1). 2x + 3y = 29 and y = x + 3, what is the value of x?
View Answer Correct Answer: 4 2x+3y = 29 ...(i) and y = x+3 ...(ii) Putting the value of y from Eq. (i) to Eq. (ii), we get 2x+3y = 29 \( \Large 2x+3 \left(x+3\right)=29 \) 2x+3x+9 = 29 = 5x = 20 Therefore, x = 4
 
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?
View Answer Correct Answer: 34 Let hens = H, goats = G 2G = 68
 
3). The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
View Answer Correct Answer: 54 Let the number be x and y.
 
4). The cost of 21 pencils and 9 clippers is Rs.819. What is the total cost of 7 pencils and 3 clippers together?
View Answer Correct Answer: Rs.273 Let cost of 1 pencil and 1 clipper be p and c, respectively Now. according to the question, \( \Large 21p + 9c = Rs.819 \) \( \Large 3 \left(7p+3c\right)= Rs.819 \) \( \Large 7p + 3c = Rs.273 \) Cost of 7 pencils and 3 clippers = Rs.273.
 
5). The value of k for which kx+ 3yk+ 3=0 and 12x+ky=k, have infinite solutions, is
View Answer Correct Answer: 6 For infinite solution \( \Large \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} \) = \( \Large \frac{K}{12}=\frac{3}{K}=\frac{K+3}{K} \) = \( \Large \frac{K}{12}=\frac{3}{K}=K^{2}=36 \) Therefore, \( \Large K = \sqrt{36} = 6 \)
 
6). In a rare coin collection, there is one gold coin for every three nongold coins. 10 more gold coins are added to the collection and the ratio of gold coins to nongold coins would be 1 : 2. Based on the information; the total number of coins in the collection now becomes.
View Answer Correct Answer: 90 Let the number of gold coins initially be x and the number of nongold coins be y. According to the question, 3x = y When 10 more gold coins, total number gold coins become x + 10 and the number nongold coins remain the same at y. Now, we have \( \Large 2 \left(10+x\right)=y \) Solving these two equations, we get x = 20 and y = 60. Total number of coins in the collection at the end is equal to x+10+y = 20+10+60 = 90.
 
7). If \( \Large \frac{\sqrt{3+x}+\sqrt{3x}}{\sqrt{3+x}\sqrt{3x}}=2 \), then x is equal to
View Answer Correct Answer: \( \Large \frac{12}{5} \) Given, \( \Large \frac{\sqrt{3+x}+\sqrt{3x}}{\sqrt{3+x}\sqrt{3x}}=2 \)
 
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.
View Answer Correct Answer: 80 Let the number of correct answers be x and number of wrong answers be y Then, 4x  y = 200 ...(i) and x + y = 200 ...(ii) On adding Eqs. (i) and (ii). we get 4x  y = 200 x + y = 200 5x = 400 Therefore, x = 80
 
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?
View Answer Correct Answer: Only I and III ax + by = c and dx + ey = f
 
10). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{xy}=3 \), then what is the value of x?
View Answer Correct Answer: \( \Large \frac{17}{8} \) Given, \( \Large 2x = \frac{17}{4} = x = \frac{17}{8} \)

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