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 the number of triplets of real numbers (x, y, z) which satisfy (x + y)3 = z (y + z)3 = x (z + x)3 = y

  

  

  

  

  

If (z – 5) = 4z – 8, then which of the following could be the value of z?

  

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

If 2p + 3q = 18 and 2p – q  =2, then 2p + q =?

  

  

  

  

A man purchased 40 fruits; apples and oranges for Rs 17. Had he purchased as many as oranges as apples and as many apples as oranges, he would have paid Rs 15. Find the cost of one pair of an apple and an orange

  

  

  

  

The sum of X and Y's age is 105. When X was Y's age, she was 1.5 times Y's age then what are their present ages?

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Evaluation of 83 × 82 × 8-5    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 x2 + 1/x2 = 51 , then the value of x-1/x is

  

  

  

  

If u(m) =3m2+ 2 then what is the value of u(m + 4)?

  

  

  

  

  

Find tan 9 − tan 27 − tan 63 + tan 81 ( all angles in degrees)

  

  

  

  

  

s varies directly as the square of p. When s = 3.5, p = 0.5 If s = 90, then c would be equal to

  

  

  

  

  

The cost of 8 Sharpeners and 12 Pens is Rs. 76/- What is the cost of 20 Sharpeners and 30 Pens?  

  

  

  

  

  

The L.C.M. of 6x2 – 5x – 6 and 12x2 + 11x + 2 is

  

  

  

  

If a sum of money at certain rate of interest doubles in 5 years and at a different rate of interest becomes 3 times in 12 years, the better rate of interest is

  

  

  

  

The number of positive integers n in the range 12  ? n? 40 such that the product (n – 1) (n –2)…3.2.1 is not divisible by n is 

  

  

  

  

If e varies directly as n and e/d = 10, then what is the value of e when d = 30?

  

  

  

  

  

Solve for real x: 6x2 + 5x - 6 ≥ 0

  

  

  

  

If l + m + n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x + 3y -4z = l, 2x - y - z = m, x + y - 2z = n has at least one ?

  

  

  

  

  

The largest value of min (2 + x², 6 - 3x) when x > 0 is

  

  

  

  

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?

  

  

  

  

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 f (x+(y/8), x-(y/8)) = xy, then f (m, n) + f (n, m) = 0

  

  

  

  

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

  

  

  

  

Simplify the expression (1+i)6+(1+i)4 .

  

  

  

  

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

  

  

  

  

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