MCQ 11 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $x^2+y^2+4 x-8 y-84=0$ the equation of the circle concentric with the circle $x^2+y^2+4 x-8 y-6=0$, having the radius double of its radius.
Reason: The equation of the circle is $x^3+y^3+2 g x+2 f y+c=0$.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 21 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The circumference of a circle must be a positive real number.
Reason: If $r(> 0)$ is the radius of the circle, then its circumference $2\pi\text{r}$ is a positive real number.
- ✓
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: A. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
View full question & answer→MCQ 31 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Reason: As we know that any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 41 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Circle has a diameter $142.8\ mm.$ Then its radius is $71.4\ mm.$
Reason: $\text{Radius}=\big(\frac{1}{2}\big)\times\text{diameter}.$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 51 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Sector is a region of a circle between the arc and the two radii of the circle.
Reason: Sector is the region between the chord and its corresponding arc.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 61 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Tangent to a circle is always perpendicular to the radius.
Reason: Tangent to a circle is a line that touches the circle at one point, which is known as Tangency.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
View full question & answer→MCQ 71 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The measure of $\angle\text{AOC}=60^\circ.$
Reason: Angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by arc on the circumference. - A
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- ✓
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: B. Both assertion and reason are true but reason is not the correct explanation of assertion.
Join $BO.$
In $\triangle\text{AOB}$ we have
$\text{OA}=\text{OB}$ [radius]
$\angle\text{OBA}=\angle\text{OAB}$ [Angle opposite to equal sides of a triangle are equal]
$\angle\text{OBA}=30^\circ ...(1)$
Similarly, in $\triangle\text{BOC},$ we get $\text{OB}=\text{OC}$
$\angle\text{OCB}=\angle\text{OBC}$
$\angle\text{OBC}=40^\circ ...(2)$
$\angle\text{ABC}=\angle\text{OBA}+\angle\text{OBC}$
$=30^\circ+40^\circ=70^\circ[ $Using $(1)$ and $(2)]$
Since angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by the arc on the circumference.
$\angle\text{AOC}=2\times\angle\text{ABC}$
$=2\times70^\circ=140^\circ$ View full question & answer→MCQ 81 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The size of Angle $WXY=111^\circ $
Reason: Opposite angle of cylic quadrilateral are add to $180^\circ .$ - ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 91 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The perimeter of semi circle is $36\ cm$ and area of a semi - circle is $77\ sq\ cm$ having a radius of $7\ cm$
Reason: Area of semi circle $= {(\pi\text{r}^2)}{2}$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 101 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Rectangle is a cyclic quadrilateral.
Reason: Their vertices lies on the circumference of a circle.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 111 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Given a circle of radius r and with centre $O. A$ point $P$ lies in a plane such that $OP > r$ then point $P$ lies on the exterior of the circle.
Reason: The region between an arc and the two radii, joining the centre of the end points of the arc, is called a sector.
- A
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- ✓
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: B. Both assertion and reason are true but reason is not the correct explanation of assertion.
Both assertion and reason are true but reason is not the correct explanation of assertion.
View full question & answer→MCQ 121 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A circle has only one centre.
Reason: A circle is defined as the path traced by a moving point that always remains at a fixed distance from a given fixed point.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 131 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The measure of angle a is $65^\circ .$
Reason: Angle in same segment of a circle are equal. - ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 141 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The length of the minute hand of a clock is $7\ cm.$ Then the area swept by the minute hand in $5$ minutes is $\frac{12^5}{6}\text{cm}^2.$
Reason: The length of an arc of a sector of angle $\theta$ and radius r is given by $ \text{l}=\frac{\theta}{360}\times2\pi\text{r}$
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
View full question & answer→MCQ 151 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Equal arcs on a circle cannot be said as a major arc or a minor arc.
Reason: If a circle is divided into three equal arcs, each is a major arc
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 161 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $AB$ and $CD$ are two chords of a circle intersecting at point $E,$ as in the given figure then $< BEQ = < CEQ.$
Reason: Equal chord are always equidistant from the circle
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 171 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The area of a circle is the amount of flat space inside the circle’s circumference.
Reason: $\text{Area of circle}=\pi\text{r}^2.$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 181 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the outer and inner diameter of a circular path is $10m$ and $6m$ then area of the path is $ 16\pi\text{m}^2.$
Reason: If $R$ and $r$ be the radius of outer and inner circular path $= \pi(\text{R}^2-\text{r}^2).$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 191 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A circle of radius $3\ cm$ is drawn inscribed in a right angle triangle $ABC,$ right angled at $C.$ If $AC$ is $10$ then the value of $CB$ is 10.$5\ cm.$
Reason: Tangent from the external points are unequal.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 201 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: An inscribed angle is the angle formed between two chords when they meet on the boundary of the circle.
