**The value of (1.073*1.073 - 0.927*0.927 / 1.073 - 0.927 ) + (3**^{4})^{4 }*9^{6 }/ (27)^{7}*(3)^{9}is- 2
- 1/9
- 2 1⁄9
- 3 1⁄9

Answer : Option C.

Solving this expression, we get:

=> (1.073)^{2}- (0.927 )^{ 2}/ 1.073 - 0.927 ) + (3)^{16 }*(3^{2})^{6 }/ (3^{3})^{7}*(3)^{9}=> (1.073 -0.927)(1.073+0.927) / (1.073 -0.927) + (3)^{16 }*(3)^{12 }/ (3)^{21}*(3)^{9}=> (1.073+0.927) + (3)^{28 }/ (3)^{30}=> 2 + 1/3We get the answer as C option.^{2 }= 2 + 1/9 = 19/9 = 2 1⁄9**The odds against a certain event are 5 : 2 and the odds in favour of another independent event are 6 : 5. The probability that at least one of the events will happen is:**- 12/77
- 25/77
- 52/77
- 65/77

Answer : Option C.

Required probability = 1 – P (NO event will happen) = 1 – (5/7 × 5/11) = 52/77.

**Number of times the hands of a clock are in a straight line every day is:**- 44
- 24
- 42
- 22

Answer : Option A.

In 12 hour, the hands of clock coincide 11 times and they make 180° also 11 times, thus total of 22 times. So in 24 hours, the hands of clock will be forming a straight line 22 + 22 = 44 times.**A motor boat can travel at 10 km/h in still water. It traveled 91 km downstream in river and then returned, taking altogether 20 hours. Find the rate of flow of river.**- 3 kmph
- 5 kmph
- 6 kmph
- 7 kmph

Answer : Option A.

Let the rate of flow be y kmph. The equation that will be formed is 91/(10+y) + 91/(10-y) = 20

Solving we get y = 3.**If x**^{4}+ 1/x^{4}= 47, find the value of x^{3}+ 1/x^{3}.- 18
- 20
- 22
- 24

Answer : Option A.

x^{4}+ 1/x^{4}^{2}+ 1/x^{2}= 7;Also,x^{2}+ 1/x^{2}Now,( x+1/x)^{3 }=x^{3}+ 1/x^{3}=> 27 = x^{3}+ 1/x^{3}=>x^{3}+ 1/x^{3}Intergraph Preparation Links- Sample Aptitude Questions of Intergraph
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**A person invests Rs. 5508 in '4% stock at 102'. He afterwards sells out at 105 and reinvests in '5% stock at 126'. What is the change in his income?**- Rs. 20
- Rs. 7
- Rs. 10
- Rs. 9

Answer : Option D.

Old income = 5508/102 × 4 = Rs. 216. No. of shares purchased = 5508/102 = 54. So sale proceeds = (54 × 105) = Rs. 5670.

Therefore, New income = (5670 × 5)/126 = Rs. 225.

So change in income = 225 – 216 = Rs. 9.**The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between the measure of their interior angles is 2 : 3. The number of sides of these polygons are respectively:**- 4, 8
- 5, 10
- 6, 12
- 8, 16

Answer : Option A.

Going by options, if the no of sides are 4 and 8, then the interior angles of the polygons is 90° and 135° (int angles = 180°(N-2)/N)

Which are in the ratio 2 : 3. So the answer is 1st option.**How many two-digit odd numbers can be formed from the digits 1, 2, 3, 4, 5, if repetition of digit is allowed?**- 5
- 15
- 35
- 25

Answer : Option B.

Here unit place can be filled in 3 ways (i.e. 1, 3, 5)

Ten's place can be filled in 5 ways. Required number of numbers = 5×3 = 15**Three equal glasses are filled with mixtures of sprit and water. The ratio of the sprit to water is as follows: in the first glass as 3 : 4, in the second glass as 4 : 5 and in the third glass as 5 : 6.The contents of the three glasses are emptied into a single vessel. What is the ratio of the sprit to water in the mixture now?**- 920 : 1159
- 820 : 1149
- 1120 : 1134
- 1010 : 1122

Answer : Option A.

Required Ratio:

3/7 + 4/9 + 5/11 / 4/7 + 5/9 + 6/11 = 920 / 1159.

Hence, answer is A option.**Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?**- 96 hours
- 102 hours
- 106 hours
- 112 hours

Answer : Option D.

If both filling pipes are working together, time taken to fill the tank will be 14 X16/(14 + 16) = 112/15 hrs. But due to leak it takes 32 min more. Hence total time taken = 112/15 + 32/60 = 8 hrs. Let the leak takes x hours to empty the tank, so, 1/14 + 1/16 - 1/x = 1/8.

By solving we get the answer as 112 hours. So answer is 4th option.