Objective Questions

An arithmetic sequence has a first term 5 and 15th term 47. What is the sum of …

Find the number of terms in the arithmetic series 7 + 10 + 13 + ... + 100

The nth term of an arithmetic sequence is 3n + 2. What is the 20th term?

Which of the following is NOT a property of geometric sequences?

A sequence is defined recursively as a₁ = 2 and a_n = a_{n-1} + 3. What type of…

In an arithmetic sequence, if the sum of the first 20 terms is 400 and the firs…

The 7th term of an arithmetic progression is 35, and the 3rd term is 19. What i…

If a geometric sequence has a negative common ratio, its terms will:

The number of permutations of 12 objects taken 3 at a time is:

If 6 nickels, 4 dimes, and 2 quarters are indistinguishable, how many distinct …

The number of combinations of n objects taken k at a time is given by:

In how many ways can 3 officers be chosen from 7 members, regardless of positio…

What is the value of 8C5?

Which expression represents the kth term in the expansion of (x+y)ⁿ?

What is the coefficient of x³y² in the expansion of (x+y)⁵?

Which term is the sixth in the expansion of (x+y)⁸?

Which identity justifies that (1+a)ⁿ > 1+na for a > 0?

What is the result of A ∩ B' given A = {1, 3, 5} and B = {3, 4, 5}?

What is the cardinality of A ∪ B if n(A) = 10, n(B) = 15, and n(A ∩ B) = 5?

The nth term of a geometric sequence is given by:

What is the correct result for the sum 1+2+3+...+n using induction?

In proving that 1+2+...+n = n(n+1)/2 by induction, what is added to both sides …

What is a limitation of basic mathematical induction?

Which method is used to validate a statement for all natural numbers?

Find the correct trigonometric identity.

Find the center and radius of the circle x² + y² + 8x - 10y + 5 = 0.

If p and q are integers and a number is represented in the form of p/q, then it…

Find the parametric equation of the circle x² + y² - 2x - 6y - 6 = 0.

Use principle of mathematical induction to find the value of k, where for all p…

Value of (cos15°/sin15°) - (sin15°/cos15°) is:

What is the first step in mathematical induction?

In a class of 40 students, 32 are good in mathematics, 24 in physics, and 4 tak…

For all k ∈ N, 2^(5k) − 1 is divisible by

Find the coefficient of x^4 in the binomial expansion of (1 - 2x)^7

Suppose that n is an integer and j ≤ n. Then C(n, j) is equal to

In a sample of 1000 foodstuffs scores taken at a market, 200 stock rice, 240…

The point (2,3) lies on the circle x² + y² + 4x - 2y - 15 = 0 at one end of a d…

Given that z₁ = 5 - 2i and z₂ = -1 - i. Find 2z₁ - z₂.

Which of the following set of numbers does not define a right-angled triangle?

We can arrange three objects out of five different objects in how many ways?

Find the equation of a circle passing through the points (1,5), (5,3) and (3,-1…

If n ∈ Z⁺, then 5(5ⁿ) - 4n - 5 is divisible by

Solve the equation 3x/2 = 7/4

Simplify (csc y + cot y)(csc y - cot y)/csc y

Given that z₁ = 1 - i and z₂ = 1 + i. Find the product of z₁ and z₂.

The sum 1³ + 2³ + ... + n³ is?

135° in radians is?

Suppose the base case for the mathematical induction is to show that P(1) is tr…

Given that z₁ = 1 - 7i and z₂ = -2 + 5i. Find the magnitude of z₁ - z₂.

The exact value of cos35° cos25° - sin35° sin25° is:

Given that z = -2 - 3 - 2i. Evaluate

If tan α = 4/3, α lies in quadrant III, and cos β = 20/29, β lies in quadrant I…

The sum or difference of two irrational numbers is always

Find the equation of a circle whose center is at the point (-1,6) and passes th…

If f(n) = 2ⁿ + 6ⁿ, then what is f(k+1)?

If z = 1 - i√3. Find the value of |z|.

The largest number that divides 70 and 125, which leaves the remainders 5 and 8…

Write in simplest form: 2/(3+√5)

Evaluate (cosec θ - cot θ)(cosec θ + cot θ).

In a class of 40 students, 32 are good in mathematics, 24 in physics, 4 do not …

Use principle of mathematical induction to find the value of k, where for all p…

Which of the following is not the same as tan(t)?

The area of triangle PQR is given by:

A complex number consists of two parts:

Find the equation of a circle with center (-3,2) and radius 4.

If n ∈ N, then 11^(n+2) + 12^(2n+1) is divisible by

In a sample of 1000 foodstuff sellers at a market, 200 stock rice, 240 stock be…

Find the equation of the circle whose center is the same as that of the circle …

Find the equation of a circle passing through the point (4,1) and (1,5) and hav…

Find the value of log(-5).

The value of (sin 150° - 5 cos 300° + 7 tan 225°)/(tan 135° + 3 sin 210°) is:

A circle has its center on the y-axis and passes through (-1,3) and (2,5). Find…

Complex number can be represented in the following form except:

Given that z₁ = 2 - 2i and z₂ = 1 + i, find z₁/z₂

If P(k) = k²(k+3)(k²-1) is true, then what is P(k+1)?

Given that z₁ = 1 - 7i and z₂ = -2 + 5i. Find the value of z₁ - z₂.

What type of reasoning is mathematical induction classified under?

A quadratic equation with two equal real roots must have a discriminant:

If the discriminant of a quadratic is negative, the roots are:

What is the 11th term of the sequence: \(m - 2n, m - n, m, \ldots\)?

If \(A \cap B = A\), then:

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

Determine the moduli for the complex roots of the quadratic equation given by: …

The roots of the quadratic equation \(2x^2 + x + 4 = 0\) are

Which formula holds for \(\sum_{k=1}^n 2^k\) for all \(n \geq 1\)

To convert angles in radian to degrees, multiply the angle by which of the foll…

The inequality \(|x| > 4\) is equivalent to:

In a survey of 290 newspapers readers, 181 of them read the Daily Times, 142 re…

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

If \(z = 4(\cos 110^\circ + i \sin 110^\circ)\), find \(z^3\).

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

If \(z_1 = 3+2i\) and \(z_2 = 2-3i\), then \(\frac{z_1}{z_2} = \)

Which of the following is always true?

The coefficient of \(x^7\) in the expansion of \((x - m)^{12}\) is

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

Solve the equation \(x^2 - 2x + 5 = 0\).

In a survey of 120 students... Now, suppose 10 Students offer the three Subject…

If the coefficient of \(y^4\) in \((1+y)^n\) is \(x\), find the coefficient of …

Let x < 1. Using the binomial theorem, which represents (1 + x)^{-1}?

Determine the square root of \(z = 4(\cos70^\circ + i\sin70^\circ)\)