Revision (mixed)
10/11/21
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1) The number of ways in which nine different toys can be distributed among four children so that the youngest child gets 3 toys and each of the other gets 2 toys is
A) 2520 B)5120 C)7560 D) 9072
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1) If a and b are whole numbers (a,b ≠1), such that aᵇ= 49 then the value (a-b)/(a+b) is
A) 5/9 B) 5 C) 9 D) n
2) evaluate: (xᵇ/xᶜ)ᵇ⁺ᶜ⁻ᵃ .(xᶜ/xᵃ)ᶜ⁺ᵃ⁻ᵇ (xᵃ/xᵇ)ᵃ⁺ᵇ⁺ᶜ
A) x⁰ B) xᵃᵇᶜ C) xᵃ⁺ᵇ⁺ᶜ. D) none
3) If 3ᵃ + 5ᵇ = 34 and 3ᵃ⁺¹+ 5ᵇ⁺¹ = 152, then the value of a and b
A)3,3 B) 5,5 C) 2,2 D) 1,3
4) If 2ⁿ - 2ⁿ⁻¹= 4, then find the value of nⁿ.
A) 8 B) 27 C) 125 D) n
5) If 4ˣ = 8ʸ, what is the value of x/y -1 ?
A) 3 B) 2 C) 0.5 D) -0.5
6) If x¹⁾³+ y¹⁾³+z¹⁾³= 0, then find the value of (x+y+z)³
A) 0 B) xyz C) 27xyz D) n
7) If fᵃᵇᶜ = fᵃ. fᵇ. fᶜ, where a,b, c and f are all positive integers, then a²+ b²+c²=?
A) 16 B) 14 C) 18 D) 3
8) If E= 10¹⁵⁰ ÷ 10¹⁴⁶, then E+ 101?
A) 11001 B) 10101 C) 100101 D) 1000101
9) Evaluate: (0.000064)⁵⁾⁶
A) 0.0032 B) 0.00032 C)0.0000032 D) n
10) find the value of : {(p² - 1/q²)ᑫ (p-1/q)}ᵖ⁻ᑫ/{(q²-1/p²)ᑫ(q-1/p)}ᵖ⁻ᑫ
A)(p/q)ᵖ⁺ᑫ B) 1 C) p/q D) q/p
11) If E= {(x⁻¹.y²)/(x²y⁻⁴)}⁷ ÷ {(x³ y⁻⁵)/(x⁻²y³)}⁻⁵ {(x⁷⁾².y⁻¹⁾³)/(x⁵⁾².y⁻¹⁰⁾³}²⁾³. Then E+1=?
A) 3 B) 2 C) 11 D) xy+ 1.
12) if 2ˣ= 3ʸ = 6ᶻ then value of z
A) xy B) x+y C) x-y D) xy/(x+y)
13) If (a/b)ˣ⁻¹ = (b/a)ˣ⁻³, then the value of x is
A) 3 B) 2. C) 1. D) 0
14) If Q=1/(1+ aⁿ⁻ᵐ) + 1/(1+aᵐ⁻ⁿ) the Q +1 =
A) 5 B) 2 C) 11 D) 0
15) If 2= 1pᵐ and 3= 10ⁿ, then find the value of 0.15
A)10 ⁿ⁻ ᵐ⁻¹ B) 10ᵐ⁻ⁿ⁺¹ C)10ᵐ⁺ⁿ⁺¹ D) n
16) 27ᵖ= 9/3ᵖ, then the value of 1/p² is..
A) 9 B) 4. C) 16 D) 1
17) If pᵃ = qᵇ = rᶜ and pqr= 1, then which of the following is true ?
A) a+b+c= 0 B) a= b+c C) b= c+a
D) ab+ bc = 0
18) find the value of n, if 2ⁿ⁺¹. 5ⁿ = 200
A) 1 B) 2 C) 3 D) none
19) find the value of n, if
3⁵ⁿ. 9⁴ⁿ⁻²= 27³ⁿ⁻⁸/81⁻³ⁿ
A) 5 B) 2 C) 1 D) 5/2
20) For how many non positive values of x, the equation 4ˣ⁺¹+ 4ˣ⁻¹ equal to 17
A) 1 B) 2. C) 0 D) 4
21) ₘ√m = (√m)ᵐ find the value of m
A) 1 B) 4 C) 1or4 D) 1 and 4
22) If x= 0.6, then find the value of [1- {1- (1-x⁵)⁻¹}⁻¹]⁻²⁾⁵.
A) 0.36 B) 0.6 C) 0.625 D) n
23) If 2ᵃ = 4ᵇ = 8ᶜ and 1/2x +1/4y +1/8z=22/7, find (x,y,z)
A)123 B) 16/7,32/7,48/7
C) 7/16,7)32,7/48 D) n
24) Simplify: (e²ˣ + e ⁻ˣ -eˣ -1)/(e²ˣ - e⁻ˣ + eˣ-1).
