Objective Questions

Find the equation whose roots are the squares of the roots of \( x^2 + x + 2 = …

Interval \((-\infty, b]\) can be written as:

If \( x(A) = 20 \), \( x(B) = 15 \), \( x(A \cup B) = 5 \), find \( x(A \cap B)…

Simplify \( (\csc x + \cot x)^2 \csc x - \cos x \)

The 2nd, 3rd and 9th terms of an AP are the three consecutive terms of a GP. Fi…

The number 0.454545... is called

For \( x \geq 1, y = 2x + 1 \), Which is correct?

The roots of a quadratic equation \( ax^2 + bx + c = 0 \) are 1, 1 and -6. What…

The equation \( 1x + 2 = x + 2 \) holds for:

Select one:

For \( x = 2, y = 2x + 1 \), Which is correct?

Find the coefficient of \( x^{-12} \) in \( (x^3 - 1/x)^{24} \).

The modulus and argument of \( \sqrt{3} + \sqrt{2}i \) are

The coefficients of the second and third term of the expansion of \( (1 + cx)^3…

Simplify: \( (5 + 4i) + (3 - 2i) \)

Suppose that \( (x + y) + i(x - y) = 4 \), find \( x - y \) in the equation

If \( (a - 2b) + i(2a - b) = 4 + 2i \), find \( a \) and \( b \).

If \( n(A) = p \), \( n(B) = q \), \( n(U) = N \), and \( A \cap B = \emptyset …

Which of the following is not true about (a + x)ⁿ, where n is a positive intege…

If the coefficients of \( x^2 \) and \( x^3 \) in the expansion of \( (3 + ax)^…

Complex number \(\frac{5 - 2i}{3 - 4i} = \frac{5 + 2i}{3 + 4i}\) can be written…

Let \( A, B, C \subseteq U \). Simplify \( (A \cap B) \cup (A \cap B^c) \)?

Solve for x and y in the equations: \(\log(x+1) + 2\log(y-2\log 3) = \log(8)\) …

Solve \( (\log_2 m)^2 - \log_2 m^3 = 10 \).

Solve: \( |3x - 6| \leq 3 \)

Find the term independent of \( x \) in \( (2x + 1/x^2)^9 \).

The exact value of \( \cos 35^\circ \cos 25^\circ - \sin 35^\circ \sin 25^\circ…

Given \( U = \{1, 2, 3, 4, 5, 6\} \), \( A = \{1, 2, 4\} \) and \( B = \{1, 3, …

If \( n(A)=20 \), \( n(B)=15 \), \( n(A \cap B)=5 \), find \( n(A \cup B) \)?

In complex structure, what is the equivalence if \( z = (\cos \theta + i \sin \…

If \( a > b > 0 \), then

By mathematical induction \( 1 + 3 + 5 + \dots + (2k-1) \) is

Given \( U = \{1, 2, 3, ..., 10\} \), \( N = \{\text{even numbers}\} \), \( F =…

If \( (3+i)x + (1-2i)y + 7 = 0 \), then the values of x and y respectively are

Given \( z_1 = (\cos 25^\circ + i \sin 25^\circ) \) and \( z_2 = (\cos 120^\cir…

Polar form of \( 4 + 4\sqrt{3}i \) is

Which of the following is an irrational number?

\( (\cos \theta + i \sin \theta)^n \) is equal to

Which of the following is true about this numbers (-5, -4, -3, -2, -1)?

If n(A) = 20, n(A ∪ B) = 15, and n(A ∩ B) = 5, find n(B).

Using the trigonometric formulae, which of the following option is not true?

In a survey of 120 students in the Faculty of Physical and Earth Sciences, 7…

The expansion of \( (1 + y)^{-1} \) is:

If i is a root of the quadratic equation \( x^2 - mx + 1 = 0 \), then the value…

Given that \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(3…

Find the quadratic equation whose sum and product of roots are respectively \(\…

For \(n \geq 1\), \(3^{2n+1}\). Which is correct?

The exact value of \(\cos 35^\circ \cos 25^\circ - \sin 35^\circ \sin 25^\circ\)

Evaluate \(\cos(-225^\circ)\) without the use of e-calculator or figures tables.

Suppose that \((x + y) + i(x - y) = 4\), find \(x - y\) in the equation

Given that \(m, 2m - 1\) and \(3m - 5\) are three consecutive terms of a GP. Fi…

If \((3+i)x + (1-2i)y + 7i = 0\), then the values of x and y respectively are

Let \(A, B, C \subseteq U\). Simplify \((A \cap B) \cup (A \cap B^c)\)?

A set with no elements is called:

If f(x) = 2x - 8, and f: A → B where A = {1,2,3}, what is the range B?

The set {x ∈ N | x² ≤ 25} is:

Which of the following is true about ∅?

If n(A) = 5 and n(B) = 3, what is the maximum number of elements in A ∪ B?

How many men received medals in exactly two of three sports if 38 got football,…

Which set includes all rational and irrational numbers?

What is the additive identity in the set of real numbers?

Which property states that a + b = b + a?

The result of multiplying a real number by its multiplicative inverse is:

Simplify: (3x² - 1)(x² + x + 1)

Simplify: (x³ + 1)/(x + 1)

log_b(xy) equals:

Change log₅ 2 to base 10:

What is the number of permutations of 7 objects taken 3 at a time?

How many combinations of 7 objects taken 3 at a time exist?

The formula for the number of permutations of n objects taken k at a time is:

The number of distinguishable arrangements of 6 nickels, 4 dimes, and 2 quarter…

How many subsets of a set with 10 elements exist?

Which of the following is NOT a property of binomial coefficients?

Express \( e^{(1 - \frac{\pi}{4}i)} \) as a product

If P(n): n! > 2ⁿ for n ≥ 4, what is the smallest n for which this holds?

Find the coefficient of x^3 in (2 − x)^5

If sinθ = 1/2, find cosθ (θ acute)

Find |A ∪ B| if |A| = 20, |B| = 15, |A ∩ B| = 5

Evaluate tan45° + cot45°

Which set is finite?

Find (cos60° − sin60°)

Find the coefficient of x in (1 + x)^4

The ends of a diameter have coordinates (5, 4) and (-3, 6). Find the equation o…

What is the sum of the coefficients in the binomial expansion of (x - y)^n?

The sum of the first 10th term of an Arithmetic Progression is 50, and the firs…

What is the result of A ∪ ∅?

The value of (1+2)⁵ using Binomial Theorem is:

What is the sum of coefficients in the expansion of (x+y)ⁿ?

The roots of the equation x² - 6x + 9 = 0 are:

The sum 1³+2³+...+n³ is?

What is a portion of the circumference called?

What is the value of 9P3?

The binomial coefficient nCk is equal to:

The value of cot 30° / tan 60° is:

Find the sum of the coefficients in the binomial expansion of (x + y)^n

If \( x^2 < 4 \), then: