Equation and Inequality

if y/x = 1/3 and x + 2y = 10, then x is--/যদি y/x = 1/3 এবং x + 2y = 10 হয় তাহলে x = ?

• ক. 2
• খ. 3
• গ. 4
• ঘ. 6

What is the value of x if 4/x + 3/5 = 10/x?

• ক. 50
• খ. 12
• গ. 40
• ঘ. 10

If two non-zero positive integers p and q are such that p = 4q and p < 8, then q =?

• ক. 1
• খ. 2
• গ. 3
• ঘ. 4

Which of the following describes all values of x for which 1 - x2 ≥ 0?

• ক. x ≥ 1
• খ. x ≤ - 1
• গ. 0 ≤ x ≤ 1
• ঘ. x ≤ - 1 or x ≥ 1

A 40 meters long rope is divided into two parts and the one part is 18 meters more than the other one. What is the smaller part?

• ক. 5 meters
• খ. 6 meters
• গ. 7 meters
• ঘ. 11 meters

A dealer had 24 mobile phones. He sold some of them at a profit of Tk.950 each and he sold the rest at a loss of Tk.500 each. If his total profit was Tk.9750, how many phones did he sell at a loss?

• ক. 6
• খ. 10
• গ. 15
• ঘ. 9

If x + 2y = 2x + y, then x - y equal to--

• ক. 0
• খ. 2
• গ. 4
• ঘ. 5

If x ≥ 10 and y ≤ 7, which of the following must be true?

• ক. x + y ≥ 3
• খ. x + y ≤ 7
• গ. x - y ≤ 3
• ঘ. x - y ≤ 10

If x = 2y = 3z = 36 then the arithmetic mean of x, y and z is:

• ক. 33
• খ. 22
• গ. 18
• ঘ. 12

If b < 2 and 2x - 3b = 0, which of the following must be true?

• ক. x > -3
• খ. x < 2
• গ. x = 3
• ঘ. x < 3

If y = (3x - 6)/x, then for what values of x, y will be positive?

• ক. x > 2 or x < 0
• খ. x > 0
• গ. x < 0
• ঘ. -2 < x < 2

If C/5 = R/4 = (F - 32)/9, then what will be the value of C and R if F = 140?

• ক. C = 0, R = 0
• খ. C = 60, R = 48
• গ. C = 80, R = 100
• ঘ. C = 140, R = 140

Last season, Ellen and Janet together won 32 tennis matches. Ellen won 6 more matches than Janet. How many matches did Ellen win?

• ক. 13
• খ. 16
• গ. 19
• ঘ. 25

Tapo earns Tk.5.00 for every hour he works. Last week he worked for x hours. He purchased y kg of rice. Price of per kg rice is Tk.12.00. He saved the remaining amount. Which expression below ahows his savings?

• ক. Tk.(5.00x + 12x + 12.00y)
• খ. Tk.(5x - 12.00y)
• গ. Tk.5.00(x - y)
• ঘ. Tk.7.00(x - y)

Rahim, Karim and James paid a total of Tk. 45 for their dinner at a restaurant. If Rahim paid of the total amount, Karim paid Tk.17 and James paid the rest then what fraction of the total amount did james pay?

• ক. 2
• খ. 14
• গ. 1
• ঘ. 7

f(x) = -1 for all x > 0. If f(a) = -1 and f(ab) = -1 then b =?

• ক. 1
• খ. 3
• গ. -1
• ঘ. -3

If 2x = 2y = 4-z then 1/x + 1/y + 1/z is equal to:

• ক. 0
• খ. 1
• গ. 3/2
• ঘ. -1/2

If x = ya, y = zb and z = xc then the value of abc is--

• ক. 4
• খ. 3
• গ. 2
• ঘ. 1

If p = 3/5, q = 7/9 and r = 5/7, then

• ক. p < q < r
• খ. q < r < p
• গ. p < r < q
• ঘ. None of these

Which of the following inequalities is true?

• ক. 0 < 1/10 < 0.01
• খ. 0.12 < 1/8 < 0.13
• গ. 0.30 < 1/4 < 0.50
• ঘ. 0.30 < 1/3 < 0.33

(2uv)2 + (u2 - v2)2 =?

• ক. 2uv
• খ. (u2 + v2)2
• গ. u2 + v2
• ঘ. (2uv)2 + (u2 + v2)2

If 5/8 = 3/x and y = 1/5, what is the value of (x + 6y)?

