32581 + Interview Questions in Mathematics

1.	Draw a circle of radius 3 centimetres and draw a rhombus with one angle 40°, all four sides touching the circle.
Answer» Draw a circle of radius 3 centimetres and draw a rhombus with one angle 40°, all four sides touching the circle.

Discussion

2.	One angle of a ΔABC which is circumscribed by a circle, has one of the angles as 135∘ and its opposite side is 5 cm as shown in the figure. The diameter of its circumcircle is equal to
Answer» One angle of a $Δ A B C$ which is circumscribed by a circle, has one of the angles as $135^{\circ}$ and its opposite side is 5 cm as shown in the figure. The diameter of its circumcircle is equal to

2.

One angle of a ΔABC which is circumscribed by a circle, has one of the angles as 135∘ and its opposite side is 5 cm as shown in the figure. The diameter of its circumcircle is equal to

Answer»

One angle of a $Δ A B C$ which is circumscribed by a circle, has one of the angles as $135^{\circ}$ and its opposite side is 5 cm as shown in the figure. The diameter of its circumcircle is equal to

Discussion

3.	In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contant T, are of lengths 12 cm and 9 cm respectively. If the area fo \Delta PQR = 189 cm^2 then the length of side PQ is (a) 17.5 cm (b) 20 cm (c) 22.5 cm (d) 25 cm
Answer» In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contant T, are of lengths 12 cm and 9 cm respectively. If the area fo \Delta PQR = 189 cm^2 then the length of side PQ is (a) 17.5 cm (b) 20 cm (c) 22.5 cm (d) 25 cm

3.

In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contant T, are of lengths 12 cm and 9 cm respectively. If the area fo \Delta PQR = 189 cm^2 then the length of side PQ is (a) 17.5 cm (b) 20 cm (c) 22.5 cm (d) 25 cm

Answer»

In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contant T, are of lengths 12 cm and 9 cm respectively. If the area fo \Delta PQR = 189 cm^2 then the length of side PQ is

(a) 17.5 cm (b) 20 cm (c) 22.5 cm (d) 25 cm

Discussion

4.	In the given figure, the minute hand of a clock is 7 cm long and it moves its position from OA to OB in a time span of 20 minutes. The area of the shaded region is equal to
Answer» In the given figure, the minute hand of a clock is $7 cm$ long and it moves its position from $O A$ to $O B$ in a time span of $20 minutes$ . The area of the shaded region is equal to

Discussion

5.	Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?
Answer» Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?

Discussion

6.	In figure, AB \|\| DC. Find the value of x
Answer» In figure, AB \|\| DC. Find the value of x

6.

In figure, AB || DC. Find the value of x

Answer»

In figure, AB || DC. Find the value of x

Discussion

7.	In the figure, AC=10 cm, PC=15 cm, AB=8 cm, find PB.
Answer» In the figure, $A C = 10 c m, P C = 15 c m, A B = 8 c m,$ find PB.

Discussion

8.	Question 1 (iii)Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.3x - 5y = 20 ; 6x - 10y =40
Answer» Question 1 (iii) Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 3x - 5y = 20 ; 6x - 10y =40

Discussion

9.	For the equation of straight line 2x−3y+5=0, match the following.
Answer» For the equation of straight line $2 x - 3 y + 5 = 0$ , match the following.

Discussion

10.	A heap of rice is in the form of a cone with a diameter of 9m and a height of 3.5m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
Answer» A heap of rice is in the form of a cone with a diameter of 9m and a height of 3.5m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Discussion

11.	If A=13⎡⎢⎣−1−2−221−2x−2y⎤⎥⎦is such that it is orthogonal, then x,y satisfy
Answer» If $A = \frac{1}{3} ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & - 2 2 & 1 & - 2 x & - 2 & y \end{matrix} ⎤ ⎥ ⎦$ is such that it is orthogonal, then $x, y$ satisfy

Discussion

12.	Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.
Answer» Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

