Q. If the Binomial Theorem is applied to (x + y)^4, what is the term containing x^2y^2?
A.
6x^2y^2
B.
4x^2y^2
C.
8x^2y^2
D.
12x^2y^2
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Solution
The term containing x^2y^2 in the expansion of (x + y)^4 is given by 4C2 * x^2 * y^2 = 6x^2y^2.
Correct Answer:
A
— 6x^2y^2
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Q. If the Binomial Theorem is used to expand (3x - 2)^4, what is the constant term?
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Solution
The constant term occurs when x^0, which is the term with k = 4: C(4, 4)(-2)^4 = 16, thus the constant term is -16.
Correct Answer:
B
— -81
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Q. If the Binomial Theorem is used to expand (a + b)^7, how many terms will be in the expansion?
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Solution
The number of terms in the expansion of (a + b)^n is n + 1, so for n = 7, there will be 8 terms.
Correct Answer:
C
— 8
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Q. If the Binomial Theorem is used to expand (x + 1/x)^6, what is the term containing x^0?
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Solution
The term containing x^0 occurs when k = 3, which gives 6C3 * 1^3 * (1/x)^3 = 20.
Correct Answer:
B
— 20
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Q. If the circumference of a circle is 31.4 cm, what is the radius of the circle? (Use π = 3.14) (2022)
A.
5 cm
B.
7 cm
C.
10 cm
D.
15 cm
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Solution
Circumference = 2πr. Therefore, r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the circumference of a circle is 31.4 cm, what is the radius?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what does C(n,k) represent?
A.
The number of ways to choose k items from n.
B.
The total number of terms in the expansion.
C.
The sum of the coefficients.
D.
The product of the coefficients.
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Solution
C(n,k) represents the number of ways to choose k items from n, which corresponds to the coefficient of x^k.
Correct Answer:
A
— The number of ways to choose k items from n.
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Q. If the common ratio of a GP is negative, which of the following statements is true?
A.
The terms will always be positive.
B.
The terms will alternate in sign.
C.
The sum of the terms will be negative.
D.
The first term must be negative.
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Solution
In a GP with a negative common ratio, the terms will alternate in sign, starting from the sign of the first term.
Correct Answer:
B
— The terms will alternate in sign.
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Q. If the compound interest on a sum of money for 2 years is $400 and the principal is $1600, what is the rate of interest? (2023)
A.
10%
B.
12.5%
C.
15%
D.
20%
Show solution
Solution
Using the formula CI = P[(1 + r)^n - 1], we can set up the equation 400 = 1600[(1 + r)^2 - 1]. Solving gives r = 12.5%.
Correct Answer:
B
— 12.5%
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Q. If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, what are the coordinates of the point?
A.
(6, 4)
B.
(5, 5)
C.
(4, 6)
D.
(2, 8)
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Solution
Solving the equations x + y = 10 and x - y = 2 simultaneously gives x = 6 and y = 4.
Correct Answer:
A
— (6, 4)
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Q. If the coordinates of point C are (x, 0) and it lies on the line y = -3x + 6, what is the value of x?
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Solution
Setting y = 0 in the equation -3x + 6 = 0 gives x = 2.
Correct Answer:
B
— 2
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Q. If the coordinates of points D and E are (2, 3) and (4, 7) respectively, what is the slope of the line DE?
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Solution
The slope m is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.
Correct Answer:
B
— 2
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Q. If the cost price of an article is Rs. 500 and the selling price is Rs. 600, what is the profit percentage?
A.
20%
B.
25%
C.
30%
D.
35%
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Solution
Profit = Selling Price - Cost Price = 600 - 500 = 100. Profit Percentage = (Profit/Cost Price) * 100 = (100/500) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If the cost price of an item is Rs. 500 and the selling price is Rs. 600, what is the gain percentage?
A.
20%
B.
25%
C.
30%
D.
15%
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Solution
Gain = Selling Price - Cost Price = 600 - 500 = 100. Gain percentage = (Gain/Cost Price) * 100 = (100/500) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If the decimal number 10 is converted to binary, what is the resulting binary number? (2023)
A.
1010
B.
1001
C.
1100
D.
1110
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Solution
The decimal number 10 is represented as 1010 in binary.
Correct Answer:
A
— 1010
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Q. If the decimal number 15 is converted to binary, what is the resulting binary number?
A.
1110
B.
1111
C.
1101
D.
1011
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Solution
The decimal number 15 is represented as 1111 in binary.
Correct Answer:
B
— 1111
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Q. If the decimal number 255 is converted to binary, what is the resulting binary number?
A.
11111111
B.
