>> Aptitude >> Linear Equations
1). 2x + 3y = 29 and y = x + 3, what is the value of x?
A). 4 B). 5
C). 6 D). 7
2). Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
A). 32 B). 36
C). 34 D). Cannot be determined
3). The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
A). 56 B). 63
C). 42 D). 54
4). The cost of 21 pencils and 9 clippers is Rs.819. What is the total cost of 7 pencils and 3 clippers together?
A). Rs.204 B). Rs.409
C). Rs.273 D). Rs.208
5). The value of k for which kx+ 3y-k+ 3=0 and 12x+ky=k, have infinite solutions, is
A). 0 B). -6
C). 6 D). 1
6). In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2. Based on the information; the total number of coins in the collection now becomes.
A). 90 B). 80
C). 60 D). 50
7). If \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \), then x is equal to
A). \( \Large \frac{5}{12} \) B). \( \Large \frac{12}{5} \)
C). \( \Large \frac{5}{7} \) D). \( \Large \frac{7}{5} \)
8). In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions stud and scored 200 marks. Find the number of questions he answered correctly.
A). 82 B). 80
C). 68 D). 60
9). The graphs of ax + by = c, dx + ey = f will be
I. parallel, if the system has no solution.
II. coincident, if the system has finite numbers of solutions.
III. intersecting, if the system has only one solution.
Which of the above statements are correct?

A). Only I and II B). Only ll and Ill
C). Only I and III D). I, II and Ill
10). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?
A). \( \Large \frac{17}{16} \) B). \( \Large \frac{17}{8} \)
C). \( \Large \frac{17}{4} \) D). \( \Large \frac{15}{4} \)