Discussion

13.	The corresponding sides of two triangles △ABC and △PQR are in the ratio 4:23.If ∠B=60∘ and ∠A=40∘, find the measure of ∠R.
Answer» $The corresponding sides of two triangles △ A B C and △ P Q R are in the ratio 4:23.$ $If ∠ B = 60^{\circ} and ∠ A = 40^{\circ}, find the measure of ∠ R .$

Discussion

14.	Question 1 (iii)Find the distance between the following pairs of points:(iii) (a, b), (− a, − b)
Answer» Question 1 (iii) Find the distance between the following pairs of points: (iii) (a, b), (− a, − b)

Discussion

15.	Find the mode, median and mean for the following data:Marks obtained25−3535−4545−5555−6565−7575−85Number ofstudents7313317111
Answer» Find the mode, median and mean for the following data: $\begin{matrix} Marks obtained & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 Number of students & 7 & 31 & 33 & 17 & 11 & 1 \end{matrix}$

Discussion

16.	From the figure, name(a) Tangents drawn from A to circle C1.(b) Tangents drawn from A to circle C2.(c) Tangents drawn from B to circles C1 and C2.(d) Sets of equal tangents.
Answer» From the figure, name (a) Tangents drawn from A to circle C₁. (b) Tangents drawn from A to circle C₂. (c) Tangents drawn from B to circles C₁ and C₂. (d) Sets of equal tangents.

16.

From the figure, name(a) Tangents drawn from A to circle C1.(b) Tangents drawn from A to circle C2.(c) Tangents drawn from B to circles C1 and C2.(d) Sets of equal tangents.

Answer»

From the figure, name

(a) Tangents drawn from A to circle C₁.

(b) Tangents drawn from A to circle C₂.

(c) Tangents drawn from B to circles C₁ and C₂.

(d) Sets of equal tangents.

Discussion

17.	Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec230 = ? Plz note they are degrees. Thank you
Answer» Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec²30 = ? Plz note they are degrees. Thank you

17.

Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec230 = ? Plz note they are degrees. Thank you

Answer»

Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec²30 = ?

Plz note they are degrees. Thank you

Discussion

18.	A chessboard contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of the chess board.
Answer» A chessboard contains 64 equal squares and the area of each square is $6.25 c m^{2}$ . A border around the board is 2 cm wide. Find the length of the side of the chess board.

Discussion

19.	The square of (5x + 1) is equal to 16. x = ___?
Answer» The square of (5 $x$ + 1) is equal to 16. $x$ = ___?

Discussion

20.	two pipes running can fill a tank in 6 minute. if one pipe take more than other to fill the tank find the time n which each pipe could fill the tank seperately
Answer» two pipes running can fill a tank in 6 minute. if one pipe take more than other to fill the tank find the time n which each pipe could fill the tank seperately

Discussion

21.	From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given bytan α tan βtan α+tan β
Answer» From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by $\frac{\tan α \tan β}{\tan α + \tan β}$

Discussion

22.	If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is (a) 3200(b) 1600(c) 200(d) 2800
Answer» If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is (a) 3200 (b) 1600 (c) 200 (d) 2800

Discussion

23.	During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarised as follows: Number of heart-beats per minute.65−6868−7171−7474−7777−8080−8383−86Number of patients2438742 Find the mean heartbeats per minute for these patients, choosing a suitable method.
Answer» During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarised as follows: $\begin{matrix} Number of heart- beats per minute. & 65 - 68 & 68 - 71 & 71 - 74 & 74 - 77 & 77 - 80 & 80 - 83 & 83 - 86 Number of patients & 2 & 4 & 3 & 8 & 7 & 4 & 2 \end{matrix}$ Find the mean heartbeats per minute for these patients, choosing a suitable method.

Discussion

24.	If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then p2 is equal to
Answer» If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then $p^{2}$ is equal to

Discussion

25.	Let A(-6, -5) and B(-6, 4) be the two points such that a point P on the line AB satisfies AP = (2/9) AB.
Answer» Let A(-6, -5) and B(-6, 4) be the two points such that a point P on the line AB satisfies AP = (2/9) AB.

