MCQ 11 Mark
Statement-1 (A): The distance of the point $(-3,5)$ from the $x$ axis is 3 units.
Statement-2 (R): Abscissa of a point gives the distance of the point from the $y$-axis.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: D. Statement-1 is false, Statement-2 is true.
View full question & answer→MCQ 21 Mark
Statement-1 (A): The point which divides the line segment joining the points $A(1,2)$ and $B(-1,1)$ internally in the ratio $1: 2$ is $\left(-\frac{1}{3}, \frac{5}{3}\right)$.
Statement-2 (R) : The coordinates of the point which divides the line segment joining the points $A\left(x_1, y_1\right)$ and $B\left(x_2, y_2\right)$ in the ratio $m_1: m_2$ are $\left(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}\right)$.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: D. Statement-1 is false, Statement-2 is true.
View full question & answer→MCQ 31 Mark
Statement-1 (A): Mid-point of a line segment divides the line segment in the ratio $1: 1$.
Statement-2 (R) : The ratio in which the point $(-3, k)$ divides the line segment joining the points $(-5,4)$ and $(-2,3)$ is $1: 2$.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: C. Statement-1 is true, Statement-2 is false.
View full question & answer→MCQ 41 Mark
Statement-1 (A): If the points $A(4,3)$ and $B(x, 5)$ lie on a circle with centre $O(2,3)$, then the value of $x$ is 2 .
Statement-2 (R) : Centre of the circle is the mid-point of each chord of the circle.
- A
Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
- B
Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
- ✓
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement- 2 is True.
AnswerCorrect option: C. Statement-1 is True, Statement-2 is False.
(C)Statement-1 is True, Statement-2 is False.
Clearly, $O A=O B=$ Radius
$
\begin{array}{ll}
\Rightarrow & O A^2=O B^2 \\
\Rightarrow & (4-2)^2+(3-3)^2=(x-2)^2+(5-3)^2 \Rightarrow 4=(x-2)^2+4 \Rightarrow(x-2)^2=0 \Rightarrow x=2
\end{array}
$
So, statement- 1 is true. Clearly, statement- 2 is not true as the centre of a circle is the mid-point of chords passing through it.
View full question & answer→MCQ 51 Mark
Statement-1 (A): Point $P(0,2)$ is the point of intersection of $y$-axis with the line $3 x+2 y=4$.
Statement-2 (R) : The distance of the point $P(0,2)$ from $x$-axis is 2 units.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
View full question & answer→MCQ 61 Mark
Statement-1 (A): The point $A(3,4), B(2,7), C(4,4)$ and $D(3,5)$ are such that one of them lies inside the triangle formed by the remaining three points.
Statement-2 (R) : Centroid of a triangle always lies inside the triangle.
- ✓
Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
- B
Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement- 2 is True.
AnswerCorrect option: A. Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
We observe that the coordinates of the centriod of $\triangle A B C$ are $\left(\frac{3+2+4}{3}, \frac{4+7+4}{3}\right)$ i.e. $(3,5)$ which are coordinates of $D$. Thus, $D$ is the centroid of $\triangle A B C$. We find that the statement -2 is always true and hence $D$ lies inside $\triangle A B C$. Thus, both the statements are true and statement- 2 is a correct explanation for statement-1. Hence option (a) is correct.
View full question & answer→MCQ 71 Mark
Statement-1 (A): If $c$ is a variable, then the centroids of the triangles having vertices at $P(1, a), Q(c, b)$, and $R\left(c^2, 1\right)$ will never lie on $y$-axis.
Statement-2 (R) : If $x$-coordinate of a point is not zero, it does not lie on $y$-axis.
- ✓
Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
- B
Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement- 2 is True.
AnswerCorrect option: A. Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
The coordinates of the centroid of $\triangle P Q R$ are $\left(\frac{1+c+c^2}{3}, \frac{a+b+1}{3}\right)$.
Now, $\quad c^2+c+1=c^2+2\left(\frac{1}{2}\right) c+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2+1=\left(c+\frac{1}{2}\right)^2+\frac{3}{4} \geq \frac{3}{4} \quad\left[\because\left(c+\frac{1}{2}\right)^2 \geq 0\right.$ forall $\left.c\right]$
Thus, $\quad 1+c+c^2 \neq 0$ for any $c \Rightarrow \frac{1+c+c^2}{3} \neq 0$ for any $c$
Thus, $x$-coordinate of the centroid of $\triangle P Q R$ cannot be zero for any value of $c$. Consequently, centroid of $\triangle P Q R$ does not lie on $y$-axis. So, statment- 1 is true.
Statement-2 is also true and it is a correct explanation for statement-1. Hence, option (a) is correct.
View full question & answer→MCQ 81 Mark
Statement-1 (A): If the centroid of the triangle having its vertices at $A(1, a), B(2, b)$ and $C\left(c^2-3\right)$ lies on $x$-axis, then $a+b=3$.
Statement-2 (R): On y-axis, $x$-coordmate of every point is zero.
- A
Statement-1 and Statement-2 are True; Statement- 2 is a correct explanation for Statement-1.
- ✓
Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement- 2 is True.
AnswerCorrect option: B. Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
(B)Statement -1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1,
The coordinates of the centroid of $\triangle A B C$ are $\left(\frac{3+c^2}{3}, \frac{a+b-3}{3}\right)$. If it lies on $x$-axis, then its $y$-coordinate is zero.
$
\therefore \quad \frac{a+b-3}{3}=0 \Rightarrow a+b=3
$
Thus, statement-1 is true. Clearly, statement-2 is also true. But it is not a correct explanation for statement-1. Hence, option (b) is correct.
View full question & answer→MCQ 91 Mark
Statement-1 (A): If $a \neq 0, b \neq 0$, then the points $O(0,0), A\left(a, a^2\right), B\left(b, b^2\right)$ are non-collinear.
Statement-2 (R): If points $P, Q$ and $R$ are collinear, then $P Q+Q R=P R$.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: C. Statement-1 is true, Statement-2 is false.
View full question & answer→MCQ 101 Mark
Statement-1 (A): A triangle with vertices at $(4,0),(-1,-1)$, and $(3,5)$ is isosceles right angled triangle.
Statement-2 (R): If $A B C$ is an isosceles triangle, then it is right angled.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: C. Statement-1 is true, Statement-2 is false.
View full question & answer→MCQ 111 Mark
Statement-1 (A): If the coordinates of the mid-points of sides $A B$ and $A C$ of $\triangle A B C$ are $D(3,5)$, and $E(-3,-3)$ respectively, then $B C=20$ units.
Statement-2 (R): The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
- A
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
View full question & answer→MCQ 121 Mark
Statement-1 (A): If origin is the centroid of triangle whose vertices are $P(a, b), Q(b, c)$ and $R(c, a)$, then $a^3+b^3+c^3=3 a b c$.
Statement-2 (R): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$.
- ✓
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
View full question & answer→MCQ 131 Mark
Statement-1 (A): If $a+b+c=0$, then the centroid of the triangle whose vertices are $P(a, b)$, $Q(b, c)$ and $R(c, a)$ is at the origin.
Statement-2 (R) : The coordinates of the centroid of the triangle whose vertices are
$
A\left(x_1, y_1\right), B\left(x_2, y_2\right) \text { and } C\left(x_3, y_3\right) \text { are }\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right) \text {. }
$
- ✓
Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.
View full question & answer→