24740 + Interview Questions in Mathematics

1.	Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
Answer» Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.

Discussion

2.	An equilateral triangle ABC of side 10 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is
Answer» An equilateral triangle ABC of side 10 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

2.

An equilateral triangle ABC of side 10 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

Answer»

An equilateral triangle ABC of side 10 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

Discussion

3.	The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information, and draw its graph.
Answer» The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information, and draw its graph.

Discussion

4.	The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are ___________.
Answer» The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are ___________.

Discussion

5.	If √25−√−64 is expressed as a - bi, the correct value will be
Answer» $If \sqrt{25} - \sqrt{- 64} is expressed as a - bi, the correct$ value will be

Discussion

6.	Find the unknown side in the following triangle.
Answer» Find the unknown side in the following triangle.

Discussion

7.	In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
Answer» In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

7.

In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Answer»

In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Discussion

8.	Represent √9.3 on a number line
Answer» Represent √9.3 on a number line

Discussion

9.	The number of circles which can pass through three non-collinear points is:
Answer» The number of circles which can pass through three non-collinear points is:

Discussion

10.	In the given figure, O is the centre of the circle with radius 7 cm. If OC = CD, then the length of chord AB is
Answer» In the given figure, O is the centre of the circle with radius 7 cm. If OC = CD, then the length of chord AB is

Discussion

11.	In which of the following quadrant does the point (-6,1) lie?
Answer» In which of the following quadrant does the point (-6,1) lie?

Discussion

12.	Factorise: (x+1x)2+3(x+1x)+2
Answer» Factorise: ${(x + \frac{1}{x})}^{2} + 3 (x + \frac{1}{x}) + 2$

Discussion

13.	A field is in the shape of a trapezium whose parallel sides are of 25m and 10m. The non-parallel sides are 12m and 13m. Find the area of the field
Answer» A field is in the shape of a trapezium whose parallel sides are of 25m and 10m. The non-parallel sides are 12m and 13m. Find the area of the field

Discussion

14.	What are the common factors of 3x3y,5xy2 and 15xy?
Answer» What are the common factors of $3 x^{3} y, 5 x y^{2} a n d 15 x y ?$

Discussion

15.	The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?(a) 24π(b) 48π(c) 32π(d) 48π
Answer» The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder? (a) $\frac{24}{π}$ (b) $\frac{48}{π}$ (c) $\frac{32}{π}$ (d) $\frac{48}{π}$

Discussion

16.	Angle between the hour and minute hand of a clock at 11 : 15 is -
Answer» Angle between the hour and minute hand of a clock at 11 : 15 is -

Discussion

17.	he base of an isosceles triangle whose area is 12 cm2 and the equal sides is 5 cm each is(1) 6 cm(3) Both (1) & (2)(2) 8 cm(4) None of these
Answer» he base of an isosceles triangle whose area is 12 cm2 and the equal sides is 5 cm each is(1) 6 cm(3) Both (1) & (2)(2) 8 cm(4) None of these

Discussion

18.	The quotient when 4x3+x2+5x+8 is divided by (x+1) is .
Answer» The quotient when $4 x^{3} + x^{2} + 5 x + 8$ is divided by $(x + 1)$ is .

Discussion

19.	The length of a uniform rod is 100.0 cm and radius is 1.00 cm. If length is measured with a meter rod ham least count 1 mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder iserror in calculated volume of cylinder is
Answer» The length of a uniform rod is 100.0 cm and radius is 1.00 cm. If length is measured with a meter rod ham least count 1 mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder is error in calculated volume of cylinder is

Discussion

20.	The graph of y=1−x21+x2
Answer» The graph of $y = \frac{1 - x^{2}}{1 + x^{2}}$

Discussion

21.	Construct a ΔABC with perimeter 11 cm and base angles 90° and 60°.
Answer» Construct a ΔABC with perimeter 11 cm and base angles 90° and 60°.

Discussion

22.	The place values of 3 in 4328721 is:
Answer» The place values of 3 in 4328721 is:

Discussion

23.	How would you go about finding the area of the major sector?
Answer» How would you go about finding the area of the major sector?

Discussion

24.	The polynomials ax3+3x2 - 3 and 2x3 - 5x + a when divided by (x-4) leave the remainders R1 and R2 respectively. Find the values of a in each case of the following cases, if (i) R1=R2 (ii) R1+R2=0 (iii) 2R1−R2=0
Answer» The polynomials $a x^{3} + 3 x^{2}$ - 3 and $2 x^{3}$ - 5x + a when divided by (x-4) leave the remainders $R_{1}$ and $R_{2}$ respectively. Find the values of a in each case of the following cases, if (i) $R_{1} = R_{2}$ (ii) $R_{1} + R_{2} = 0$ (iii) $2 R_{1} - R_{2} = 0$

24.

