Objective Questions

Find the sum of the terms of the infinite geometric progression: \(\frac{1}{3},…

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

Find the nth term of the sequence 5, 10, 20, 40, 80...

Simplify: \(\frac{5+10i}{3+i}\)

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

Given that \(Z = z e^{ik}\) and \(W = w e^{ih}\), find \(\frac{Z}{W}\) in its s…

What is the sum of the sequence \(\sum_{k=1}^{3} (1 + k!)\)?

Find the common ratio and the 6th term of the GP: \(-\frac{1}{2}, \frac{1}{8}, …

If the value of \(\alpha + \beta = 90^\circ\) and \(\alpha : \beta = 2:1\), the…

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

The solution set of \(|2x+1| \geq 3\) is:

Find the equation whose roots are the squares of the roots of \(x^2 + x + 2 = 0…

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

The set of non-repeating, non-terminating block of digits is called

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

The sixth term in the binomial expansion of \((2x - \frac{1}{3x^2})^{10}\) is

If (3a - 2b) + i(2a - b) = 10 + 2i, find a and b.

If θ is said to be an acute angle, and 4 cos²θ - 1 = 0, then what is the value …

If the coefficients of the 2nd, 3rd and 4th terms in the expansion of (1 + x)^n…

Evaluate sin(-225°) without the use of e-calculator or figures tables.

If A ∪ B = A ∩ B, then:

Determine the coefficient of p^4 q^7 in (2p - q)^10 (p + q)^10.

The equation log₂ x = -1 implies:

For n ≥ 1, 3^{2n+1}. Which is correct?

Given that m, 2m-1 and 3m-5 are three consecutive terms of a GP. Find the possi…

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

What is the 11th term of the sequence: m - 2n, m - n, m, ...?

Given that \(k-2, k-1\) and \(3k-5\) are three consecutive terms of an A.P. Fin…

In a survey of 290 newspapers readers, 181 read the Daily Times, 142 read The G…

Simplify: \(\frac{(2+i)(3+2i)}{4+i}\)

In the expansion of (1 + rx)ⁿ, the first three terms are 1 - 10x + 40x². Find n…

The expression \(\log_a x\) is defined when:

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

What is the sum of the sequence \(\sum_{k=0}^{3} (1 + k!)\)?

The solution of \(|x^2 - 1| < 1\) is:

Suppose that the number of terms in an A.P. is 2k. If the sum of all odd terms …

Find an expression in terms of n for the coefficient of x in \((1 + 4x) + (1 + …

Find the equation of the normal to the circle 2x²+2y²-2x-5y+3=0 at (1,1).

Solve 4(x-3)+12=15-5(x+6)

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

The addition of a rational number and an irrational number is equal to:

The sum of the first n odd numbers is?

Convert π/4 radians to degrees

What is (1-cosx)/sinx?

Evaluate (8x³ + 2x² - 4x + 2) - (-x³ + x² + 5x)

Find the coefficient of x³y⁶ in the binomial expansion of (2x - y²)⁶

If the value of α + β = 90° and α - β = 21°, then what is the ratio of sinα to …

Solve 2^(2x) - 3·2^x + 2 = 0

In triangle ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C i…

One of the following is a necessary step for proving 1+3+5+...+(2n-1) = n²?

Evaluate (8x³ + 2x² - 4x + 2) - (-x⁴ + x² + 5x)

If P(x): 3ⁿ > 2ⁿ for all n ≥ 1, what is the smallest n for which this holds?

Evaluate: C(n, 0)

If the value of α + β = 90° and α : β = 2 : 1, then what is the ratio of cos α …

Find the equation of the circle which has its center at (-1, 6) and passes thro…

Expressing sin⁻¹x in terms of z, we have:

P(n) = n(n²-1). Which of the following does not divide P(k + 1)?

Simplify (sin x + cos x)² - (csc x - cot x)²

The graphical representation of complex number is called:

The largest number that divides 70 and 125, leaving remainders 5 and 8 respecti…

Given that z₁ = 2 - i and z₂ = 1 + 3i, find the product of z₁ and z₂.

Find the radius and center of a circle whose parametric equations are x = 1 + 4…

The principle of mathematical induction is used to prove:

The decimal expansion of 22/7 is:

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

If tan θ = 13, then cot(π/4 - θ) = ?

Define: R = real numbers, Q = rational numbers, V = {English vowels}, P = {prim…

Find the seventh term of the expansion of (2x - 3)^10

The statement 3^(2n) - 1 is divisible by which of the following?

Give the definition of the set of rational numbers

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

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

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

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

Find the equation of the normal to the circle 2x² + 2y² - 2x - 5y + 3 = 0 at (1…

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

Find the fourth term of (x + y)^7

A circle passes through the center of the circle x² + y² - 3x - 4y - 1 = 0 and …

What is (1-cosx)/sinx = ?

Find the radius and center of a circle whose parametric equations are x = 1 + 4…

n² - 1 is divisible by 8, if n is:

A vertical tower stands on level ground. At a point 100m from the foot of the t…

Find the constant term in the binomial expansion of (x - 1/x)¹⁰

Solve 4(x-3)+12 = 15-5(x+6)

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

Find the center and radius of the circle 4x² + 4y² - 4x - 12y + 1 = 0.

Let z = x + iy where x and y are real numbers and y ≠ 0. Compute the value of l…

Which of the following cannot be proved by induction?

Find the equation of the tangent to the circle x² + y² + 4x - 2y - 15 = 0 at (2…

Which of the following is not correct?

Which of these equations has complex roots?

The sum of the numbers in the nth row of Pascal's Triangle is:

In (x+y)ⁿ, the number of terms is:

If the roots of a quadratic equation are equal, it is said to be:

What is the solution to the equation x² - x - 6 = 0?

Determine the square root of \( z = 4(\cos 70^\circ + i \sin 70^\circ) \)

Evaluate \( \sin(-225^\circ) \) without the use of e-calculator or figures tabl…

Given \( U = \{1, 2, 3, ..., 8, 9, 10\} \), \( N = \{\text{even numbers}\} \) a…

The solution set of \( |2x + 1| \geq 3 \) is:

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