A. P
1) If the sum of the three numbers in A. P be 18 then what is the middle term?
A) 6 B) 8 C) 10 D) 25
2) If 10 be added to each term of an AP then, will the new progression be in AP also. ?
A) A. P B) G. P C) H. P D) none
3) If 5 be multiplied with each term of an AP then will the new progression an AP also?
A) A. P B) G. P C) H. P D) none
4) Find the 8th term of an AP., 13, 10, 17, 24......
A) 52 B) 62 C) 54 D) 64
5) Which term of the AP. 7, 11, 15, 19, ....... is 103?
A) 20th B) 22th C) 25th D) 30th
6) If the 7th term of an AP be 20 and the 10th term be 29 then find the first and the common difference.
A) 1,2 B) 2, 3 C) 3,4 D) 4,5
7) Can be any term of the AP 5, 10, 15.....
A) A. P B) G. P C) H. P D) none
8) In an AP 1st term be -5, last term be 25 and number of terms be 10. Find the sum of the terms.
A) 105 B) 102 C) 100 D) 98
9) What do you mean by natural numbers? Find the sum of first 100 natural numbers.
A) 5050 B) 505 C) 55 D) 5550
10) a²+ 3a + 2, 3a²+ 2a+5, 4a²+ 5a + 4 are in AP, then find a.
A) 0 B) 2 C) 4 D) 6
11) Find the arithmetic progression of which nth term is 3n -1.
A) 2, 5, 8......
B) 5, 7, 9 ...
C) 2, 8, 14,....
D) none
12) If the pth term of an AP be q and qth term be p, then find the p+ q th term.
A) 0 B) 1 C) 2 D) 4
13) The sum of first n terms of an AP is n². Find the common difference.
A) 2 B) 4 C) 6 D) 8
14) Find the sum of the first 20 terms of the AP. 20, 17, 14...
A) -170 B) 170 C) 200 D) -200
15) The 5th term and the 11th term of an AP are 41 and 20 respectively. Find the 1st term. What will be the sum of first 11 terms of this AP.
A) 55, 825/2 B) 65, 825 C) 55, 825 D) n
16) The sum of p th term of an AP is 3p²+ 5p; then the series is in
A) AP. B) G P C) HP D) none
17) Insert five A. M between 2 and 20.
18) The n th term of an AP is p. Then the sum of first (2n -1) terms is
A) (2n -1)p B) (2n -1) C) p D) (2n +1)p
19) The p th term of an AP is a, and the q th term is b. Then that the sum of first (p+ q) terms is
A) 1/2 (p+ q)(a+ b + (a- b)/(p - q)).
B) (p+ q)(a+ b + (a- b)/(p - q)).
C) 1/2 (a+ b + (a- b)/(p - q)).
D) 3/2 (p+ q)(a+ b + (a- b)/(p - q)).
20) The sum of how many terms of the series 27 + 24+21+...... will be equal to 132 ?
A) 8 B) 11 C) 8 or 11 D) 8 and 12
21) If the sum of n th term of an AP is n² + 3n, then eight term is equal to the sum of ___
A) 10th B) 11th C) 13th D) none
22) Find the sum upto n terms of the following series. 1+ 5 + 12+ 22+ 35+ .......
A) {n²(n+1)/2}. B) n(n+1)/2
C) n²(n+1) D) {n²(n-1)/2}
23) If the sum of the p, q and r terms of an AP be x, y, z respectively then value of
x/p (q- r)+ y/q (r- p)+ z/r (p- q) is
A) 0 B) 1 C) 2 D) 15
24) Find the following sum:
1²+ 3² + 5²+ ...... upto n terms.
A) n/3 (4n² - 1). B) n (4n² - 1).
C) n²/3 (4n² - 1). D) n/3 (4n² + 1).
25) The middle term of an AP having 11 terms is 12. Find the sum of the 11 terms of that progression.
A) 12 B) 21 C) 33 D) none
26) Find the sum of n terms of 2.4 + 6.8 + 10.12+ .....