The polynomials ax3+3x2 - 3 and 2x3 - 5x + a when divided by (x-4) leave the remainders R1 and R2 respectively. Find the values of a in each case of the following cases, if (i) R1=R2 (ii) R1+R2=0 (iii) 2R1−R2=0

Answer»

The polynomials $a x^{3} + 3 x^{2}$ - 3 and $2 x^{3}$ - 5x + a when divided by (x-4) leave the remainders $R_{1}$ and $R_{2}$ respectively. Find the values of a in each case of the following cases, if

(i) $R_{1} = R_{2}$

(ii) $R_{1} + R_{2} = 0$

(iii) $2 R_{1} - R_{2} = 0$

Discussion

25.	There are 216 workers in a factory out of which 75 are laborers. What would be the central angle of the sector representing laborers in a pie chart?
Answer» There are 216 workers in a factory out of which 75 are laborers. What would be the central angle of the sector representing laborers in a pie chart?

Discussion

26.	Write the coordinates of a point P on x-axis which is equidistant from the point A(–2, 0) and B(6, 0).
Answer» Write the coordinates of a point P on x-axis which is equidistant from the point A(–2, 0) and B(6, 0).

Discussion

27.	In figure, E and F are mid - points of the sides AB and AC respectively of the ΔABC. G and H are mid-points of the sides AE and AF respectively of the ΔAEF. If GH =1.8 cm, find BC.
Answer» In figure, E and F are mid - points of the sides AB and AC respectively of the $Δ A B C$ . G and H are mid-points of the sides AE and AF respectively of the $Δ A E F$ . If GH =1.8 cm, find BC.

Discussion

28.	In each of the following determine rational numbers a and b : (i) √3−1√3+1=a−b√3 (ii) 4+√22+√2=a−√b (iii) 3+√23−√2=a+b√2 (iv) 5+3√37+4√3=a+b√3 (v) √11−√7√11+√7=a−b√77 (vi) 4+3√54−3√5=a+b√5
Answer» In each of the following determine rational numbers a and b : (i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$ (ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$ (iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$ (iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$ (v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$ (vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

28.

In each of the following determine rational numbers a and b : (i) √3−1√3+1=a−b√3 (ii) 4+√22+√2=a−√b (iii) 3+√23−√2=a+b√2 (iv) 5+3√37+4√3=a+b√3 (v) √11−√7√11+√7=a−b√77 (vi) 4+3√54−3√5=a+b√5

Answer»

In each of the following determine rational numbers a and b :

(i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$

(ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$

(iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$

(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

(v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$

(vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

Discussion

29.	Determine whether an inclusive 'OR' or exclusive 'OR' is used in a statement, also give reason for your answer. 'Two lines intersect at a point or parallel'.
Answer» Determine whether an inclusive 'OR' or exclusive 'OR' is used in a statement, also give reason for your answer. 'Two lines intersect at a point or parallel'.

29.

Determine whether an inclusive 'OR' or exclusive 'OR' is used in a statement, also give reason for your answer. 'Two lines intersect at a point or parallel'.

Answer»

Determine whether an inclusive 'OR' or exclusive 'OR' is used in a statement, also give reason for your answer.

'Two lines intersect at a point or parallel'.

Discussion

30.	In the given figure if AB \|\| EF, ∠ABC=70∘ and ∠EFD=40∘, then find x.
Answer» In the given figure if AB \|\| EF, $∠ A B C = 70^{\circ}$ and $∠ E F D = 40^{\circ}$ , then find x.

Discussion

31.	Draw a histogram from the given data of a class students.Weight(kg)Number of students35.5−40.5440.5−45.51545.5−50.51250.5−55.51355.5−60.56 [4 MARKS]
Answer» Draw a histogram from the given data of a class students. $\begin{matrix} W e i g h t (k g) & N u m b e r o f s t u d e n t s 35.5 - 40.5 & 4 40.5 - 45.5 & 15 45.5 - 50.5 & 12 50.5 - 55.5 & 13 55.5 - 60.5 & 6 \end{matrix}$ [4 MARKS]

31.

Draw a histogram from the given data of a class students.Weight(kg)Number of students35.5−40.5440.5−45.51545.5−50.51250.5−55.51355.5−60.56 [4 MARKS]

Answer»

Draw a histogram from the given data of a class students.

$\begin{matrix} W e i g h t (k g) & N u m b e r o f s t u d e n t s 35.5 - 40.5 & 4 40.5 - 45.5 & 15 45.5 - 50.5 & 12 50.5 - 55.5 & 13 55.5 - 60.5 & 6 \end{matrix}$

[4 MARKS]

Discussion

32.

