Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2014 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2014

If \( y = 5x^2 + 3 \), then the tangent at \( x = 0 \), \( y = 3 \)

A

passes through \(x = 0 \), \(y = 0 \)

B

has a slope of +1

C

is parallel to the x-axis

D

has a slope of −1

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2

2015 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2015

Let \(c \in \mathbb{Z}_3\) be such that \(\frac{\mathbb{Z}_3[X]}{(X^3 + cX + 1)}\) is a field. Then \(c\) is equal to ________

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3

2015 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2015

It is known that Bessel functions \(J_n(x)\), for \(n \ge 0\), satisfy the identity \(e^{\frac{x}{2} (t - \frac{1}{t})} = J_0(x) + \sum_{n=1}^{\infty} J_n(x) \left( t^n + \frac{(-1)^n}{t^n} \right)\) for all \(t > 0\) and \(x \in \mathbb{R}\). The value of \(J_0(\frac{\pi}{3}) + 2 \sum_{n=1}^{\infty} J_{2n}(\frac{\pi}{3})\) is equal to ______

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4

2015 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2015

Consider the linear programming problem \[\begin{array}{ll} \text{Maximize} & 3x + 9y \\ \text{subject to} & 2y - x \le 2 \\ & 3y - x \ge 0 \\ & 2x + 3y \le 10 \\ & x, y \ge 0. \end{array}\] Then the maximum value of the objective function is equal to ________

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5

2016 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2016

A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?

A

−0.030

B

−0.014

C

0.014

D

0.030

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6

2020 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2020

The difference between the sum of the first \(2n\) natural numbers and the sum of the first \(n\) odd natural numbers is _____

A

\(n^2 - n\)

B

\(n^2 + n\)

C

\(2n^2 - n\)

D

\(2n^2 + n\)

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7

2020 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2020

The distance between Delhi and Agra is 233 km. A car \(P\) started travelling from Delhi to Agra and another car \(Q\) started from Agra to Delhi along the same road 1 hour after the car \(P\) started. The two cars crossed each other 75 minutes after the car \(Q\) started. Both cars were travelling at constant speed. The speed of car \(P\) was 10 km/hr more than the speed of car \(Q\). How many kilometers the car \(Q\) had travelled when the cars crossed each other?

A

66.6

B

75.2

C

88.2

D

116.5

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8

2024 · General Aptitude (GA) · General Aptitude · Algebra

Mathematics (MA) 2024

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

A

150

B

200

C

250

D

175

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