If Δ 1 = x s i n θ c o s θ - s i n θ - x 1 c o s θ 1 x and Δ 2 = x s i n 2 θ c o s 2 θ - s i n 2 θ - x 1 c o s 2 θ 1 x , x ≠ 0 ; then for all θ ∈ 0 , π 2 :

Δ 1 + Δ 2 = - 2 ( x 3 + x - 1 )

Δ 1 - Δ 2 = x ( c o s 2 θ - c o s 4 θ )

MEDIUM

Earn 100

Which component of a CAS is responsible for producing financial statements?

50% studentsanswered this correctly

Important Questions on Determinants

HARD

Mathematics>Algebra>Determinants>Determinants

The least value of the product

x y z

(such that

x, y and z

are positive real numbers) for which the determinant

|\begin{matrix} x \\ 1 \\ 1 \end{matrix} \begin{matrix} 1 \\ y \\ 1 \end{matrix} \begin{matrix} 1 \\ 1 \\ z \end{matrix}|

is non-negative is

HARD

Mathematics>Algebra>Determinants>Determinants

Let

A = [\begin{matrix} 2 & b & 1 \\ b & b^{2} + 1 & b \\ 1 & b & 2 \end{matrix}],

where

b > 0

. Then the minimum value of

\frac{\det (A)}{b}

is:

MEDIUM

Mathematics>Algebra>Determinants>Determinants

|\begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix}| = a x - 12

, then

a

is equal to:

MEDIUM

Mathematics>Algebra>Determinants>Determinants

|\begin{matrix} x & 2 & x \\ x^{2} & x & 6 \\ x & x & 6 \end{matrix}| = a x^{4} + b x^{3} + c x^{2} + d x + e

,

then

5 a + 4 b + 3 c + 2 d + e

is equal to

MEDIUM

Mathematics>Algebra>Determinants>Determinants

40

persons take

6 days

to complete a certain task working

10 hours

a day. How many hours a day will be sufficient for

30

persons to complete the same task in

10 days ?

EASY

Mathematics>Algebra>Determinants>Determinants

If the inverse of the matrix

[\begin{matrix} α & 14 & - 1 \\ 2 & 3 & 1 \\ 6 & 2 & 3 \end{matrix}]

does not exist then the value of

α

HARD

Mathematics>Algebra>Determinants>Determinants

A = [\begin{matrix} 1 & \sin θ & 1 \\ - \sin θ & 1 & \sin θ \\ - 1 & - \sin θ & 1 \end{matrix}]

, then for all

θ \in (\frac{3 π}{4}, \frac{5 π}{4})

\det (A)

lies in the interval :

MEDIUM

Mathematics>Algebra>Determinants>Determinants

The number of distinct real roots of the equation,

|\begin{matrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{matrix}| = 0

in the interval

[- \frac{π}{4}, \frac{π}{4}]

is :

EASY

Mathematics>Algebra>Determinants>Determinants

Let

A = [\begin{matrix} x & 2 y \\ - 1 & y \end{matrix}]; x, y \in R

. If

A A^{T} = [\begin{matrix} 1 & 0 \\ 0 & α \end{matrix}] (α \in R),

then

α + y^{2}

is equal to

EASY

Mathematics>Algebra>Determinants>Determinants

3 \times 3

square matrix

M = [a_{i j}]

is taken, where

i = 0,

1, 2

and

j = 0, 1, 2 .

In matrix

M,

value of each element is determined as

a_{i j} = i \times j .

What will be the value of largest minor of the matrix

M

MEDIUM

Mathematics>Algebra>Determinants>Determinants

S = \{x \in [0, 2 π] : |\begin{matrix} 0 & \cos x & - \sin x \\ \sin x & 0 & \cos x \\ \cos x & \sin x & 0 \end{matrix}| = 0\},

then

\sum_{x \in S} \tan (\frac{π}{3} + x)

is equal to:

EASY

Mathematics>Algebra>Determinants>Determinants

Consider the statement given below and decide out of which given presuppositions is it inherent in.
Statement
Doctors these days advise the consumption of rice in the dinner.
Presuppositions
I. Late night dinner produces toxin in the because the food remains undigested for a long time.
II. Rice digests quickly .

HARD

Mathematics>Algebra>Determinants>Determinants

The remainder when the value of the determinant $|\begin{array}{l} 2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022} \end{array}|$ is divided by $5$ is

EASY

Mathematics>Algebra>Determinants>Determinants

A = [\begin{matrix} \begin{matrix} 1 & 0 & 2 \\ 5 & 1 & x \\ 1 & 1 & 1 \end{matrix} \end{matrix}]

is a singular matrix, then the value of

x

HARD

Mathematics>Algebra>Determinants>Determinants

|\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| = (A + B x) {(x - A)}^{2},

then the ordered pair

(A, B)

is equal to

MEDIUM

Mathematics>Algebra>Determinants>Determinants

Δ_{1} = |\begin{matrix} x & s i n θ & c o s θ \\ - s i n θ & - x & 1 \\ c o s θ & 1 & x \end{matrix}|

and

Δ_{2} = |\begin{matrix} x & s i n 2 θ & c o s 2 θ \\ - s i n 2 θ & - x & 1 \\ c o s 2 θ & 1 & x \end{matrix}|,

x \neq 0;

then for all

θ \in (0, \frac{π}{2})

MEDIUM

Mathematics>Algebra>Determinants>Determinants

Let the numbers

2, b, c

be in an A.P. and

A = [\begin{matrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^{2} & c^{2} \end{matrix}]

. If

d e t (A) \in [2,16],

then

c

lies in the interval:

EASY

Mathematics>Algebra>Determinants>Determinants

Let

d \in R,

and

A = [\begin{matrix} - 2 & 4 + d & (\sin θ) - 2 \\ 1 & (\sin θ) + 2 & d \\ 5 & (2 \sin θ) - d & (- \sin θ) + 2 + 2 d \end{matrix}],

θ \in [0, 2 π] .

If the minimum value of

d e t (A)

8,

then a value of

d

is:

MEDIUM

Mathematics>Algebra>Determinants>Determinants

A contractor takes a contract to complete a road in

60 days

and employed

70

labourers. After

25 days

, he found that one fourth of work is completed. How many more labours he required to complete the remaining work in time?

EASY

Mathematics>Algebra>Determinants>Determinants

Which presupposition is inherent in the following statement?
Statement
Vimla said reminding her husband, "I hope you have taken your raincoat".
Presupposition
I. There is likelihood of rain.
II. Vimla is careful about the health of her husband.

Which component of a CAS is responsible for producing financial statements?

Important Questions on Determinants

Learn and Prepare for any exam you want !