If vmatrix 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c vmatrix, where a, b and c are non zero constants, then the value of 1/a + 1/b + 1/c is Option 1: -1 Option 2: 1 Option 3: 0 Option 4: abc

Algebra

Matrices & Determinants

Medium

core

If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ , where a, b and c are non zero constants, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is

-1

abc

✅ Drop

The question presents a determinant but does not specify what value it equals. This creates an incomplete statement that cannot be solved.

The expression "If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ ..." begins a conditional statement but provides no equation or value for the determinant.

A complete question would specify the determinant's value, such as:

$\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = k$

where $k$ is some given constant (commonly 0 or another specific value).

With a complete question, the solution approach would involve:

Expanding the determinant using row or column operations to express it in terms of $a$ , $b$ , and $c$ .

Setting the expanded form equal to the given value.

Algebraically manipulating the resulting equation to isolate $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ .

This question cannot be solved without the missing information about what the determinant equals.

The question should be corrected to include the value of the determinant before a solution can be provided.

2026: 30 May Shift 2

If A and B are symmetric matrices of same order, then which of the following statements are true?

(A) $AB^T+B^TA$ is a skew-symmetric matrix.

(B) $AB^T-BA^T$ is a skew-symmetric matrix

(D) $(AB)^{-1}(BA)^T=A$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

If $A$ is an invertible matrix of order 3, then

Match List-I with List-II

List-I	List-II
(A) $\vert \text{adj} A\vert$	(I) $8\vert A\vert$
(B) $\vert A(\text{adj} A)\vert$	(II) $\vert A\vert ^2$
(C) $\vert 2A\vert$	(III) $\frac{1}{\vert A\vert }$
(D) $\vert A^{-1}\vert$	(IV) $\vert A\vert ^3$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

If $x = -4$ is a root of $\begin{vmatrix}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{vmatrix} = 0$ , then the sum of the other 2 roots is

2026: 25 May Shift 1

If A and B are two non-singular matrices of same order, then which of the following statements are not correct ?

A. AB is non singular.

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

C. adj (AB) = adj B. adj A.

D. AB is not invertible.

Choose the correct answer from the options given below:

2026: 22 May Shift 1

If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) $\lvert A\rvert$	(I) 48
(B) $\lvert 2A\rvert$	(II) 36
(C) $\left\lvert\operatorname{adj}(A)\right\rvert$	(III) 12
(D) $2\lvert A\rvert$	(IV) 6

Choose the correct answer from the options given below:

2025: 30 May Shift 2

If $A = [a_{ij}]_{3 \times 2}$ where $a_{ij} = i + j$ , then

(A) A is a square matrix

(B) $a_{21} + a_{32} = 8$

(D) Transpose of $A = \begin{bmatrix}2 & 3 \\ 3 & 4 \\ 4 & 5\end{bmatrix}$

Choose the correct answer from the options given below:

If ∣1+a1111+b1111+c∣\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}​1+a11​11+b1​111+c​​, where a, b and c are non zero constants, then the value of 1a+1b+1c\frac{1}{a} + \frac{1}{b} + \frac{1}{c}a1​+b1​+c1​ is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ , where a, b and c are non zero constants, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is