Class 12 Maths assertion–reason questions, chapter-wise

Assertion (A): The function $f:\mathbb{R}\to \mathbb{R}$, $f(x)=x^2$, is one-one.

Reason (R): The function $f:\mathbb{R}\to \mathbb{R}$, $f(x)=x^2$, is not onto.

Assertion (A): ${\sin }^{-1}(\sin {\displaystyle \frac{3\pi }{4}})={\displaystyle \frac{3\pi }{4}}$.

Reason (R): The principal value branch of ${\sin }^{-1}$ has range $[-{\displaystyle \frac{\pi }{2}},{\displaystyle \frac{\pi }{2}}]$.

Assertion (A): For every square matrix $A$, the matrix $A+A^{\prime }$ is symmetric.

Reason (R): For matrices of the same order, $(A^{\prime }{)}^{\prime }=A$ and $(A+B{)}^{\prime }=A^{\prime }+B^{\prime }$.

Assertion (A): The matrix $\left[\begin{array}{cc}2& 4\\ 3& 6\end{array}\right]$ has no inverse.

Reason (R): A square matrix is invertible if and only if its determinant is non-zero.

Assertion (A): $f(x)=|x-3|$ is continuous at $x=3$ but not differentiable there.

Reason (R): Every continuous function is differentiable.

Assertion (A): $x=0$ is a point of local minimum of $f(x)=x^3$.

Reason (R): For $f(x)=x^3$, $f^{\prime }(0)=0$.

Assertion (A): ${\displaystyle {\int }_{-1}^1{x}^{3}dx=0}$.

Reason (R): For every continuous function $f$, ${\displaystyle {\int }_{-a}^{a}f(x)dx=2{\int }_0^{a}f(x)dx}$.

Assertion (A): The area of the region bounded by $y=\sin x$, the $x$-axis and the lines $x=0$ and $x=2\pi$ is $4$ square units.

Reason (R): ${\displaystyle {\int }_0^{2\pi }\sin xdx=0}$.

Assertion (A): $y=C{e}^{3x}$ is the general solution of ${\displaystyle \frac{dy}{dx}}=3y$.

Reason (R): ${\displaystyle \frac{dy}{dx}}=3y$ is a first-order linear differential equation.

Assertion (A): $\hat{i}\times \hat{j}=\hat{k}$.

Reason (R): $\hat{i}\cdot \hat{j}=0$.

Assertion (A): The lines ${\displaystyle \frac{x-1}{2}}={\displaystyle \frac{y-2}{3}}={\displaystyle \frac{z-3}{4}}$ and ${\displaystyle \frac{x-2}{4}}={\displaystyle \frac{y+1}{6}}={\displaystyle \frac{z}{8}}$ are parallel.

Reason (R): Two lines are parallel when their direction ratios are proportional.

Assertion (A): The point $(2,3)$ lies in the feasible region of the constraints $x+y\le 4$, $x\ge 0$, $y\ge 0$.

Reason (R): A point is in the feasible region only if it satisfies every constraint.

Assertion (A): If $A$ and $B$ are independent events with $P(A)=P(B)={\displaystyle \frac{1}{2}}$, then $A$ and $B$ are mutually exclusive.

Reason (R): For independent events, $P(A\cap B)=P(A)P(B)$.