Reason: Angles formed by the same arc on the circumference of the circle is always unequal.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 211 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The sum of either pair of opposite angles of a cyclic quadrilateral is $180^\circ .$
Reason: Two or more circles are called concentric circles if and only if they have different centre and radii.
- A
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- ✓
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: C. Assertion is true but reason is false.
Two or more circles are called concentric circles if and only if they have same centre but different radii
View full question & answer→MCQ 221 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The angle subtended by the diameter of a semi - circle is $180^\circ .$
Reason: The semicircle is half of the circle, hence the diameter of the semicircle will be a straight line subtending 180 degrees.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 231 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A circle of radius $3\ cm$ can be drawn through two points $A, B$ such that $AB = 6\ cm.$
Reason: Diameter of circle $= 2\ ×$ radius of circle.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 241 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: There can be infinite numbers of equal chords of a circle.
Reason: A circle has only finite number of equal chords.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 251 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In an isosceles triangles $\text{ABC}$ with $\text{AB = AC,}$ a circle is passing through $B$ and $C$ intersects the sides $\text{AB}$ and $\text{AC}$ at $D$ and $E$ respectively. Then $\text{DE}\parallel\text{BC}.$.
Reason: Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilateral
- ✓
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: A. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
To prove $\text{DE}\parallel\text{BC}$
i.e., $\angle\text{B }\angle\text{ADE}.$
In $\triangle\text{ABC},$ We have
$\text{AB}=\text{AC}$
$\angle\text{B}=\angle\text{C} ...(1)$
In the cyclic quadrilateral $\text{CBDE,}$ side $\text{BD}$ is produced to $A.$
We know that an exterior angle of cyclic quadrilateral is equal to interior opposite angle of cyclic quadrilateral.
$\angle\text{ADE}=\angle\text{C} ...(2)$
From $(1)$ and $(2),$ we get
$\angle\text{B}=\angle\text{ADE}.$
Hence, $\text{DE}\parallel\text{BC}$ View full question & answer→MCQ 261 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In the following diagram, then $124^\circ $ is the measure of $\angle\text{POQ}$ when the value of $\angle\text{PRQ}$ is given $62^\circ .$
Reason: According to the theorem of chords of a circle, the angle subtended at the center of the circle by an arc is twice the angle.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 271 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The length of the line through the centre that touches two points on the edge of the circle is called a diameter.
Reason: Diameter of the circle $= 2 × r.$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 281 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: equal arcs on a circle cannot be said as a major arc or a minor arc.
Reason: If a circle is divided into three equal arcs, each is a major arc.
- A
Both Assertion and reason are correct and reason is correct explanation for Assertion.
- B
Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- ✓
Assertion is correct but reason is false.
- D
Both Assertion and reason are false.
AnswerCorrect option: C. Assertion is correct but reason is false.
Assertion is correct but reason is false.
View full question & answer→MCQ 291 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion:
is the concentric circle.
Reason: The circles with a common centre are known as concentric circles and have diffrent radii. - ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 301 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Congruent chord are the equidistant from the center of circle.
Reason: Congruent chord have congruent central angle and congruent arcs.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
View full question & answer→MCQ 311 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The line segment joining any two points on the circumference of circle is called chord.
Reason: Radius is the longest chord.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 321 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Angle in the same segment are equal.
Reason: Angle in a semi circle is a tight angle.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 331 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A diameter of a circle is the longest chord of the circle and all diameters have equal length.
Reason: Length of a diameter = radius.
- A
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- ✓
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: C. Assertion is true but reason is false.
Assertion is true but reason is false.
View full question & answer→MCQ 341 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Tangent is a line that touches the circle at any point.
Reason: Radius is always parallel to the tangent at the point where it touches the circle.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 351 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In a cyclic quadrilateral $\text{ABCD},\angle\text{A}-\angle\text{C}= 60^\circ,$ then the smaller of two is $60^\circ .$
Reason: Opposite angles of cyclic quadrilateral are supplementary.
- A
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- ✓
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: B. Both assertion and reason are true but reason is not the correct explanation of assertion.
Since $\text{ABCD}$ is a cyclic quadrilateral, so, its opposite angles are supplementary
$\angle\text{A}+\angle\text{C}= 180^\circ ...(1)$
Also, $\angle\text{A}-\angle\text{C}= 60^\circ ...(2)$
On solving $(i)$ and $(ii),$ we get
$\angle\text{A}=120^\circ,\angle\text{C}= 60^\circ$
View full question & answer→MCQ 361 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Circle is a plane figure.