A) e²ˣ/(eˣ+1). B) (eˣ-1)/(eˣ +1) C) 1 D) n
25) (7.77)ˣ= (0.777)ʸ=1000, find the value of 1/x - 1/y
A)1 B) 1/3 C) 3 D) n
26) solve: (x √x)ˣ = xˣ √x.
A) 1 B) 0 C) 2 D) n
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Revision Test (A. P)
1) If the 3rd and 6th terms of an AP are 7 and 13 respectively, then the first term and the common difference.
A) 3, 2 B) 2,3 C) 3,4 D) 43
2) sum of all natural numbers between 100 and 1000 which are multiple of 5.
A) 90000 B)98450 C) 98500 D) n
3) how many terms of the AP -6, -11/2, -5,.... are needed to give the sum -25 ?
A) 5 B) 20 C) 5 or 20 D) 5& 20
4) Determine the sum of the first 35 terms of an AP if a₂ = 2 and a₇ = 22.
A) 2000 B)2100 C) 2300 D)2310
5) If the first term of an AP is 2 and the sum of first five terms is equal to one fourth of the sum of the next five terms, then 20th term is
A)112 B) 120 C) 210 D) 300
6) Insert 3 arithmetic mean between 2 and 10.
A) 1,4, 7 B) 4,6,8 C) 3,5,7, D) none
7) The sum of all odd numbers between 1 and 100 which are divisible by 3, is..
A) 83667 B) 90000 C) 83660 D) n
8) If 7th and 13th terms of an AP be 34 and 64 respectively, then its 18th term is.
A) 87 B) 88 C) 89 D) 90
9) If the sum of p terms of an AP is q and the sum of q terms is q, then the sum of the p + q terms will be..
A) 0 B) p-q C) p+q D) -(p +q)
10) If the sum of n terms of AP be n² - n and its common difference is 6, then its first term is..
A) 2 B) 3 C) 1 D) 4
11) Sum of all two digit numbers which when divided by 4 yield Unity as reminder is..
A) 1200 B) 1210. C)1250. D) n
12) In n AM's introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3:1, then the value of n is..
A) 6 B) 8 C) 4 D) n
13) The 1st and last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be.
A) 5 B) 6 C) 7 D) 8
14) If four numbers in AP are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are:
A) 5,10,15,20 B) 4,10,16,22
C) 3,7,11,15 D) none
15) If the sum of the first n even natural number is equal to K times the sum of the first n odd natural numbers, then k is..
A) 1/n B) (n-1)/n C)(n+1)/2n D)(n+1)/n
16) If the first, second and last term of an AP are a,b and 2a respectively, then its sum is
A) ab/{2(b-a)} B) ab/(b-a)
C) 3ab/{2(b-a)} D) none
17) If x is the sum of an arithmetic progression of n odd number of terms and y the sum of the terms of the series in odd places, then x/y is
A) 2n/(n+1) B) n/(n+1)
C) (n+1)/2n D) (n+1)/n
18) If the first term of an AP is 2 and common difference is 4, then the sum of its 40 terms is
A) 3200 B) 1600 C) 200 D) 2800
19) The number of terms of the AP 3, 7, 11, 15, ... to be so that the sum is 406 is...
A) 5 B) 10 C) 12 D) 14 E) 20
20) If a(1/b+ 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP , then
A) a, b, c are in AP
B) 1/a, 1/b, 1/c are in AP
C) a, b, c are in HP
D) 1/a, 1/b, 1/c are in GP.
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Revision(A.P)
1) which term of the AP 19, 91/5, 92/5,......is the first negative term.
A) 25 B) 20 C) 15 D) 10
2) If the mth term of a given AP is n and its nth term is m then its pth term is..
A) n+m+p B) n+m-p C) n-m+p D) n-m-p
3) 15th term from the end of the AP 3, 5, 7, 9,.....201 is
A) 100 B) 152 C) 173 D) 194
4) The sum of all odd integers from 1 to 1001 is
A) 250000 B) 250001 C) 251000 D) 251001
5) 1+6+11+....+x=148. Then x is
A) 36 B) 30 C) 26 D) 20
6) Find the sum of 32 terms an AP whose 3rd term is 1 and 6th term is -11.