• ক. 41/30
• খ. 2
• গ. 6
• ঘ. 16/5

If x = 5y = 16 and x = -3, then the value of y is--

• ক. -24
• খ. -8
• গ. -2
• ঘ. 2

If x/bc = y/ca = z/ab, then x + y + z =?

• ক. (a + b + c)/abc
• খ. 1
• গ. 0
• ঘ. a + b + c

A ferry can carry 20 buses or 32 cars. If there are 15 buses on the ferry. How many cars can be loaded into it?

• ক. 12
• খ. 15
• গ. 6
• ঘ. 8

Five times a number less 3 is 32. What is twice the number?

• ক. 16
• খ. 7
• গ. 3
• ঘ. 5

If the result obtained by multiplying a number x by a number 1 less itself is 4 less than multiplying x by itself, then x =?

• ক. 4
• খ. 5
• গ. 6
• ঘ. 2

If x + y > 5 and x _ y > 3, then which of the following gives all & only possible values of x?

• ক. x > 4
• খ. x < 5
• গ. x > 5
• ঘ. x < 3

If -3t + 8 > t - 6, then--

• ক. t > 7/2
• খ. t < 7/2
• গ. t > 1
• ঘ. t > -7/2

If 2x - 4 < 4, then--

• ক. x > 2
• খ. x < 2
• গ. 2 < x < 4
• ঘ. x < 4

If x/y = -1 and xy = -1, then x - y =?

• ক. -1
• খ. -2
• গ. 2
• ঘ. 1

If 3x/(1 + x) = 1, then x =?

• ক. -1
• খ. 2
• গ. 10
• ঘ. 1

If 2x - y = 4 then 6x - 3y =?

• ক. 12
• খ. 10
• গ. 4
• ঘ. 6

If x + y = 1 and x - y = 5, then what x is equal to?

• ক. 2
• খ. 4
• গ. 3
• ঘ. 5

In the expression of (x - y)3, the coefficient of y2 is:

• ক. 1
• খ. 3
• গ. 3a
• ঘ. -3a2

If a + b = √5 and a - b = √3, then a2 + b2 =?

• ক. √8
• খ. 6
• গ. 4
• ঘ. 4√2

If 1/3 + 1/2 + 1/x = 4, then x =?

• ক. 18/5
• খ. 19/6
• গ. 24/11
• ঘ. 6/19

If 0.04 ×0.4 × a = 0.4 × 0.04 ×b, then the value of a/b is:

• ক. 0.016
• খ. 1.60
• গ. 0.16
• ঘ. None of these

If 2n = 128 and y = 5, then 2n - 1 × 5n - 2y - 1 =?

• ক. 100000
• খ. 1000000
• গ. 10000000
• ঘ. None of these

What is the value of t2 + 2t + 1t + 1 × n2 + nn3 + 2n2 + n =?

• ক. t/n
• খ. (t + 1)/(n + 1)
• গ. t2/n
• ঘ. (t + 1)/(n - 1)

The solution set of the inequality (2x + 1) < 9(4 - x) is--

• ক. -5 < x < 7/4
• খ. x ≤ -5 and x ≥ 7/4
• গ. -7/4 < x < 5
• ঘ. x > 5 and x < -7/4

If x = -1, which of the following has the largest value?

• ক. 2x
• খ. 4x
• গ. 8x
• ঘ. x/2

8 is added to x. The sum is multiplied by 3. The product is devided by 2. Then 7 is subtracted from the quotient. The remainder is 50. Therefore x is--

• ক. 35
• খ. 20
• গ. 30
• ঘ. 40

An employer pays 3 workers X, Y and Z a total of Tk.610 or 36600.00 a week. X is paid 125% of the amount of Y is paid and 80% of the amount of Z is paid. How much does X make a week?

• ক. Tk.150 or 8500
• খ. Tk.175 or 11700
• গ. Tk.180 or 10800
• ঘ. Tk.195 or 9000

If 2x + 2y = 7z, then what is the average of x, y and z?

• ক. 1.5z
• খ. 3z
• গ. 2z + 1
• ঘ. z/3

If 1/x > 1/y, then which of the following must be true?

• ক. y > x
• খ. x > y
• গ. x < 0
• ঘ. y < 0

If 6x - 14 < 8x + 2 which of the following must be true?

• ক. x < 2
• খ. x > 8
• গ. x < 8
• ঘ. x > -8

Babu's income is Tk.1000 more than that of Selim. Their total salary is Tk.x. What is Selim's salary?

• ক. x/2 - 500
• খ. (x + 1000)/2
• গ. (2x - 500)/2
• ঘ. 2x - 1000

If 3/x = 2 and y/4 = 3, then (3 + y)/(x + 4) =?

