Determinants — JEE Main PYQs

80 previous year questions on Determinants (Mathematics), newest first. Open any question for its complete step-by-step solution.

If $1, lo g_{10} (4^{x} - 2)$ and $lo g_{10} (4^{x} + \frac{18}{5})$ are in arithmetic progression for a real number x , then the value of the determinant …
JEE Main 2021View solution →
The solutions of the equation
$1 + sin^{2} x cos^{2} x 4 sin 2 x sin^{2} x 1 + cos^{2} x 4 sin 2 x sin^{2} x cos^{2} x 1 + 4 sin 2 x = 0, (0 < x < π)$ , are :
JEE Main 2021View solution →
Let $α, β, γ$ be the real roots of the equation, $x^{3} + a x^{2} + b x + c = 0, (a, b, c \in R$ and $a, b \neq = 0)$ . If the system of equations(inu,v,w) given by …
JEE Main 2021View solution →
If the system of linear equations $2 x + 2 a y + a z = 0, 2 x + 3 b y + b z = 0, 2 x + 4 cy + cz = 0$ where $a, b, c \in R$ are non-zero and distinct; has a non-zero solution, then:
JEE Main 2020View solution →
Let $A = [a_{ij}]$ and $B = [b_{ij}]$ be two $3 \times 3$ real matrices such that $b_{ij} = (3)^{(i + j - 2)} a_{ji}$ , where $i, j = 1, 2, 3$ . If the dete …
JEE Main 2020View solution →
Let $a - 2 b + c = 1$ . If $f (x) = x + a x + b x + c x + 2 x + 3 x + 4 x + 1 x + 2 x + 3$ , then:
JEE Main 2020View solution →
If $a + x = b + y = c + z + 1$ , where $a, b, c, x, y, z$ are non-zero distinct real numbers then $x y z a + y b + y c + y x + a y + b z + c$ is equal to:
JEE Main 2020View solution →
If $Δ = x - 2 2 x - 3 3 x - 5 2 x - 3 3 x - 4 5 x - 8 3 x - 4 4 x - 5 10 x - 17 =$
$A x^{3} + B x^{2} + C x + D$ , then $B + C$ is equal to:
JEE Main 2020View solution →
The sum of distinct values of $λ$ for which the system of equations
$(λ - 1) x + (3 λ + 1) y + 2 λ z = 0$
$(λ - 1) x + (4 λ - 2) y + (λ + 3) z = 0$
$2 x + (3 λ + 1) y + 3 (λ - 1) z = 0$ ,
has non-zero solutions, is ______.
JEE Main 2020View solution →
If the minimum and the maximum values of the function $f : [\frac{π}{4}, \frac{π}{2}] \to R$ , defined by …
JEE Main 2020View solution →
Let $m$ and $M$ be respectively the minimum and maximum values of …
JEE Main 2020View solution →
Let the numbers $2, b, c$ be in an A.P and $A = 124 1 b b^{2} 1 c c^{2}$ . If $det (A) \in [2, 16]$ then $c$ lies in the interval
JEE Main 2019View solution →
Let $α$ and $β$ be the roots of the equation $x^{2} + x + 1 = 0$ . Then for $y \neq = 0$ in $R$ , $y + 1 α β α y + β 1 β 1 y + α$ is equal to:
JEE Main 2019View solution →
Let $d \in R$ , and $A = - 2 15 4 + d (sin θ) + 2 (2 sin θ) - d (sin θ) - 2 d (- sin θ) + 2 + 2 d, θ \in [0, 2 π]$ . If the minimum value of $det (A)$ is 8, then a value of $d$ is:
JEE Main 2019View solution →
If $a - b - c 2 b 2 c 2 a b - c - a 2 c 2 a 2 b c - a - b = (a + b + c) (x + a + b + c)^{2}$ , $x \neq = 0$ and $a + b + c \neq = 0$ , then x is equal to:
JEE Main 2019View solution →
The sum of the real roots of the equation
$x 2 - 3 - 6 - 3 x 2 x - 1 x - 3 x + 2 = 0$ is equal to
JEE Main 2019View solution →
If $[x]$ denotes the greatest integer $\leq x$ , then the system of linear equations
$[sin θ] x + [- cos θ] y = 0$
$[cot θ] x + y = 0$
JEE Main 2019View solution →
A value of $θ \in (0, π /3)$ , for which $1 + cos^{2} θ cos^{2} θ cos^{2} θ sin^{2} θ 1 + sin^{2} θ sin^{2} θ 4 cos 6 θ 4 cos 6 θ 1 + 4 cos 6 θ = 0$ , is:
JEE Main 2019View solution →
If $A = 1 - sin θ - 1 sin θ 1 - sin θ 1 sin θ 1$ ; then for all $θ \in (\frac{3 π}{4}, \frac{5 π}{4})$ , $det (A)$ lies in the interval :
JEE Main 2019View solution →
If $Δ_{1} = x sin θ cos θ sin θ - x 1 cos θ 1 x$ and …
JEE Main 2019View solution →
If $x - 4 2 x 2 x 2 x x - 4 2 x 2 x 2 x x - 4 = (A + B x) (x - A)^{2}$ , then the ordered pair $(A, B)$ is equal to :
JEE Main 2018View solution →
The system of linear equations
$x + λ y - z = 0$
$λ x - y - z = 0$
$x + y - λ z = 0$
has a non-trivial solution for :
JEE Main 2016View solution →
If $α, β \neq = 0$ , and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4) = K (1 - α)^{2} (1 - β)^{2} (α - β)^{2}$ , then K is equal to
JEE Main 2014View solution →
The number of values of k for which the linear equations
$4 x + k y + 2 z = 0; k x + 4 y + z = 0; 2 x + 2 y + z = 0$ possess a non-zero solution is
JEE Main 2011View solution →
Let $a, b, c$ be such that $b (a + c) \neq = 0$ . If $a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 + a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c = 0$ , then the v …
JEE Main 2009View solution →
If $D = 111 1 1 + x 1 11 1 + y$ for $x \neq = 0, y \neq = 0$ then $D$ is
JEE Main 2007View solution →
Let $A = 500 5 α α 0 α 5 α 5$ . If $A^{2} = 25$ , then $∣ α ∣$ equals
JEE Main 2007View solution →
If $a^{2} + b^{2} + c^{2} = - 2$ and $f (x) = 1 + a^{2} x (1 + a^{2}) x (1 + a^{2}) x (1 + b^{2}) x 1 + b^{2} x (1 + b^{2}) x (1 + c^{2}) x (1 + c^{2}) x 1 + c^{2} x$ then …
JEE Main 2005View solution →
If $a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots$ are in G.P., then the determinant …
JEE Main 2005View solution →
If $a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots$ are in G.P., then the value of the determinant $lo g a_{n} lo g a_{n + 3} lo g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8}$ , is
JEE Main 2004View solution →