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

Given:

Total number of coins = 50

Total amount = Rs 11.25

Let the number of 20 paise coins be x

Let the number of 25 paise coins be y

Formula Used:

x + y = 50

0.20x + 0.25y = 11.25

Calculation:

From the first equation:

y = 50 - x

Substitute y in the second equation:

0.20x + 0.25(50 - x) = 11.25

⇒ 0.20x + 12.5 - 0.25x = 11.25

⇒ -0.05x + 12.5 = 11.25

⇒ -0.05x = 11.25 - 12.5

⇒ -0.05x = -1.25

⇒ x = -1.25 / -0.05

⇒ x = 25

Substitute x = 25 in the first equation:

y = 50 - 25

⇒ y = 25

The man has 25 coins of 20 paise and 25 coins of 25 paise.

The initial price increase of \(20\%\) makes the price \(b + 0.20b = 1.20b\). A subsequent \(15\%\) decrease results in \(1.20b - 0.15(1.20b) = 1.20b - 0.18b = 1.02b\). Therefore, the final price is \(1.02b\), showing that the combination of increases and decreases results in a net increase of \(2\%\).

The shirt's price is initially \(b\) dollars. A \(60\%\) reduction means the new price is \(b - 0.60b = 0.40b\). After the reduction, the price increases by \(50\%\). An increase of \(50\%\) means the price becomes \(0.40b + 0.50(0.40b) = 0.40b + 0.20b = 0.60b\). Therefore, the final price is \(0.60b\) of the original price \(b\).

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.

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 \(z\).