JEE Advanced Algebra — practice questions
72 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Algebra in the app →For the system $a_1x+b_1y=c_1$, $a_2x+b_2y=c_2$, Cramer's rule givesWhich property of determinants is correct?If $M_{ij}$ is the minor of an element $a_{ij}$, then its cofactor $C_{ij}$ isFor the matrix equation $AX=B$, if $|A|\neq 0$, the unique solution isWhich of the following statements about rank is given in the chapter?In a non-zero matrix $A$, the rank $r$ means thatA square matrix $A$ is orthogonal whenIf $A$ is skew-symmetric, which of the following must be true?A square matrix $A$ is symmetric ifIf $A=\begin{bmatrix}2&-3&-1\\4&2&3\end{bmatrix}$, then $A'$ isIf $A$ is of order $2\times 3$ and $B$ is of order $3\times 4$, then the product $AB$ is defined and has orderFor matrix addition $A+B$ to be defined, which condition must hold?Which of the following is a diagonal matrix?Which of the following best defines a matrix of order $m\times n$?$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:If $A$ is a matrix of order $3 \times 4$ and $B$ is of order $4 \times 5$, then the order of the product $AB$ The identity matrix $I_n$ is a square matrix in which:For any square matrix $A$, the matrix $A + A'$ is:The diagonal entries of any skew-symmetric matrix are:If $A$ and $B$ are matrices for which $AB$ is defined, then $(AB)'$ equals:A square matrix $A$ is **invertible** if and only if:If $A$ and $B$ are invertible $n \times n$ matrices, then $(AB)^{-1}$ equals:For a non-singular $n \times n$ matrix $A$, the relation between $\det(\operatorname{adj} A)$ and $\det A$ is:A square matrix $A$ is called **idempotent** if:For the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$, the inverse $A^{-1}$ iThe trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is:A square matrix $A$ satisfies $A^T A = I$. Such a matrix is called:If $A$ is a square matrix with $|A| = 3$ and order $n = 3$, then $|\operatorname{adj}(A)|$ equals:sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:cos(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α:For $n$ even, the maximum value among the binomial coefficients ${}^nC_r$ occurs atThree numbers are in harmonic progression if and only if their reciprocals are inIf $S_n=an^2+bn+c$, then the $n$th term $t_n$ of the sequence isThe principal argument of a complex number is defined to lie in which interval?
$ in(90^\circ - \theta)$ equals:The general solution of $\cos x = 1/2$ is:The angle 90° in radians is:The function f(x) = tan x has vertical asymptotes at: