ac + ab + bc + b + c + 1
ac + ab + a + c + 2
ab + ac + a + b + 1
ac + bc + ab + b + c + 2
ab + ac + 2a + b + c + 1
Correct answer is E
Soln. a*b = ab + a + b,
a ♦ b = a + b + 1
a*c = ac + a + c
(a*b) ♦ (a*c) = (ab + a + b + ac + a + c + 1)
= ab + ac + 2a + b + c + 1
\(\frac{1}{12}\)
\(\frac{6}{35}\)
\(\frac{19}{300}\)
\(\frac{7}{200}\)
\(\frac{5}{100}\)
Correct answer is D
Let the cost of living = y.
The new cost of living = \(y + \frac{15y}{100} = 1.15y\)
The food bill now = \((1 - \frac{90}{100})(1.15y)\)
= \(1.035y\)
The fractional increase in food bill = \((1.035 - 1) \times 100% = 3.5%\)
= \(\frac{35}{1000} = \frac{7}{200}\)
If y = 2x2 + 9x - 35. Find the range of values for which y < 0.
7 < x < \(\frac{5}{2}\)
-5 < 7 < x
-7 < x < 5
-7 < x < \(\frac{5}{2}\)
Correct answer is D
y = 2x2 + 9x - 35
2x2 + 9x = 35
x2 + \(\frac{9}{2}\) = \(\frac{35}{2}\)
x2 + \(\frac{9}{2}\) + \(\frac{81}{16}\) = \(\frac{35}{2}\) = \(\frac{81}{16}\)
(x + \(\frac{9}{4}\))2 = \(\frac{361}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{\sqrt{361}}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{19}{4}\)
= 2.5 or -7
-7 < x < \(\frac{5}{2}\)
75 years
60 years
98 years
80 years
105 years
Correct answer is D
Let the present ages of father be x and son = y
five years ago, father = x - 5
son = y - 5
x - 5 = 3(y - 5)
x - 5 = 3y - 15
x - 3y = -15 + 5 = -10 ......(i)
x + y = 110......(ii)
eqn(ii) - eqn(i)
4y = 120
y = 30
sub for y = 30 in eqn(i)
x -10 = 3(30)
x -10 = 90
x = 80
What is the number whose logarithm to base 10 is 2.3482?
223
2228
2.235
22.37
0.2229
Correct answer is A
\(\begin{array}{c|c} Nos. & log \\ \hline 222.9 & 2.3482\end{array}\)
N : b Look for the antilog of .3482 which gives 222.9