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#800 Mathematics Applications of Derivatives

MCQ_SINGLE APPLY 2023

Competency 1 Marks

If f(x)=a(x-cos\~x) is strictly decreasing in R, then 'a' belongs to

(A) {0}

(B) (0,∞)

(C) (-∞,0)

(D) (-∞,∞)

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#799 Mathematics Applications of Derivatives

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

The interval in which the function f(x)=2x³+9x²+12x-1 is decreasing, is

(A) (-1, ∞)

(B) (-2,-1)

(C) (-∞, -2)

(D) [-1, 1]

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#798 Mathematics Continuity and Differentiability

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If $y=\frac{\cos x-\sin x}{\cos x+\sin x}$ then $\frac{dy}{dx}$ is:

(A) $-\sec^{2}(\frac{\pi}{4}-x)$

(B) $\sec^{2}(\frac{\pi}{4}-\pi)$

(C) $\log|\sec(\frac{\pi}{4}-x)|$

(D) $-\log|\sec(\frac{\pi}{4}-x)|$

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#797 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

The value of k for which function $f(x)=\begin{cases}x^{2},&x\ge0\\ kx,&x<0\end{cases}$ is differentiable at $x=0$ is:

(A) 1

(B) 2

(C) any real number

(D) 0

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#796 Mathematics Continuity and Differentiability

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

7. If $y=\sin^{2}(x^{3})$, then $\frac{dy}{dx}$ is equal to :

(A) $2\sin x^{3}\cos x^{3}$

(B) $3x^{3}\sin x^{3}\cos x^{3}$

(C) $6x^{2}\sin x^{3}\cos x^{3}$

(D) $2x^{2}\sin^{2}(x^{3})$

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#795 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

6. The function $f(x)=|x|$ is

(A) continuous and differentiable everywhere.

(B) continuous and differentiable nowhere.

(C) continuous everywhere, but differentiable everywhere except at $x=0$.

(D) continuous everywhere, but differentiable nowhere.

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#794 Mathematics Continuity and Differentiability

MCQ_SINGLE APPLY 2023 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

The value of k for which$ f(x)=\begin{cases}3x+5,&x\ge2\\ kx^{2},&x<2\end{cases}$ is a continuous function, is :

(A) $-\frac{11}{4}$

(B) $\frac{4}{11}$

(C) 11

(D) $\frac{11}{4}$

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#793 Mathematics Continuity and Differentiability

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If x=A cos 4t + B sin 4t, then d²x/dt² is equal to

(A) x

(B) -x

(C) 16x

(D) -16x

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#792 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

The function f(x)=[x], where [x] denotes the greatest integer less than or equal to x, is continuous at

(A) x=1

(B) x=1.5

(C) x=-2

(D) x=4

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#791 Mathematics Continuity and Differentiability

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

The derivative of x²ⁿ w.r.t. x is

(A) x²ⁿ⁻¹

(B) 2x²ⁿ log x

(C) 2x²ⁿ(1+log x)

(D) 2x²ⁿ(1-log x)

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#790 Mathematics Inverse Trigonometric Functions

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

sin[ π/3 + sin⁻¹(1/2) ] is equal to

(A) 1

(B) 1/2

(C) 1/3

(D) 1/4

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#789 Mathematics Relations and Functions

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

Let A={3,5}. Then number of reflexive relations on A is

(A) 2

(B) 4

(C) 0

(D) 8

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#788 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If
\[
A =
\begin{bmatrix}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix},
\]
then $A^{-1}$ is

(A) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}

(B) \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}

(C) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

(D) \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

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#787 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

A is a square matrix of order 2 such that det(A)=4 , then det(4adjA) is

(A) 16

(B) 64

(C) 256

(D) 512

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#766 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

Let
\[
A = \begin{pmatrix}
1 & -2 & -1 \\
0 & 4 & -1 \\
-3 & 2 & 1
\end{pmatrix}, \quad
B = \begin{pmatrix}
-2 \\
-5 \\
-7
\end{pmatrix}, \quad
C = \begin{pmatrix}
9 & 8 & 7
\end{pmatrix},
\]
which of the following is defined?

(A) Only AB

(B) Only AC

(C) Only BA

(D) All AB, AC and BA

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Key: A
Sol:

The problem is to determine which matrix multiplication is defined. A product of two matrices $P \times Q$ is defined if and only if the number of columns of $P$ equals the number of rows of $Q$.

The order of Matrix A is 3×3

The order of Matrix B is 3×1 and

The order of Matrix C is 1×3

Checking Products

AB: $A_{3 \times 3} \times B_{3 \times 1}$ $\to 3 = 3$ . Defined.
AC: $A_{3 \times 3} \times C_{1 \times 3}$ $\to 3 \neq 1$ . Not Defined.
BA: $B_{3 \times 1} \times A_{3 \times 3}$ $\to 1 \neq 3$ . Not Defined.

Hence The correct option is Only AB.

#765 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If
$
A = \begin{pmatrix}
7 & 0 & x \\
0 & 7 & 0 \\
0 & 0 & y
\end{pmatrix}
$
is a scalar matrix, then $y^x$ is equal to

(A) $0$

(B) $1$

(C) $7$

(D) $\pm 7$

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#764 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If $A$ and $B$ are invertible matrices, then which of the following is not correct?

(A) $(A + B)^{-1} = B^{-1} + A^{-1}$

(B) $(AB)^{-1} = B^{-1} A^{-1}$

(C) $\text{adj}(A) = |A| A^{-1}$

(D) $|A^{-1}| = |A|^{-1}$

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#763 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025

KNOWLEDGE 1 Marks

If $A=\begin{bmatrix}1&12&4y\\ 6x&5&2x\\ 8x&4&6\end{bmatrix}$ is a symmetric matrix, then $(2x+y)$ is

(A) $-8$

(B) 0

(C) 6

(D) 8

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#762 Mathematics Matrices and Determinants

MCQ_SINGLE UNDERSTAND 2025

KNOWLEDGE 1 Marks

Which of the following can be both a symmetric and skew-symmetric matrix ?

(A) Unit Matrix

(B) Diagonal Matrix

(C) Null Matrix

(D) Row Matrix

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#761 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2025 AISSCE(Board Exam)

Competency 1 Marks

Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify $4~AB+3(AB+BA)-4~BA,$ where A and B are both matrices of order $2\times2$. It is known that $A\ne B\ne I$ and $A^{-1}\ne B$. Their answers are given as:
Abhay: $6 AB$,
Bina : $7 AB-BA$,
Chhaya: $8 AB$,
Devesh: $7 BA - AB$.
Who answered it correctly?

(A) Abhay

(B) Bina

(C) Chhaya

(D) Devesh

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