Following offsets were taken from a survey line to a hedge:Distance (in m)051015203040Offsets (in m)345.55644.5The area between survey line and the hedge is (by trapezoidal method):

Answer»

Following offsets were taken from a survey line to a hedge:

Distance (in m)	0	5	10	15	20	30	40
Offsets (in m)	3	4	5.5	5	6	4	4.5

The area between survey line and the hedge is (by trapezoidal method):

Discussion

33.	Question 5Draw a triangle ABC with side BC=6 cm, AB=5 cm and∠ABC=60∘. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.
Answer» Question 5 Draw a triangle ABC with side $B C = 6 c m, A B = 5 c m a n d ∠ A B C = 60^{\circ}$ . Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle ABC.

Discussion

34.	Show that the following points are the vertices of a rectangle.(i) A(−4, −1), B(−2, −4) C(−3, 2) and D(0, −1) (ii) A(2, −2), B(14, 10) C(11, 13) and D(−1, 1)(iii) A(0, −4), B(6, 2) C(3, 5) and D(−3, −1)
Answer» Show that the following points are the vertices of a rectangle. (i) A(−4, −1), B(−2, −4) C(−3, 2) and D(0, −1) (ii) A(2, −2), B(14, 10) C(11, 13) and D(−1, 1) (iii) A(0, −4), B(6, 2) C(3, 5) and D(−3, −1)

Discussion

35.	Which of these is a condition for a parallelogram to be a square?
Answer» Which of these is a condition for a parallelogram to be a square?

Discussion

36.	Question 12 (iii) A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at a number greater than 2?
Answer» Question 12 (iii) A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at a number greater than 2?

Discussion

37.	In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.
Answer» In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

37.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

Answer»

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

Discussion

38.	Question 3 (ii)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.
Answer» Question 3 (ii) The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

Discussion

39.	23. If the non parallel sides of a trapezium are equal, prove that it is cyclic?
Answer» 23. If the non parallel sides of a trapezium are equal, prove that it is cyclic?

Discussion

40.	A wall of length 10m was to be built across an open ground. The height of the wall is 4m and thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are 24cm20cm8cm, then how many bricks would be required?
Answer» A wall of length 10m was to be built across an open ground. The height of the wall is 4m and thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are 24cm20cm8cm, then how many bricks would be required?

Discussion

41.	Tim calculated the digits in the repeating block of 433. While writing, he accidently added 1 to every repeating digit. What is the newly obtained fraction?
Answer» Tim calculated the digits in the repeating block of $\frac{4}{33}$ . While writing, he accidently added 1 to every repeating digit. What is the newly obtained fraction?

Discussion

42.	the remainder when x4-3x2+4x+5 is divided by x2-x+1
Answer» the remainder when x4-3x2+4x+5 is divided by x2-x+1

Discussion

43.	Prove that sum of deviation is zero for 121 122 123 124 125 126 127 128 129 130
Answer» Prove that sum of deviation is zero for 121 122 123 124 125 126 127 128 129 130

Discussion

44.	Question 7 The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.
Answer» Question 7 The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

Discussion

45.	If the supplement of an angle is two-third of itself , then its supplement is
Answer» If the supplement of an angle is two-third of itself , then its supplement is

Discussion

46.	AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED : area of △ ABC =_____.
Answer» AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED : area of △ ABC =_____.

Discussion

47.	Question 72A quadrilateral in which a pair of opposite sides is parallel is ___.
Answer» Question 72 A quadrilateral in which a pair of opposite sides is parallel is ___.

Discussion

48.	The area of the triangle formed by the lines x = 3, y = 4 and x = y is
Answer» The area of the triangle formed by the lines x = 3, y = 4 and x = y is

Discussion

49.	Question 5 (v) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (v) (cosA−sinA+1)(cosA+sinA−1)=cosecA+cotA, using the identity cosec2A=1+cot2A.
Answer» Question 5 (v) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (v) $\frac{(c o s A - s i n A + 1)}{(c o s A + s i n A - 1)} = c o s e c A + c o t A$ , using the identity $c o s e c^{2} A = 1 + c o t^{2} A$ .

Discussion

50.

If x=20∘ and y=30∘ in the given figure, find the value of z.

Answer»

If $x = 20^{\circ}$ and $y = 30^{\circ}$ in the given figure, find the value of z.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.

An equilateral triangle ABC of side 10 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information, and draw its graph.

The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are ___________.

If √25−√−64 is expressed as a - bi, the correct value will be

Find the unknown side in the following triangle.

