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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If x2 + 1/x2 = 51 , then the value of x-1/x is

  

  

  

  

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?

  

  

  

  

Ujakar and Keshab atternplted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

  

  

  

  

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

  

  

  

  

  

If (c – 5) = 4c – 7, then which of the following could be the value of c?

  

  

  

  

  

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?

  

  

  

  

If x=1+2a+3a2+4a2+……( -1 < a < 1 ) and y=1+3b+6b2+10b3+……( -1 < b < 1 )then find 1+ab+(ab)2+(ab)3+….. in terms of x and y.

  

  

  

  

Solve the following equation 3 (x + 2) + 5 (x + 6) = 56

  

  

  

  

  

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.

  

  

  

  

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?

  

  

  

  

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 a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.

  

  

  

  

(xn - an) is completely divisible by (x - a), if

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Find the number of solutions in positive integers (k; a1, a2, . . . , ak; b1, b2, . . . , bk) to the equation a1(b1) + a2(b1 + b2) + · · · + ak(b1 + b2 + . . . + bk) = 7

  

  

  

  

  

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

  

  

  

  

If o = 4/3 and h = 6 then h/o + 4/o2 =

  

  

  

  

  

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

  

  

  

  

  

If p and q are real numbers; p ≠  0, then the equation 3x – 5 + q = px + 1 has no solution, if

  

  

  

  

The number of solutions of x2 - 5|x| + 6 = 0 is

  

  

  

  

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

  

  

  

  

If n(x) = x2 - 10x, then n(-10) =

  

  

  

  

  

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

  

  

  

  

  

Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2,where k, t are integers. Then m + n equals:

  

  

  

  

  

If the interest on Rs. 800 exceeds that on Rs. 600 by Rs. 15.50 in 6 months, find the rate percent p.a

  

  

  

  

What is the minimum value of x for which the expression x3 – 7x2 + 11x – 5 gives positive values

  

  

  

  

If 7s + 2e = 14 and s – 2e = 5, then what is the value of s?

  

  

  

  

  

If a + b = 0, then (1 + xa)-1 + (1 + xb)-1 - xa+b =

  

  

  

  

If 1 + 2 + 22 + 23 +.......+ 250 is divided by 7, what will be the remainder?

  

  

  

  

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