1 .
What is the sum of two consecutive even numbers, if the difference of their squares is 92?
Answer & Explanation
Answer : Option D |
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Explanation : |
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Let the number be x and x+2.
Then ,$(x+2)^2$-$x^2$=92
Or,(x+2+x)(x+2-x)=92
Or,(2x+2)x2=92
Or, x+1 =23
Or,x = 22
So, sum of the numbers =
x+x+2=22+22+2=46 |
2 .
Find the factor of 8$x^2$- 18x + 9.
Answer & Explanation
Answer : Option D |
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Explanation : |
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The given expression = 8$x^2$-18x+9
=8$x^2$-(12+6)x+9
=8$x^2$-12x-6x+9
=4x(2x-3)-3(2x-3)
=(2x-3)(4x-3) |
3 .
If a - b = 3 and $a^2$+ $b^2$= 29, then find the value of ab
Answer & Explanation
Answer : Option A |
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Explanation : |
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$A^2$+$b^2$=29….(i)
And a-b =3….(ii)
Now ,squaring both sides of the equation (ii),We have,
$(a-b)^2$=$(3)^2$
=$a^2$+$b^2$-2ab=9
=29-2ab=9 [So,$a^2$+$b^2$=29(given)]
=-2ab=-20
= ab = $20\over 2$ = 10 |
4 .
Which of the following is not the reciprocal of $(2 \over 3)^4$ ?
Answer & Explanation
Answer : Option D |
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Explanation : |
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Reciprocal of $(2\over 3)^4$ = $(3 \over 2)^4$ = $3^4 \over 2^4$ |
5 .
If a number is divided by 223 the remainder is 79. If the same number is divided by 179 it gives a quotient 315. Find the remainder
Answer & Explanation
Answer : Option A |
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Explanation : |
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Let the number be N
Then,N=223k+79
Again , 179x315=56385
If 56385 is divided by 233,We get 252
as quotient and 189 as remainder.
So,Reqd remainder = 79 +(223-189)=79+34=113 |
6 .
If x = 81 then the value of $x ^{1 \over 4} - 1$$x ^{1 \over 4} + 1$ is
Answer & Explanation
Answer : Option B |
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Explanation : |
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7 .
The simplified value of $3.47 \times 3.47 - 2.53 \times 2.53 \over 0.94$ - $12.50 \over 6.25$ is
Answer & Explanation
Answer : Option C |
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Explanation : |
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8 .
$\sqrt {x \over y}$ + $\sqrt {y \over x}$ = $12 \over 7$ and x + y = 12, then the value of xy will be
Answer & Explanation
Answer : Option D |
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Explanation : |
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9 .
If 3 men or 4 women can do a piece of work in 43 days then in how many days will 7 men and 5 women do the same piece of work?
Answer & Explanation
Answer : Option A |
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Explanation : |
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10 .
A man, a woman and a boy can do a piece of work in 3 days, 4 days and 12 days respectively. How many boys should help a man and a woman to do the same piece of work in $1 \over 4$ day?
Answer & Explanation
Answer : Option A |
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Explanation : |
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1 man does the work in $1 \over 4$ day $1\over 3$ x $1 \over 4$ = $1 \over 12$ part
1 woman does the work in $1 \over 4$ day $1 \over 4$ x $1 \over 4$ = $1 \over 16$ part
Total work done by one man and one woman = $1 \over 12$ + $1 \over 16$ = $4 + 3 \over 46$ = $7 \over 48$
So, Remaining work = 1 - $7 \over 48$ = $41 \over 48$ part
So, The number of boys = $41 \over 48$ $\times$ 48 = 41 boys |
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