A) 4n/3 (n+1)(4n -1)
B) 4n (n+1)(4n -1)
C) 4n/3 (n+1)(4n +1) D) none
27) The p th, q th and r th terms of an AP are P, Q , R respectively. Then the value of p(Q - R) + q(R - P) + r(P - Q)
A) 0 B) 1 C) 2D) none.
28) The sum of the three numbers in AP is 21 and their product is 231. Find the numbers.
A) 3, 7,11 B) 11, 7, 3 C) both A and B C) either A or B
29) There are n arithmetic means between 4 and 31. If the second mean: last mean= 5: 14 then find the value of n.
A) 8 B) 10 C) 12 D) 32
30) If the sum of the first P terms of an AP be equal to the sum of the first Q terms then the value of sum of the first P+ Q terms is
A) zero. B) 1 C) 2 D) 4
31) The sum of n, 2n and 3n of an AP are a, b, c respectively. then the value 3(b - c).
A) a B) b C) c D) none
32) Find the sum of 1² - 2²+ 3²- 4² + 5² - 6²+ ......
A) n/2 (n+ 1). B) n (n+ 1)
C) n/2 (n- 1). D) none
33) If the sum of p terms of an AP is to the sum of q terms as p² : q², then the value of (p th term)/(q th term)
A) (2p -1)/(2q -1). B) 2p/3q
C) n/2 (n+ 1). D) none
34) The interior angles of a polygon are in AP. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.
A) 9 B) 6 C) 9 or 6 D) 9 and 6
35) The sides of a right angled triangle are in AP. If the smallest side is 5cm then find the largest side.
A) 2 B) 5 C) 3 D) 25/3
38) A man divided ₹24000 among his four sons in such a way that the amounts of four sons are in AP. The product of the amounts of 1st and 3rd sons is to the product of amounts of 2nd and 4th sons as 7: 15. Calculate the amounts received by each son.
39) Two posts are offered to a man. In the one, the starting salary is ₹1200 and increases annually by ₹80; in the other, the salary starts at 850 and increases annually by ₹120. The man decides to accept the post that will give him better total income in the first 16 years. Which post will be accept ?
A) 1st offer B) 2nd offer C) both F) either A or B
40) A polygon has 25 sides, the lengths of which starting from the smallest side are in AP. If the perimeter of the polygon is 2100 cm, and the length of the largest side is 20 times that of the smallest, find the length of the smallest side and the common difference of the AP. 8, 19/3
41) The first term of an AP is a and the sum of first p terms is zero. Show that the sum of next q terms is -{aq(p+q)}/(p - 1).
42) If the sum of p-terms of an AP be q and the sum of q terms be p then show that the sum of its (p+ q) terms is -(p+ q).
Logarithm
1) What is the value of x, if y= log₇x and 5(y/log7⁵)A) 7 B) 28 C) 49 D) 14 E) 21
2) If logₐx = Logₘˣ what is the value of logₐm if x≠ 1 ?
A) x B) x² C) 1 D) 1- x E) 2 - x
3) if Log₁₀x = y and logₑ10= 1/m, what is x (in terms of y, e and m) ?
A) y/m B) logₘy C) eʸ⁾ᵐ D) m logₑy E) m/y
4) Which of the following is true?
A) 1/4> log₁₀ 2 > 1/8
B) 1/2 > log₂₀ 3 > 1/3
C) 1/9 < log₁₀ 3 < 1/3
D) 1/4> log₁₀ 4 > 1/4
E) 1/5 < log₁₀ 2 < 1/4
5) solve for x: log₂ log₂ logₓ6561= 2 and x> 0
A) 3 B) 2 C) √7 D) 9 E) √3
6) If x= 1+ logₐmc, y= 1+ logₘca, k = 1 + log꜀am what is the value of xy + yk + kx
A) logₓᵧₖamc B) xyk
C) (logx + log y+ log k)/log amc
D) 1 E) 2xyk
7) Solve for x: if logₓ[log₅{√(x +5) +√x)}] = 0
A) 1 B) 9 C) 12 D) 3 E)4
8) If aˣ = nʸ = cᵐ and y² = xm what is the value of ( logₙa)/(log꜀n)
A) 1 B) logᵧx /logₘy C) xm/y D) xym E) xy/m
9) If a is a perfect square what is the value of a given aˣ = 1/8 and x= 3/2[(log₂a) - 3]?
