Aptitude - Equations Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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Find tan 9 − tan 27 − tan 63 + tan 81 ( all angles in degrees)

  

  

  

  

  

If h = 2/3 and k = 6 then k/h + 4/h2 =

  

  

  

  

  

Evaluation of 83 × 82 × 8-5    is:

  

  

  

  

n4 − 20n2 + 4 = k where k is a prime number and n is an integer. How many such k exist?

  

  

  

  

  

A pole has to be erected on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrical opposite fixed gates A and B on the boundary is 7 meters. The distance of the pole from one of the gates is:

  

  

  

  

A ship 55 kms. From the shore springs a leak which admits 2 tones of water in 6 min; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.

  

  

  

  

If x3+ ax2+bx +6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), the value of a and b respectively are

  

  

  

  

For prime numbers p and q, p + q = 102 and p > q. What is the least possible value of p − q?

  

  

  

  

  

P lent Rs.600 to Q for 2 years and Rs.150 to R for 4 years and received altogether from both Rs.90 as interest. Find the rate of interest, simple interest being calculated

  

  

  

  

If r varies directly as n and r/m = 10, then what is the value of r when m = 2.2?

  

  

  

  

  

If a1 = 1 and an+1 = 2an + 5, n = 1, 2 ...., then a100 is equal to :

  

  

  

  

A singles tennis tournament is held, in which 30 men participated. If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner

  

  

  

  

The difference in the money between A and B is Rs.1450.C has money twice of B and difference in the money between A and C is Rs.700.So the amount with A is?

  

  

  

  

3x=5y=45z, then

  

  

  

  

 If g = log, (ax) then pz =

  

  

  

  

  

A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible.

  

  

  

  

  

If  a * b – 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to:

  

  

  

  

If xy = 96 and 3y = 2x, then what is the value of x

  

  

  

  

  

If x + y = 2, xy = 1, then the values of x and y are respectively

  

  

  

  

The value of 1/4 + 1/9 + 1/16 + ... +1/n2 is

  

  

  

  

If n(x) = x2 - 10x, then n(-10) =

  

  

  

  

  

Madhu has received admission in all schools listed above. She wishes to select the highest overall ranked school whose a) annual tuition fee does not exceed $23,000 and b) median starting salary is at least $70,000. Which school will she select?

  

  

  

  

If a2 = b4 = c8 = d16, then logd2 (abc)1/3

  

  

  

  

a, b, c, d be real numbers in G.P. If u, v,w satisfy the equations u + 2v + 3w = 6; 4u + 5v + 6w = 12; 6u + 9v = 4 then roots of the equations (1/u + 1/v + 1/w)x2 + [(b − c)2 + (c − a)2 + (d − b)2]x + u + v + w = 0 and 20x2 + [10(a − d)2]x − 9 = 0 are

  

  

  

  

  

If x = 3 –  √5 , then the value of x2+16/x2 is equal to

  

  

  

  

Which of the following value of x do not satisfy the inequality (x² - 3x + 2 > 0) at all?

  

  

  

  

If 8a + 4b = 11 and 2a + 4g = 5. The value of b = 2. You need to find the value of a and g.

  

  

  

  

  

If (x + 4) (x + 6) (x +1) 2> 0, then the solution set for the inequality is

  

  

  

  

If x + y = 2, then the value of x4 + y4 – x3 y2 – x2 y3+16xy is equal to

  

  

  

  

The ratio of ages of a father and son is 17:7 respectively. 6 years ago the ratio of their ages was 3:1 respectively. What is the father's present age?

  

  

  

  

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