Discussion

26.	I have problem in solving word problems of equations
Answer» I have problem in solving word problems of equations

Discussion

27.	Prove that if a, b, c are positive numbers and if the equation ax2 + bx + c = 0 has solutions then they are negative numbers.
Answer» Prove that if a, b, c are positive numbers and if the equation ax² + bx + c = 0 has solutions then they are negative numbers.

Discussion

28.	Question 7 In the given figure, ∠Q>∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM=12(∠Q−∠R)
Answer» Question 7 In the given figure, $∠ Q > ∠ R$ , PA is the bisector of $∠ Q P R$ and PM $⊥$ QR. Prove that $∠ A P M = \frac{1}{2} (∠ Q - ∠ R)$

Discussion

29.	Find the frequency of 40 in the following given set of data.10, 40, 80, 100, 60, 40, 30, 40, 20, 40.
Answer» Find the frequency of 40 in the following given set of data. 10, 40, 80, 100, 60, 40, 30, 40, 20, 40.

29.

Find the frequency of 40 in the following given set of data.10, 40, 80, 100, 60, 40, 30, 40, 20, 40.

Answer»

Find the frequency of 40 in the following given set of data.

10, 40, 80, 100, 60, 40, 30, 40, 20, 40.

Discussion

30.	The perimeter (in cm) of a square circumscribing a circle of radius a cm, is
Answer» The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

Discussion

31.	If pth, qth, rthterm of an AP are a, b, c respectively then show that a(q-r) +b(r-p)+c(p-q)=0
Answer» If pth, qth, rthterm of an AP are a, b, c respectively then show that a(q-r) +b(r-p)+c(p-q)=0

Discussion

32.	Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.
Answer» Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

Discussion

33.	Question 67 Three bags contain 64.2 kg of sugar. The second bag contains 45 of the contents of the first and the third contains 4512% of what there is in the second bag. How much sugar is there in each bag?
Answer» Question 67 Three bags contain 64.2 kg of sugar. The second bag contains $\frac{4}{5}$ of the contents of the first and the third contains $45 \frac{1}{2} %$ of what there is in the second bag. How much sugar is there in each bag?

33.

Question 67 Three bags contain 64.2 kg of sugar. The second bag contains 45 of the contents of the first and the third contains 4512% of what there is in the second bag. How much sugar is there in each bag?

Answer»

Question 67

Three bags contain 64.2 kg of sugar. The second bag contains $\frac{4}{5}$ of the contents of the first and the third contains $45 \frac{1}{2} %$ of what there is in the second bag. How much sugar is there in each bag?

Discussion

34.	What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π=3.14]
Answer» What length of tarpaulin $3 m$ wide will be required to make a conical tent of height $8 m$ and base radius $6 m$ ? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20 c m$ . [Use $π = 3.14]$

Discussion

35.	73. Pooja and Ritu can do a piece of work in 120/7 days. If one day work of Pooja be three fourth of one day work of Ritu . Find in how many days each will do the work alone
Answer» 73. Pooja and Ritu can do a piece of work in 120/7 days. If one day work of Pooja be three fourth of one day work of Ritu . Find in how many days each will do the work alone

Discussion

36.	_____ and ____ are the two components of GST.
Answer» _____ and ____ are the two components of GST.

Discussion

37.	If 2p.3q.5r=60, which of the following is true? Given; p, q, r are natural numbers.
Answer» If $2^{p} {.3}^{q} {.5}^{r} = 60$ , which of the following is true? Given; p, q, r are natural numbers.

Discussion

38.	In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:(i) (ii) (iii) (iv) (v) (vi) (vii)
Answer» In the following equations, find which variables x, y, z etc. represent rational or irrational numbers: (i) (ii) (iii) (iv) (v) (vi) (vii)

Discussion

39.	If A , B ,C are interior angles of ∆ABC then show that sin ( B + C )/2 = cos A/2
Answer» If A , B ,C are interior angles of ∆ABC then show that sin ( B + C )/2 = cos A/2

Discussion

40.	Question 1 (iv)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(iv) 2x2+x+4=0
Answer» Question 1 (iv) Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iv) $2 x^{2} + x + 4 = 0$

Discussion

41.	A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.
Answer» A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.