A) 1696 B) -1696 C) 1876 D) -1876
7) If the sum of n terms of an AP is (3n²+ 5n) and it's mth term is 164, then value of m is
A) 22 B) 25 C) 27 D) 29
8) Arithmetic mean between (a-b) and (a+b) is
A) ab B) b C) 1/ab D) a
9) There are five numbers between 8 and 26. Find the 4th term
A) 17 B) 20 C) 13 D) 11
10) The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the 2nd term
A) 1 B) 8/7 C) 9/7 D) 10/7
11) The sum of all natural numbers lying between 100 and 1000, which are multiple of 5 is.
A) 98000 B) 98700 C) 98450 D) n
12) Number of terms needed for the series -6, -11/2, -5,....to give the sum -25
A) 5 B) 10 C) 16 D) 20
Revision Test (S. I & C. I)
1) Amount due in 3 years on ₹5000, when the rate of compound interest for successive years is 6%, 8%, 10% respectively.
A) 6240.96 B) 6296.40.
C) 5790 D) 7690.40
2) A sum of ₹9600 is invested for 3 years at 10% p.a at compound interest. Find the difference between the intrest of second and first year.
A) 1000 B) 1056. C) 1100 D) 1200
3) The simple interest on a certain sum computes to ₹400 in 2 years and the compound interest on the same sum at the rate and for the same time computes to ₹410. Find the rate per cent.
A) 2% B) 3% C) 4 % D) 5%.
4) A certain sum of money, placed at compound interest amount to ₹6272 in 2 years and to ₹7024.56 in 3years. Find the rate of interest
A) 10% B) 12%. C) 14% D) 15%
5) A certain sum of money, placed at compound interest amount to ₹6272 in 2 years and to ₹7024.56 in 3years. Find the sum of money
A) 5000. B)10000 C) 15000 D) 4000
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8/8/21
1) If ⁿP₅ = 20x ⁿP₃, then n is
A) 8. B) 10 C) 12 D) 14
2) In how many ways can 5 persons occupy 3 vacant seats?
A) 60. B) 72 C) 120 D) 420
3) σₓ² = 2.25, σᵧ²= 1 and Cov(x,y)= 0.9 then rₓᵧ is..
A) 0.1 B) 0.3 C) 0.4 D) 0.6.
4). X Y
92 86
89 83
86 77
87 91
83 68
71 52
77 85
63 82
53 57
50 57 then rank correlation
A) 0.715. B) 0.517 C) 0.175 D) 0.75
5) If f(x)= (x+1)/(x-1), x≠1, then (fofofof) is...
A) 1/x B) x. C) x² D) indeterminate
6) If f(x)= 2x -1, when x ≤ 0
x², when x > 0
then f(-1/2) is
A) 2 B) -1/2 C) -2. D) 1/2
7) At what rate percentage simple interest, would a sum double itself in 6 years ?
A) 15% B) 16% C) 50/3%. D) none
7/7/21
1) sasank walks 20m in front and 20m to the right. Then every time turning to his left, he walks 10, 20, 20m respectively. How far is he now from his starting point?
A) 10m B) 20m C) 20m D) 25m E) n
2) L.C.M of 3!, 6!, 8!.
A) 40320.B) 43200 C) 30420 D) n
3) If bᵧₓ = 1.4 and bₓᵧ = 0.3 then r is
A) 1 B) 0.56 C) 0.65. D) none
4) If ∑ D²= 33 and N= 10, then R is
A) 0.7 B) 0.8. C) 0.9 D) 1
5) A sum of ₹800 amounts to 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to ..
A) 929 B) 992. C) 299 D) none
6) The compound interest, calculated yearly, on a certain sum of money for the second year is ₹880 and for the third year it is ₹968. Then the rate is..
A) 10% B) 20% C) 15% D) 25%
7) Given f(x)= 3x², g(x)=2x+3 then {f(-2)+ g(-3)}/{g(-2)+ f(-3)} is..
A) 1/8 B) 12/8 C) 15/8. D) n
8) How many numbers greater than a million can be formed with the digits 2,3,0,3,4,2,3 ?
A) 60 B) 360. C) 420 D) 1020
1) Five boys and three girls are seated at random in a row. The probability that no boys sits between two girls is:
A) 1/56. B)1/8. C)3/28. D) none
2) Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace is:
A) 1/34 b)8/221 c)1/26. D) 2/51
3) A five digits number is written down at random. The probability that the number is divisible by 5 and no two consecutive digits are identical, is
A) 1/5. B)1/5 .(9/10)³ c)(3/5)⁴ d)N
4) If the letters of the word ATTEMPT are written down at random, the chance that all Ts are consecutive.
