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

  

  

  

  

  

When x5– 5x4+ 9x3– 6x2– 16x + 13 is divided by x2 – 3x + a, the quotient and the remainder are x3 2x2+ x + 1 and  – 15x + 11, respectively. The value of a is equal to

  

  

  

  

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 ?

  

  

  

  

  

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

  

  

  

  

  

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:

  

  

  

  

  

Solve the following equation 3s + 5 = s – 1

  

  

  

  

  

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

  

  

  

  

If r(x) is the remainder obtained by dividing a polynomial p(x) by another polynomial q(x), then

  

  

  

  

[{√196-√64}*-2.5]=(?)  

  

  

  

  

  

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:

  

  

  

  

If 2x – ky + z = 0 is a factor of 9y2– z2 – 2xz + 6xy, then the value of k is equal to

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

  

If x = 1 – q and y = 2q + 1, then for what value of q, x is  equal to y?

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If α, β are the roots of (x –√ 3) (x –√ 5) =√ 7, the roots of (x –α) (x –β) +√ 7= 0 are

  

  

  

  

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

  

  

  

  

  

3x=5y=45z, then

  

  

  

  

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

  

  

  

  

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 logx/(a2+b2+ab) = logy/(b2+c2+bc) = logz/(c2+a2+ac) then, the value of x(a-b).y(b-c).z(c-a) is

  

  

  

  

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?

  

  

  

  

Which of the following is true?

  

  

  

  

If 8e + 2p = 12 and y – 3p = 4, then what is the value of y?

  

  

  

  

  

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

  

  

  

  

If a=b2-b,b34,then a2 -2a is always divisible by

  

  

  

  

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

  

  

  

  

  

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

  

  

  

  

  

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