Maths MCQ Quiz in मराठी - Objective Question with Answer for Maths - मोफत PDF डाउनलोड करा

The equation of a circle in the standard form is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Here, the center is \((3, -2)\), so \(h = 3\) and \(k = -2\).

The radius is \(6\), so \(r^2 = 36\).

Substituting these values, the equation becomes \((x - 3)^2 + (y + 2)^2 = 36\).

Option 3 is correct. Option 1 is identical to option 3. Option 2 incorrectly switches the signs for \(h\) and \(k\), and option 4 uses the radius instead of the radius squared.

The correct answer is option 1: Decreasing exponential. The liquid’s temperature decreases by a fixed percentage (10%) each hour, which indicates exponential decay. This situation is best modeled by a decreasing exponential function because the temperature reduces by a constant proportion over time. Option 2 would imply a fixed amount of temperature loss each hour, which is not the case here. Options 3 and 4 describe increasing trends, which do not fit the cooling scenario.

To find the median, list the scores in ascending order, which is already done: 55, 60, 65, 70, 75, 80, 85. The median is the value in the middle of a data set. With 7 values, the median is the 4th number, which is 70. Therefore, option 2 (70) is correct. Options 1 (65), 3 (75), and 4 (80) are incorrect because they do not represent the middle value in the ordered list.

Tripling all numbers above the median and halving all numbers below the median results in a significant change in the spread of the data. The median remains unchanged as it is the central value of the ordered list. The mean, which depends on the total sum, will change due to the drastic modifications in individual values. The total sum changes as the transformations alter the overall sum of the data. The standard deviation, which measures the spread of the data points from the mean, will definitely increase due to the increased variability in the data. Thus, the standard deviation is altered.

The initial number of users is 5,000 and the number doubles every 6 months. In terms of years, this is equivalent to \(2t\) since doubling occurs every half year. Therefore, the equation for the number of users \(U\) after \(t\) years is \(U = 5000(2)^{2t}\). Option 3 correctly represents this relationship. Option 1 is incorrect because it suggests doubling every month, not every 6 months. Option 2 is incorrect because it implies doubling every 6 years. Option 4 is incorrect because it suggests doubling every year, not 6 months.

To find the equation of a line parallel to \( y = 4x + 2 \), we must use the same slope, which is \( 4 \). A parallel line will also have a slope of \( 4 \). The point given is \( (3, 9) \), and we can use the point-slope form of a line: \( y - y_1 = m(x - x_1) \). Substituting the values, we get \( y - 9 = 4(x - 3) \). Simplifying, \( y - 9 = 4x - 12 \), so \( y = 4x - 3 \). Thus, the equation is \( y = 4x - 3 \), making option 2 correct. Options 1, 3, and 4 are incorrect as they do not satisfy both the condition of passing through \( (3, 9) \) and having the slope \( 4 \).

Let \( x \) represent the number of cows and \( y \) represent the number of chickens. We know that cows have 4 legs and chickens have 2 legs. Therefore, the equations are: \( x + y = 50 \) and \( 4x + 2y = 140 \). Solving these equations, we first multiply the first equation by 2: \( 2x + 2y = 100 \). Subtracting this from the second equation gives \( 4x + 2y - 2x - 2y = 140 - 100 \), which simplifies to \( 2x = 40 \). Dividing by 2, we find \( x = 20 \). Therefore, the farmer has 20 cows.

Subtract \(15\) from both sides of \(4z + 15 = 47\) to get \(4z = 32\). Divide both sides by \(4\) to solve for \(z\), giving \(z = 8\). Thus, option 1 is correct. Options 2, 3, and 4 are incorrect since they do not satisfy the equation when substituted for \(z\).

To solve the equation \(3x + 12 = 30\), we first need to isolate the variable \(x\). Start by subtracting \(12\) from both sides to obtain \(3x = 18\). Next, divide both sides by \(3\) to solve for \(x\), yielding \(x = 6\). Therefore, the value of \(x\) is \(6\). Option 3 is the correct answer. Options 1, 2, and 4 are incorrect because substituting \(x = 4, 5,\) or \(7\) into the equation \(3x + 12\) does not equal \(30\).

The correct answer is 27.

It's given that a triangular prism has a volume of 216 cubic centimeters (cm3) and the volume of a triangular prism is equal to Bh, where B is the area of the base and h is the height of the prism.
Therefore, 216 = Bh. It's also given that the triangular prism has a height of 8 cm.
Therefore, h = 8.
Substituting 8 for h in the equation 216 = Bh yields 216 = B(8).
Dividing both sides of this equation by 8 yields 27 = B.
Therefore, the area, in cm2, of the base of the prism is 27 .