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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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?

  

  

  

  

If x varies as y2 + 2 and is equal to 36 when y = 4, find x when y = 12.

  

  

  

  

The system of equations x + 2y = 3 and 2x + 4y = 3, has

  

  

  

  

If 2x + 3y -31, y – z - 4 and x + 2z – 11, then what is the value of x + y + z ?

  

  

  

  

The number of non-negative real roots of 2x – x – 1 = 0 equals

  

  

  

  

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

  

  

  

  

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

  

  

  

  

  

[{√196-√64}*-2.5]=(?)  

  

  

  

  

  

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

  

  

  

  

If ( p - q) 2 = ( x – y ) 2, then x =

  

  

  

  

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?

  

  

  

  

If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:

  

  

  

  

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

  

  

  

  

  

Which of the following is true?

  

  

  

  

If a + b + c = 3, a2 + b2 + c2 = 9, a3 + b3 + c3 = 24 , Then find a4 + b4 + c4

  

  

  

  

  

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 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.

  

  

  

  

H.C.F. of two polynomials is a + 5 and their L.C.M. is (a + 5) (a + 4) (a – 1). If one of the polynomial is a2+ 4a – 5,then the other polynomial is

  

  

  

  

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

  

  

  

  

  

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

  

  

  

  

 If s varies directly as e and s/e = 6, then what is the value of s when e = 2.2?

  

  

  

  

  

Let tan θ = tan 10 − tan 50 + tan 70 then θis ?( all angles in degress)

  

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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 ?

  

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The g.c.d. of x3 + x2 – x – 1 and x2 – 1 is

  

  

  

  

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