In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Represent √9.3 on a number line

The number of circles which can pass through three non-collinear points is:

In the given figure, O is the centre of the circle with radius 7 cm. If OC = CD, then the length of chord AB is

In which of the following quadrant does the point (-6,1) lie?

Factorise: (x+1x)2+3(x+1x)+2

A field is in the shape of a trapezium whose parallel sides are of 25m and 10m. The non-parallel sides are 12m and 13m. Find the area of the field

What are the common factors of ​3x3y,5xy2 and 15xy?

The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?(a) 24π(b) 48π(c) 32π(d) 48π

Angle between the hour and minute hand of a clock at 11 : 15 is -

he base of an isosceles triangle whose area is 12 cm2 and the equal sides is 5 cm each is(1) 6 cm(3) Both (1) & (2)(2) 8 cm(4) None of these

The quotient when 4x3+x2+5x+8 is divided by (x+1) is .

The length of a uniform rod is 100.0 cm and radius is 1.00 cm. If length is measured with a meter rod ham least count 1 mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder iserror in calculated volume of cylinder is

The graph of y=1−x21+x2

Construct a ΔABC with perimeter 11 cm and base angles 90° and 60°.

The place values of 3 in 4328721 is:

How would you go about finding the area of the major sector?

The polynomials ax3+3x2 - 3 and 2x3 - 5x + a when divided by (x-4) leave the remainders R1 and R2 respectively. Find the values of a in each case of the following cases, if (i) R1=R2 (ii) R1+R2=0 (iii) 2R1−R2=0

There are 216 workers in a factory out of which 75 are laborers. What would be the central angle of the sector representing laborers in a pie chart?

Write the coordinates of a point P on x-axis which is equidistant from the point A(–2, 0) and B(6, 0).

In figure, E and F are mid - points of the sides AB and AC respectively of the ΔABC. G and H are mid-points of the sides AE and AF respectively of the ΔAEF. If GH =1.8 cm, find BC.

In each of the following determine rational numbers a and b : (i) √3−1√3+1=a−b√3 (ii) 4+√22+√2=a−√b (iii) 3+√23−√2=a+b√2 (iv) 5+3√37+4√3=a+b√3 (v) √11−√7√11+√7=a−b√77 (vi) 4+3√54−3√5=a+b√5

Determine whether an inclusive 'OR' or exclusive 'OR' is used in a statement, also give reason for your answer. 'Two lines intersect at a point or parallel'.

In the given figure if AB || EF, ∠ABC=70∘ and ∠EFD=40∘, then find x.

Draw a histogram from the given data of a class students.Weight(kg)Number of students35.5−40.5440.5−45.51545.5−50.51250.5−55.51355.5−60.56 [4 MARKS]

Following offsets were taken from a survey line to a hedge:Distance (in m)051015203040Offsets (in m)345.55644.5The area between survey line and the hedge is (by trapezoidal method):

Question 5Draw a triangle ABC with side BC=6 cm, AB=5 cm and∠ABC=60∘. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.

Show that the following points are the vertices of a rectangle.(i) A(−4, −1), B(−2, −4) C(−3, 2) and D(0, −1) (ii) A(2, −2), B(14, 10) C(11, 13) and D(−1, 1)(iii) A(0, −4), B(6, 2) C(3, 5) and D(−3, −1)

Which of these is a condition for a parallelogram to be a square?

Question 12 (iii) A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at a number greater than 2?

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

Question 3 (ii)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

23. If the non parallel sides of a trapezium are equal, prove that it is cyclic?

A wall of length 10m was to be built across an open ground. The height of the wall is 4m and thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are 24cm*20cm*8cm, then how many bricks would be required?

Tim calculated the digits in the repeating block of 433. While writing, he accidently added 1 to every repeating digit. What is the newly obtained fraction?

the remainder when x4-3x2+4x+5 is divided by x2-x+1

Prove that sum of deviation is zero for 121 122 123 124 125 126 127 128 129 130

Question 7 The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

If the supplement of an angle is two-third of itself , then its supplement is

AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED : area of △ ABC =_____.

Question 72A quadrilateral in which a pair of opposite sides is parallel is ___.

The area of the triangle formed by the lines x = 3, y = 4 and x = y is

Question 5 (v) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (v) (cosA−sinA+1)(cosA+sinA−1)=cosecA+cotA, using the identity cosec2A=1+cot2A.

If x=20∘ and y=30∘ in the given figure, find the value of z.

What are the common factors of 3x3y,5xy2 and 15xy?

A wall of length 10m was to be built across an open ground. The height of the wall is 4m and thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are 24cm20cm8cm, then how many bricks would be required?