• ক. 10/9
• খ. 3/2
• গ. 20/11
• ঘ. 30/11

By how much is the value of {-10 - (-7)} greater than the value of {-10 + (-7)}?

• ক. -20
• খ. 20
• গ. 0
• ঘ. 14

Karim's school is 10 kms from his home. From there he travels 4 kms to get his friend's house and then travels 3 kms to get to the cricket ground. If he is then x miles from home, what is the range of possible values of x?

• ক. 3 ≤ x ≤ 12
• খ. 3 ≤ x ≤ 17
• গ. 3 ≤ x ≤ 10
• ঘ. 3 ≤ x ≤ 14

The reciprocal of p/n is n/p and vice versa. Which of the following is the reciprocal of 3/√12?

• ক. √2/3
• খ. 2/√3
• গ. 4√3/3
• ঘ. 12/9

In a cricket team scores X runs on average over N games and then scores Y runs in the next game, then the average score for the team over the (N + 1) games is---

• ক. (X + Y)/(N + 1)
• খ. (NX + Y)/(N + 1)
• গ. {N(X + Y)}/(N + 1)
• ঘ. {N(X + Y) - 1}/N

If (x2 - 4x + 9) = 6, which of the following must be false?

• ক. x = 1
• খ. x = 3
• গ. x > 3
• ঘ. x > 0

If (x2 - 8x + 22) = 6, which of the following must be false?

• ক. x = 4
• খ. x = -4
• গ. x > 0
• ঘ. x > 3

If point P is on line AB, which of the following is always true?

• ক. AP = PB
• খ. AP > PB
• গ. PB > AP
• ঘ. AB > AP

If x + y > 4 and x > 3, then y > 1 is true.

• ক. always
• খ. only if x < 0
• গ. only if x > 0
• ঘ. only if x = 0

If -1 < x ≤ 1 and x is an integer, then value of x is--

• ক. 0 only
• খ. 1 only
• গ. 0 and 1
• ঘ. one value more than 1

If 3 - 2x ≤ 7, then--

• ক. x ≤ 2
• খ. x ≤ -2
• গ. x ≥ 2
• ঘ. x ≥ -2

If x = 1, then -(x4 + x3 + x2 + x) =

• ক. -10
• খ. -4
• গ. 0
• ঘ. 4

If a = 2/7, b = 1/3, x = 1/8, the value of y = a - 3b + 16x is--

• ক. 16/7
• খ. 9/7
• গ. 7/16
• ঘ. 1

If y = 5x2 - 2x and x = 3, then y =?

• ক. 24
• খ. 27
• গ. 39
• ঘ. 51

If x + 5y = 16 and x = -3, then y =?

• ক. -24
• খ. -8
• গ. -2
• ঘ. 2

If 3 subtracted from a number, the result is 6 more than twice the number. The number is--

• ক. -3
• খ. -9
• গ. 3
• ঘ. 9/7

(2x + 2y + x2 - y2)/(x + y) =?

• ক. (x - y)/(x + y)
• খ. (x - y)2/(x + y)
• গ. x - y
• ঘ. 2(x - y)

If x + 2y = 4, and x/y = 2 then determine the value of x and y.

• ক. 1, 2
• খ. 2, 4
• গ. 2, 1
• ঘ. 3, 4

If x + 2y ≤ 3, x > 0 and y > 0, then one of the solutions is--

• ক. x = -1, y = 2
• খ. x = 2, y = 1
• গ. x = 1, y = 1
• ঘ. x = 0, y = 0

Which of the following inequalities is the solution to the inequality 7x - 5 < 2x + 18?

• ক. x < 13/5
• খ. x > 23/9
• গ. x < 23/9
• ঘ. x > 23/5

If 3x - 4y > 2x + 3y, then which of the following must be true?

• ক. x > y
• খ. y > x
• গ. x > 0
• ঘ. y > 0

If 5(3x - 7) = 20, then what is the value of (3x - 8)?

