What approximate value will come in place of question mark (?) in the following question ?
(49.001)² = ?
Answer: B
Correct answer: 2400
\( 49^2 = 2401 \), and 49.001 differs from 49 by so little that the square is still about 2401. To the nearest figure offered that is 2400.
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A sum of Rs.1890 has to be used to give 9 prizes to the customers of a super market for their overall academic purchases. If each prize is Rs.30 less than its preceding price, what is the least value of the price ?
Answer: A
Let the least value of the prize = Rs. x
Then the next value of the prize is x+30 , x+60, x+90, ....x+240.
Given total amount of cash prizes = Rs.1890
--> x + (x+30) + (x+60) + (x+90) + ....+ (x+240) = 1890
--> 9x + (30 + 60 + 90 + 120 + 150 + 180 + 210 + 240) = 1890
--> 9x + 30(1 + 2 + 3 + 4....+ 8) = 1890
--> 9x + 30(36) = 1890
--> 9x = 810 --> x=90
Hence the least value of the prize x=90
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The solution of 3(2u + v) = 7 uv and 3(u + 3v) = 11 uv is _____
Answer: B
Correct answer: u = 1, v = 3/2
Putting \( u = 1 \) and \( v = \tfrac32 \) into the first equation gives \( 3(2 + \tfrac32) = 10.5 \) and \( 7uv = 7 \times \tfrac32 = 10.5 \); into the second, \( 3(1 + \tfrac92) = 16.5 \) and \( 11uv = 11 \times \tfrac32 = 16.5 \). Both hold, so that is the solution.
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If × means ÷, - means ×, ÷ means + and + means- than (3 - 15 ÷ 19) × 8 + 6 = ?
Answer: C
Correct answer: 2
Replacing the symbols gives \( (3 \times 15 + 19) \div 8 - 6 \), and working the bracket first, \[ \frac{45+19}{8} - 6 = 8 - 6 = \mathbf{2} \]
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In a group of buffaloes and ducks the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?
Answer: C
Let the number of buffaloes be x
and number of ducks be y.
Now, number of heads = x+y
Number of legs = 4x+2y .......(1)
But given that legs = 2(x+y)+24 ......(2)
solving (1) & (2),we get
4x+2y=2x+2y+24
--> x=12.
Therefore number of buffaloes =12
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5x - 6 = 3x - 8
Solve the above equation.
Answer: B
Correct answer: -1
Bringing the terms together: \( 5x - 3x = -8 + 6 \), so \( 2x = -2 \) and \[ x = \mathbf{-1} \]
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The value of -4-(-10) is how much greater then the value of -10-(-4) ?
Answer: C
Correct answer: 12
\( -4 - (-10) = -4 + 10 = 6 \) and \( -10 - (-4) = -10 + 4 = -6 \). The first exceeds the second by \[ 6 - (-6) = \mathbf{12} \]
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What is 7 + 7 ÷ 7 + 7 × 7 − 7 =
Answer: B
Correct answer: 50
By the usual order, division and multiplication come before addition and subtraction: \[ 7 + 1 + 49 - 7 = \mathbf{50} \]
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X²+X² =
Answer: C
Here the given expression,
X² + X² is an algebraic expression. Here in this expression the terms are like terms. Now to add them, add their coefficients.
Here in the given expression, the like terms are two X²
Hence, adding their coefficients i.e, 1 + 1 = 2
Therefore,
X² + X² = 2X².
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Can you Solve 7 + 7 ÷ 7 + 7 x 7 + 7 − 7 ÷ 7 + 7 x 7
Answer: A
Correct answer: 112
Doing the divisions and multiplications first turns the expression into \( 7 + 1 + 49 + 7 - 1 + 49 \), which adds up to \[ \mathbf{112} \]
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