Discussion

42.	what is co domain , how to find co domain and how to find a relation R for a single set A for instance ?
Answer» what is co domain , how to find co domain and how to find a relation R for a single set A for instance ?

Discussion

43.	2. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half of the difference of the angles subtended by the chords AC and DE at the centre.
Answer» 2. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half of the difference of the angles subtended by the chords AC and DE at the centre.

Discussion

44.	Question 60State whether the following statement is true or false:The surface area of a cube formed by cutting a cuboid of dimensions 2×1×1 in 2 equal parts, is 2 sq. units.
Answer» Question 60 State whether the following statement is true or false: The surface area of a cube formed by cutting a cuboid of dimensions $2 \times 1 \times 1$ in 2 equal parts, is 2 sq. units.

44.

Question 60State whether the following statement is true or false:The surface area of a cube formed by cutting a cuboid of dimensions 2×1×1 in 2 equal parts, is 2 sq. units.

Answer»

Question 60

State whether the following statement is true or false:

The surface area of a cube formed by cutting a cuboid of dimensions $2 \times 1 \times 1$ in 2 equal parts, is 2 sq. units.

Discussion

45.	A and B are partners sharing profits and losses in the ratio of 2 : 1. They take C as a partner for 1/5th share. Goodwill Account appears in the books at ₹ 15,000. For the purpose of C's admission, goodwill of the firm is valued at ₹ 15,000. C is to pay proportionate amount as premium for goodwill which he pays to A and B privately.Pass necessary entries.
Answer» A and B are partners sharing profits and losses in the ratio of 2 : 1. They take C as a partner for 1/5th share. Goodwill Account appears in the books at ₹ 15,000. For the purpose of C's admission, goodwill of the firm is valued at ₹ 15,000. C is to pay proportionate amount as premium for goodwill which he pays to A and B privately. Pass necessary entries.

Discussion

46.	Given a straight line 30∘+y sin 30∘=2 Determine the equation of the other line which is parallel to it and passes through (4, 3).
Answer» Given a straight line $30^{\circ} + y s i n 30^{\circ} = 2$ Determine the equation of the other line which is parallel to it and passes through (4, 3).

Discussion

47.	Question 93If the length of each edge of a cube is tripled, what will be the change in its volume?
Answer» Question 93 If the length of each edge of a cube is tripled, what will be the change in its volume?

47.

Question 93If the length of each edge of a cube is tripled, what will be the change in its volume?

Answer»

Question 93

If the length of each edge of a cube is tripled, what will be the change in its volume?

Discussion

48.	Question 3Find the area of a sector of a circle of radius 28 cm and central angle 45∘.
Answer» Question 3 Find the area of a sector of a circle of radius 28 cm and central angle $45^{\circ}$ .

Discussion

49.	AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is ___ and ___ respectively.
Answer» AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is ___ and ___ respectively.

Discussion

50.	In the given figure ABC is a right-angled triangle with ∠BAC=90∘ [4 MARKS] i) Prove that ΔADB∼ΔCDA ii) IF BD = 18 cm, CD = 8 cm, find AD iii) Find the ratio of the area of ΔADB is to area of ΔCDA
Answer» In the given figure ABC is a right-angled triangle with $∠ B A C = 90^{\circ}$ [4 MARKS] i) Prove that $Δ A D B \sim Δ C D A$ ii) IF BD = 18 cm, CD = 8 cm, find AD iii) Find the ratio of the area of $Δ A D B$ is to area of $Δ C D A$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Draw a circle of radius 3 centimetres and draw a rhombus with one angle 40°, all four sides touching the circle.

One angle of a ΔABC which is circumscribed by a circle, has one of the angles as 135∘ and its opposite side is 5 cm as shown in the figure. The diameter of its circumcircle is equal to

In the given figure, the minute hand of a clock is 7 cm long and it moves its position from OA to OB in a time span of 20 minutes. The area of the shaded region is equal to

Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?

