+bbncd (where a,b,c,dϵ N), then ?

  • a+b+c+d=28
  • b+d=a+c
  • ac=b+d
  • dc=ab
Sum of the series 1+2.2+3.22+4.23+..+100.299 is
  • 100.2100+1
  • 99.2100+1
  • 99.21001
  • 100.21001
The value of sum n=n=123nis equal to:
  • 1
  • 3
  • 15/4
  • 7/3
Pam likes the numbers 1689 and 6891. Knowing this, which pair of numbers will she like among the ones below?
  • 1981 and 1891
  • 19 and 91
  • 190 and 160
  • 1198911 and 1168611
Let Sn=312+512+23+712+23+33+912+23+33+43+....... up to n terms, then limnSn  is equal to  
  • 2
  • 3
  • 6
  • 1
A=(2+1)(22+1)(24+1).....(22016+1). The value of (A+1)12016 is
  • 4
  • 2016
  • 24032
  • 2
Let nth term of sequence 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,..... is given by tn , then ?
  • t100=14
  • t200=20
  • t300=24
  • t400=28

given relation is  1n+1+1n+2+.....+12n>1324< for all natural numbers n>1

  • True
  • False
0:0:1


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