A) 1 B) 64 C) 4 D) 16 E) 8
10) It is given that f(x) =(e²ˣ + e⁻²ˣ)/2, what is the value of f(logₑ3) ?
A) e⁶ B) e⁶ᶻ C) 1 D) 41/9 E) 9e⁶
11) If a, m, c are distinct values, what is the value of abc if (logₘa) (log꜀a)+ (logₐm)(log꜀m)+ (logₐc) (logₘc) - 3 = 0 ?
A) 2 B) 0 C) 1 - log a - log b - log c D) 3 E) 1
12) If log₁₂ 27= a, what is the value of log₆16 ?
A) 4(3- a)/(3+a)
B) 3(9- 4a)/(3- 2a)
C) a⁴ - 9 D) (3 + a)/(3 - a)
E) (3- a)/(3+a)
13) Express log[³√a⁴/√(b³c) ÷ (a²b³/c³)¹⁾⁶] in terms of log a, log b, and log c.
A) log a - log b
B) 1/2 log a +1/3 log b - log c
C) 1/3 log a + 1/2 log c
D) log a - 2 log b
E) none
14) If z log y + log(log x) = log[log x + log y+ log z], which of the following is true, given that x, y and z are distinct.
A) ₓzʸ = 1 B) ₓyᶻ = cyz
C) xʸ = z D) y² = z E) ᵧxᶻ = 1
15) If log₆ 161= a, log 23= b, what is the value of log₇6 in terms of a and b ?
A) a)b B) a+ b C) 1/(a - b) D) b/a E) 1/(a+ b)
16) If log₄3= 1/a, what is log√₃ 36 + log√₃ 36 + ......20 times ?
A) 9a/4 B) 80+ 40a C) √3 a/36 D) (9a+ 4)/√3 E) 4/9
17) 1/(log 2/log x + log 4/log x + log 8/log x) = log₂y, then what is the relation between x and y.
A) x= y⁶ B) x= y³ C) x= y² D) x= y E) x= y⁴
18) Solve for x: if log₂(1- (1/2)ˣ)= x - 2.
A) 0 B) 3 C) 2 D) 4 E) 1
19) If logₓ2 logₓ/₁₆2 = logₓ/₆₄2 , then the value of x is
A) 2 B) 4 C) 8
D) choice B or choice C
E) choice A or choice C
20) If log₂[5(2ˣ)+ 1)], log₄(2¹⁻ ˣ +1), and 1 are in AP, then what is the value of x ?
A) 1 B) log₂√5 C) log₂(2/5) D) log√₂ 5 E) log₂5
21) Value of 1/logₐx + 1/log√ₐx¹⁾⁴ + 1/log³√ₐx¹⁾⁹ + ....+ 1/log²⁰√ₐx¹⁾⁴⁰⁰ is
A) logₓa²¹⁰ B) x²⁰ + a C) logx D) logₐx⁴⁴ E) logₓa
₂
22) value of x: ₄₉log₇5+ log₂2² = 31 + log ₁₀ˣ.
A) 0 B) 1 C) 10 D) 10⁵ E) 10¹⁰
23) If log₁₀1234= 3.0913,
log₁₀769874= 5.88642 find the value of ⁸√0.000000001234
A) 0.0769874 B) 0.030913
C) 0.00769874 D) 0.0030913 E) 0.00678947
24) The logarithm of 7623 is 3.8821. find the number whose logarithm is -0.1179.
A) 0.08821 B) 0.7623 C) 0.07623 D) 0.8821 E) 0.6732
25) How many digits are there in (441)⁵⁰ if log 3= 0.4771 and log 7= 0.845
A) 50 B) 21 C) 442 D) 133 E) 213
26) The number of zeros immediately after the decimal of N is 5. If 0< N < 1,