11011111
C.
10111111
D.
10011111
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Solution
The decimal number 255 converts to binary as 11111111.
Correct Answer:
A
— 11111111
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Q. If the derivative of a function f(x) is positive for all x in its domain, what can be inferred about the function?
A.
The function is decreasing.
B.
The function is constant.
C.
The function is increasing.
D.
The function has a maximum point.
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Solution
If the derivative of a function is positive for all x, it indicates that the function is increasing throughout its domain.
Correct Answer:
C
— The function is increasing.
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Q. If the diagonal of a square is 10√2 cm, what is the area of the square?
A.
100 cm²
B.
200 cm²
C.
50 cm²
D.
150 cm²
Show solution
Solution
The diagonal d of a square is related to the side length s by the formula d = s√2. Therefore, s = d/√2 = 10√2/√2 = 10 cm. The area is s² = 10² = 100 cm².
Correct Answer:
B
— 200 cm²
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Q. If the diagonals of a quadrilateral are equal and bisect each other, which type of quadrilateral can it be?
A.
Trapezium
B.
Rectangle
C.
Rhombus
D.
Parallelogram
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Solution
If the diagonals of a quadrilateral are equal and bisect each other, it can be classified as a rectangle.
Correct Answer:
B
— Rectangle
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Q. If the diagonals of a quadrilateral bisect each other at right angles, which of the following can be concluded?
A.
It is a rectangle.
B.
It is a rhombus.
C.
It is a trapezium.
D.
It is a square.
Show solution
Solution
If the diagonals of a quadrilateral bisect each other at right angles, it indicates that the quadrilateral is a rhombus.
Correct Answer:
B
— It is a rhombus.
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Q. If the diagonals of a quadrilateral bisect each other at right angles, which of the following could it be?
A.
Rectangle
B.
Square
C.
Trapezium
D.
Kite
Show solution
Solution
A kite has diagonals that bisect each other at right angles.
Correct Answer:
D
— Kite
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Q. If the diagonals of a quadrilateral bisect each other, which of the following can be inferred?
A.
The quadrilateral is a parallelogram.
B.
The quadrilateral is a rectangle.
C.
The quadrilateral is a rhombus.
D.
The quadrilateral is a trapezium.
Show solution
Solution
A quadrilateral with diagonals that bisect each other is a parallelogram, but it can also be a rectangle or rhombus.
Correct Answer:
A
— The quadrilateral is a parallelogram.
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Q. If the diagonals of a quadrilateral bisect each other, which of the following can be concluded? (2023)
A.
The quadrilateral is a rectangle.
B.
The quadrilateral is a rhombus.
C.
The quadrilateral is a parallelogram.
D.
The quadrilateral is a trapezium.
Show solution
Solution
If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.
Correct Answer:
C
— The quadrilateral is a parallelogram.
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Q. If the diagonals of a quadrilateral bisect each other, which of the following could be true?
A.
It is a rectangle.
B.
It is a trapezium.
C.
It is a parallelogram.
D.
It is a kite.
Show solution
Solution
If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.
Correct Answer:
C
— It is a parallelogram.
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Q. If the diagonals of a quadrilateral bisect each other, which of the following must be true?
A.
It is a rectangle.
B.
It is a parallelogram.
C.
It is a square.
D.
It is a trapezium.
Show solution
Solution
A quadrilateral with diagonals that bisect each other is a parallelogram.
Correct Answer:
B
— It is a parallelogram.
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Q. If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% is $50, what is the principal? (2000)
A.
$1000
B.
$1200
C.
$1500
D.
$2000
Show solution
Solution
The difference between CI and SI for 2 years is given by P * (r^2)/100^2. Setting this equal to $50 and solving gives P = $1500.
Correct Answer:
C
— $1500
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Q. If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% per annum is $50, what is the principal? (2000)
A.
$1000
B.
$1200
C.
$1500
D.
$2000
Show solution
Solution
The difference between compound interest and simple interest for 2 years is given by SI * (r/100)^2. Setting this equal to $50 and solving gives Principal = $1200.
Correct Answer:
B
— $1200
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Q. If the difference between the compound interest and simple interest on a sum of money for 2 years at 10% per annum is $50, what is the principal? (2000)
A.
$1000
B.
$1200
C.
$1500
D.
$2000
Show solution
Solution
The difference SI and CI for 2 years is given by P * r^2 / 200. Setting this equal to 50 gives P = $1500.
Correct Answer:
C
— $1500
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Q. If the equation 2x + 3 = 11 is solved for x, what is the value of x?
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Solution
To solve for x, subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4.
Correct Answer:
C
— 4
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