Reason: Circle is a $2d$ figure and it can be drawn on a plane.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 371 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Points $A, B$ and $C$ all lie on the circumference of a circle with centre $O$ then the value of $x$ is $49^\circ $
Reason: The angle at the centre is twice the angle at the circumference. - ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 381 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $8$ Ft will be the radius of a circle having an area $200.96\ sq\ Ft.$
Reason: $\text{Area of circle}=\pi\text{r}^2.$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 391 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: There is only one tangent at a point of the circle.
Reason: The tangents drawn at the extremities of the diameter of a circle are parallel.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
View full question & answer→MCQ 401 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The line $2 x+y=5$ is a diameter of the circle $x^2+y^2-6 x+2 y=0$.
Reason: Normal of a circle always pass through the center of a circle.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 411 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If $P$ and $Q$ are any two points on a circle, then the line segment $PQ$ is called a chord of the circle.
Reason: Equal chords of a circle subtend equal angles at the centre.
- ✓
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: A. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Both assertion and reason are true but reason is not the correct explanation of assertion.
View full question & answer→MCQ 421 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $AB$ and $CD$ are two parallel chords of a circle whose diameter is $AC.$ Then $\text{AB}\neq\text{CD}.$
Reason: Perpendicular from the centre of a circle bisects the chord.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Assertion is wrong statement but Reason is correct statement.
View full question & answer→MCQ 431 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Two or more circles that have different radii.
Reason: In concentric circle radii are different but center is same.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→MCQ 441 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: All the diameter of the circle have the same length.
Reason: Diameter is the half of radius.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 451 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R) $have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: All right angles are equal to one another.
Reason: A unique line passes through a single point.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→MCQ 461 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The region between the arc and the two radii, joining the centre to the end points of the arc is called minor arc.
Reason: The region between a chord and either of its arc is called major arc.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- ✓
Both assertion and reason are false.
AnswerCorrect option: D. Both assertion and reason are false.
Both assertion and reason are false.
View full question & answer→MCQ 471 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A semi - circle is one fourth part of the circle.
Reason: A semi - circle is obtained when a circle is divided into two unequal parts.
- A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- ✓
Both assertion and reason are false.
AnswerCorrect option: D. Both assertion and reason are false.
Both assertion and reason are false.
View full question & answer→MCQ 481 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The length of a chord which is at a distance of 5\ cm from the centre of a circle of radius $10\ cm$ is $17.32\ cm$
Reason: The perpendicular from the centre of a circle to a chord bisects the chord.
- ✓
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: A. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Let, $PQ$ be a chord of a circle with centre $O$ and radius $10\ cm$ . Draw $\mathrm{OR} \perp \mathrm{PQ}$.
Now, $O P=10 \mathrm{~cm}$ and $O R=5 \mathrm{~cm}$
In right triangle ORP, we get
$O P^2 ~P R^2 ~O R^2$
$P R^2 ~O P^2 ~O R^2$
$P R^2 ~10^2-5^2=75$
$\mathrm{PR}=\sqrt{75}=8.66$
Since, the perpendicular from the centre to a chord bisects the chord.
Therefore, $ PQ=2 \times PR$
$=2 \times 8.66=17.32 \mathrm{~cm}$
View full question & answer→MCQ 491 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end $-$ points is a square.
Reason: Equal chords subtend equal angles at the centre.
- ✓
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- B
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true.
AnswerCorrect option: A. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Let $\text{AB}$ and $\text{CD}$ be two perpendicular diameters of a circle with centre $O$.
Now, $\angle\text{ABC}=90^\circ [$Angle in semicircle is a right angle$]$
Similarly $\angle\text{ACD}=\angle\text{ADC}$
$=\angle\text{BAD}=90^\circ ...(1)$
In $\triangle\text{AOB}$ and $\triangle\text{AOD},$ We have
$\text{AO}=\text{AO} ($Common$)$
$\angle\text{AOB}=\angle\text{AOD} ($Each $90^\circ ,$ given$)$
$\text{BO}=\text{OD} ($Radii of circle$)$
$\triangle\text{AOB}\cong\angle\text{AOD} ($By $\text{SAS}$ congruence$)$
$\text{AB}=\text{AD}$
Similarly, we have,
$\text{AD = DC, DC = BC; BC = AB}$
Hence, $\text{AB = BC = CD = DA ...(2)}$
Also, it is given that diagonals of $\text{ABCD}$ intersect at $90^\circ ...(3)$
By $(1), (2)$ and $(3) \text{ABCD}$ is a square. View full question & answer→MCQ 501 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the sum of the circumferences of two circles with radii $R1$ and $R2$ is equal to the circumference of a circle of radius $R,$ then $R1 + R2 = R.$
Reason: Circumference of circle with radius $=2\pi\text{R}.$
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- C
Assertion is true but the reason is false.
- D
Both assertion and reason are false.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
View full question & answer→