• ক. 11/3
• খ. 3
• গ. 0
• ঘ. 3/4

If x + y = a and x - y = b, then 2xy =

• ক. (b2 - a2)/2
• খ. (a2 - b2)/2
• গ. (a - b)/2
• ঘ. ab/2

If b + a = x and a - b = y, then a2 - b2 =

• ক. (x2 - y2)/2
• খ. (x2 - y)/2
• গ. 2xy
• ঘ. xy/2

If Tk./$ = 68 and Tk./£ = 102, then cross rate of £/$ is equal to:

• ক. 3/2
• খ. 2/3
• গ. 5/2
• ঘ. 5/3

If 6 - 4x ≤ 14 then --

• ক. x ≤ 2
• খ. x ≥ 2
• গ. x ≤ -2
• ঘ. x ≥ -2

If p and q are integers such that p < 0 < q, which of the following must be true? I. 2p < 2q II. p2 < q2 III. p + q = 0

• ক. I only
• খ. II only
• গ. I and II only
• ঘ. I and III only

If 0 < a2 < b, which of the following statements is/are always true? i. a < b/a ii. a4 < a2b iii. a2/b < 1

• ক. i only
• খ. i and ii
• গ. ii and iii
• ঘ. i and iii

If u > t, r > q, s > t, t > r which of the followings must be true I. u > s II. s > q III. u > r

• ক. I only
• খ. II only
• গ. II and III only
• ঘ. III only

The average cost of 5 apples and 4 mangoes is 36 taka. The average cost of 7 apples and 8 mangoes is 48 taka. Find the total cost of 24 apples and 24 mangoes.

• ক. 1044
• খ. 2088
• গ. 720
• ঘ. 324

If 3/p = 6 and 3/q = 15 then p - q =?

• ক. 1/3
• খ. 2/5
• গ. 3/10
• ঘ. 5/6

2/(a - b) - 5/(b - a) =?

• ক. -10/(2ab -a - b)
• খ. -3/(a - b)
• গ. -7/(a - b)
• ঘ. -7/(b - a)

If the operation ^ is defined by the equation x ^ y = 2x + y, what is the value of a in 2 ^ a = a ^ 3?

• ক. 0
• খ. 1
• গ. -1
• ঘ. 4

If a and b are positive integers and (a - b)/3.5 = 4/7, then--

• ক. b < a
• খ. b > a
• গ. b = a
• ঘ. b ≥ a

If 13 = 13w/(1 - w), then (2w)2 =

• ক. 1/4
• খ. 1/2
• গ. 1
• ঘ. 2

If x = 12 which of the following has the least value?

• ক. x - 2
• খ. x/2
• গ. 2/x
• ঘ. 2 - x

What will be the result if (4x + 20)/4 is subtracted from (x + 10)?

• ক. 5
• খ. x
• গ. x/2
• ঘ. 2 - x

If (3x + 2y) = 8 and (2x - y) = 3 find the value of 'x'.

• ক. 2
• খ. 3
• গ. 4
• ঘ. 6

If the average of two numbers is M and the larger number is L, what is the other number?

• ক. M - L
• খ. L - M
• গ. 2M - L
• ঘ. L - 2M

In the equation: 31(m - n) - 32(m - n) + (m - n) =?

• ক. -n
• খ. -m
• গ. 0
• ঘ. 1

A certain sum of money consists of 30 coins, some of which are 10 paisa coins and the rest are 5 paisa coins. If the total value of the coins is Tk.2, what is the number of 10 paisa coins?

• ক. 10
• খ. 15
• গ. 12
• ঘ. 8

The total cost of a bouquet of roses at a flower shop depends on the number of roses ordered. The vase cost $5, and each rose cost $2.25. Which equation can be used to find 'c', the total cost of a bouquet with 'r' roses?

• ক. c = (5 + 2.25)r
• খ. c = 5r + 2.25
• গ. c = 5 + 2.25r
• ঘ. c = 5 + (5 - 2.25)r

Barkat/Murad bought equal numbers of 20-paisa and 30-paisa stamps. If the total cost of the stamps was Tk.10.00, what was the total number of stamps bought?

• ক. 25
• খ. 34
• গ. 40
• ঘ. 46

If (x - 1)2 = 400, which of the following could be the value of x - 5?

• ক. 15
• খ. 14
• গ. -24
• ঘ. -25

Which of the following equations is not equivalent to 25x2 = y2 - 4?

• ক. 25x2 + 4 = y2
• খ. 7x2 = 3y2 - 12
• গ. 25x2 = (y + 2)(y - 2)
• ঘ. 5x = y - 2

If x2 + 4x + 13 = 1 + x2, then find out the value of x2?

• ক. 9
• খ. 0
• গ. 4
• ঘ. 7

If x = 4, then (x2 + x1/2) =?

• ক. 16
• খ. 18
• গ. 20
• ঘ. 8

If (X + Y) = 9 and X/Y = 2, then X is equal to:

• ক. 3
• খ. 4
• গ. 5
• ঘ. 6