30 Questions
What is the value of x in the equation tan x = 1 in the interval [-π/4, π/4]?
π/4
If f(x) = x(x + 1) / (2x(x - 1)(x + 1)), then what is the value of f(100)?
1
What is the value of λ in the equation λ² + 3λ - 1 = λ + 3, given that λ - 4 is a factor?
1
What is the determinant of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
0
If pλ⁴ + qλ³ + rλ² + sλ + t = λ + 1, then what is the value of t?
1
If a1, a2, a3,..., an are in G.P., what is the value of log an+2?
log an + log an+1
If the determinant Δ = |2x+2-x, 2x-2-x, 2x-2-x; 3x+3-x, 3x-3-x, 3x-3-x; 5x+5-x, 5x-5-x, 5x-5-x|, what is the value of Δ when x = 0?
0
If x, y, z are integers in A.P., what is the value of x + z?
2y
What is the value of the determinant |a, b, c; a^2, b^2, c^2; a^3, b^3, c^3| when a, b, c are in G.P.?
0
If the quadratic equation x^2 + px + q = 0 has roots r and s, what is the value of p?
r + s
If $a$, $b$, and $c$ are distinct, then the value of $(a-b)(b-c)(c-a)(a+b+c)$ is
0
If $D=\begin{vmatrix} 1 & 1 & 1 \ a & b & c \ a^2 & b^2 & c^2 \end{vmatrix}$, then the value of $D$ is
(a-b)(b-c)(c-a)
The value of $\Delta=\begin{vmatrix} 1 & 1 & 1 \ a & b & c \ a^3 & b^3 & c^3 \end{vmatrix}$ is
(a-b)(b-c)(c-a)(a+b+c)
If $x+y+z=0$, then the value of $(x+y+z)^3$ is
0
The value of $\begin{vmatrix} x & y & z \ x^2 & y^2 & z^2 \ x^3 & y^3 & z^3 \end{vmatrix}$ is
(x-y)(y-z)(z-x)
What is the value of Δ' if Δ is the determinant of a 3x3 matrix and Δ' is the determinant formed by replacing the elements of Δ by their corresponding cofactors?
Δ
If a₁₁C₁₁ + a₂₁C₂₁ + a₃₁C₃₁ = Δ, then what is the value of a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃?
0
What is the value of the determinant Δ if Δ = a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃?
0
If Δ is a 3x3 determinant, what is the value of Δ.Δ'?
Δ
What is the value of a₃₁C₁₁ + a₃₂C₁₂ + a₃₃C₁₃?
0
If a determinant of order n remains unchanged when all elements of a row (or column) are multiplied by a non-zero number k, then what happens to the determinant?
It gets divided by k
If a determinant of order n remains unchanged when elements of a row (or column) are added to the corresponding elements of another row (or column), what property is being used?
P-6
If all elements below the leading diagonal of a determinant are zero, what is the value of the determinant?
The product of the leading diagonal elements
If a determinant becomes zero when x = α, what can be concluded?
(x - α) is a factor of the determinant
What is the maximum number of operations that can be performed on a determinant of order n?
n - 1
What is the characteristic of a symmetric determinant?
aij = a ji ∀ i, j
What is the value of a skew-symmetric determinant of odd order?
Always zero
What is the characteristic of a determinant in cyclic order?
Elements of the rows (or columns) are in cyclic order
What is the value of a determinant with a skew-symmetric determinant of even order?
Always a perfect square
What is the property of a symmetric determinant?
aij = a ji ∀ i, j
Solve trigonometric equations and find the number of distinct real roots in a given interval. Apply determinant rules to solve the system of equations. Practice your math skills with this challenging quiz.
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