A)1/42 b)6/7. C) 1/7. D) none
5) In a single cast with two dice the odd against 7 is
A)1/6. B)1/12. C)5:1. D) 1:5
6) 7 white balls and 3 black balls are placed in a row at random. The probability that no two black balls are adjacent is:
A) 1/2. B)7/15. C)2/15. D) 1/3
7) 10 apples are distributed at random among 6 persons. The probability that atleast one of them will receive none is:
A)6/143 b)14C4/15C5
c)137/143. D) none
8) 4 gentleman and 4 ladies take seats at random round a table. The probability that they are sitting alternatively is
A)4/35. B)1/70. C)2/35. D)1/35
9) Three dice are thrown simultaneously. The probability of getting a sum of 15 is
A)1/72. B)5/36. C)5/72 d) none
10) Three dice are thrown. The probability of getting a sum which is a perfect square is:
A)2/5. B)9/20. C)1/4. D) none
11) Three different numbers are selected at random from the set A={1,2,3,...10}. The probability that the product of two of the numbers is equal to the third is
A)3/4. B)1/40. C)1/8. D) none
12) solve
A) 3x² - x -7=0 and give your answer Correct to 2 decimal places.
B) solve: (4x²-1) - 3(2x +1) + x(2x+1)= 0
C) x² - 1/x² = 29/10(x - 1/x)
D) √(x+15) = x +3, x belongs N
E) √{x(x-3)}=√10
F) √(6x-5) - √(3x -2) = 2
13) If y= f(x)= (x+1)/(x+2) prove that f(y)= (2x+3)/(3x+5)
14) f(x)= x⁹-6x⁸ -2x⁷ +12x⁶ +x⁴ -7x³ +6x² +x -3 then find the value of f(6).
26/11//20
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16) If A = 0 2 3 And B= 7 6 3
2 1 4 1 4 5
Find the value of 2A +3B
17) prove by determinant
1 x x²-yz
1 y y²-zx = 0
1 z z²-xy
18) If y= (x+√(x²-1)ᵐ prove that (x²-1)(dy/dx)²= m²y²
19) If f(x)= (x-1)/(2x²-7x+5) when. X≠1 and f(x)= -1/3 when x=1, find f'(1)
20) you are given the following results on two variables x and y: mean of x and y are 36, 85 S.D of x and y are 11, 8 covariance of x,y is 0.66. find the two regression equation and estimate the value of x when y=25.
21) Find X and Y, if X+Y = 7 0
2 5
And X - Y = 3 0
0 3
22) Solve for x: x 1 1
1 x 1 = 0
1 1 x
With the help of DETERMINANT.
23) Given A= 1 2 and B= 4 5
2 3 5 6
Calculate AB and BA
24) If A= 1 2
2 1 , show that
A² - 3I= 2A,
25) Prove with the help of DETERMINANT 9 9 12
1 -3 -4 = 0
1 9 12
26) Find the value of x,y,z of
x+y+z 9
z+x = 5
y+z 7
27) If x= t log t, y=( log t)/t , then find the value of dy/dx at t=1
28) If A= 1 0 and I= 1 0
-1 7 0 1 then find K so that A² = 8A + KI
29) Without expanding the determinant prove that
a a² bc 1 a² a³
b b² ca = 1 b² b³
c c² ab 1 c² c³
30) Find the symmetric part of the matrix A = 1 2 4
6 8 2
2 -2 7
31) If P= 1 k 3
1 3 3
2 4 4
is the adjoint of a 3x3 matrix A and | A|= 4, then find the value of k.
32) Finf dy/dx of log₍₂ₓ₋₃₎(x² - 2x)
33) If A= 1 x 1
B= 1 3 2 1
0 5 1 C = 1
0 3 2 x
If A.B.C= 0 , then find x
34) If f(x)=x²+2x+7, find f′(3)
35) If xʸ + yˣ = aᵇ, find dy/dx.
36) If (3x⁴-2x+6)⁴(x-3)²⁾³ find dy/dx
37) If A= 2 -1
1 2
then Find A² +2A - 3I
38) If A= 1 3 0 and B= 1 3
2 1 4 0 2
-2 -1
find AB
39) Find the value of x, y,z from the equation 4 x-z = 4 3
2+y xz -1 10
40) Without expanding at any stage, find the value of the determinant:
2 x y+z
2 y z+x
2 z x+y
41) Find k if M= 1 2
2 3
and M² - kM - I₂ = 0
42) Find dy/dx, if x= at² & y= 2at
43) By using property of Determinant prove x x² 1+px³
y y² 1+py³
z z² 1+ pz³
= (1+pxyz)(x-y)(y-z)(z-x)
44) Evaluate A= 3 -2 3
2 1 -1
4 -3 2 and
B= -1 -5 -1
-8 -6 9
-10 1 7 as AB.
45) If the lines of Regression are 4x+2y -3= 0 and 3x+ 6y +5=0, find the correlation coefficient between x and y.
46) Find the regression coefficients of x on y and y on x
X: 2 6 4 7 5
Y: 8 8 5 6 2