In figure, AB || DC. Find the value of x

In the figure, AC=10 cm, PC=15 cm, AB=8 cm, find PB.

Question 1 (iii)Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.3x - 5y = 20 ; 6x - 10y =40

For the equation of straight line 2x−3y+5=0, match the following.

A heap of rice is in the form of a cone with a diameter of 9m and a height of 3.5m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

If A=13⎡⎢⎣−1−2−221−2x−2y⎤⎥⎦is such that it is orthogonal, then x,y satisfy

Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

The corresponding sides of two triangles △ABC and △PQR are in the ratio 4:23.If ∠B=60∘ and ∠A=40∘, find the measure of ∠R.

Question 1 (iii)Find the distance between the following pairs of points:(iii) (a, b), (− a, − b)

Find the mode, median and mean for the following data:Marks obtained25−3535−4545−5555−6565−7575−85Number ofstudents7313317111

From the figure, name(a) Tangents drawn from A to circle C1.(b) Tangents drawn from A to circle C2.(c) Tangents drawn from B to circles C1 and C2.(d) Sets of equal tangents.

Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec​​2​30 = ? Plz note they are degrees. Thank you

A chessboard contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of the chess board.

The square of (5x + 1) is equal to 16. x = ___?

two pipes running can fill a tank in 6 minute. if one pipe take more than other to fill the tank find the time n which each pipe could fill the tank seperately

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given bytan α tan βtan α+tan β

If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is (a) 3200(b) 1600(c) 200(d) 2800

If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then p2 is equal to

Let A(-6, -5) and B(-6, 4) be the two points such that a point P on the line AB satisfies AP = (2/9) AB.

I have problem in solving word problems of equations

Prove that if a, b, c are positive numbers and if the equation ax2 + bx + c = 0 has solutions then they are negative numbers.

Question 7 In the given figure, ∠Q&gt;∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM=12(∠Q−∠R)

Find the frequency of 40 in the following given set of data.10, 40, 80, 100, 60, 40, 30, 40, 20, 40.

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

If pth, qth, rthterm of an AP are a, b, c respectively then show that a(q-r) +b(r-p)+c(p-q)=0

Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

Question 67 Three bags contain 64.2 kg of sugar. The second bag contains 45 of the contents of the first and the third contains 4512% of what there is in the second bag. How much sugar is there in each bag?

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π=3.14]

73. Pooja and Ritu can do a piece of work in 120/7 days. If one day work of Pooja be three fourth of one day work of Ritu . Find in how many days each will do the work alone

_____ and ____ are the two components of GST.

If 2p.3q.5r=60, which of the following is true? Given; p, q, r are natural numbers.

In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:(i) (ii) (iii) (iv) (v) (vi) (vii)

If A , B ,C are interior angles of ∆ABC then show that sin ( B + C )/2 = cos A/2

Question 1 (iv)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(iv) 2x2+x+4=0

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.

what is co domain , how to find co domain and how to find a relation R for a single set A for instance ?

2. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half of the difference of the angles subtended by the chords AC and DE at the centre.

Question 60State whether the following statement is true or false:The surface area of a cube formed by cutting a cuboid of dimensions 2×1×1 in 2 equal parts, is 2 sq. units.

Given a straight line 30∘+y sin 30∘=2 Determine the equation of the other line which is parallel to it and passes through (4, 3).

Question 93If the length of each edge of a cube is tripled, what will be the change in its volume?

Question 3Find the area of a sector of a circle of radius 28 cm and central angle 45∘.

AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is ___ and ___ respectively.

In the given figure ABC is a right-angled triangle with ∠BAC=90∘ [4 MARKS] i) Prove that ΔADB∼ΔCDA ii) IF BD = 18 cm, CD = 8 cm, find AD iii) Find the ratio of the area of ΔADB is to area of ΔCDA

Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec230 = ? Plz note they are degrees. Thank you

Question 7 In the given figure, ∠Q>∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM=12(∠Q−∠R)

_ and are the two components of GST.

AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is _ and _ respectively.