25365 + Interview Questions in Mathematics Page 219 InterviewSolution

10901.	Identify the region in which the elements are divisible by 6.
Answer» Identify the region in which the elements are divisible by 6.

Discussion

10902.	Fill in the blank to make statement true.Out of ___ faces of a rectangular pyramid ___ are triangles and the base is ___.
Answer» Fill in the blank to make statement true. Out of ___ faces of a rectangular pyramid ___ are triangles and the base is ___.

Discussion

10903.	Draw the perpendicular bisector of a line segment which is 8 cm long.
Answer» Draw the perpendicular bisector of a line segment which is 8 cm long.

Discussion

10904.	Mary is wrapping a can of paint to gift it to a friend. If the can is 11 inches high and has a diameter of 7 inches, how many square inches of wrapping paper will be used?
Answer» Mary is wrapping a can of paint to gift it to a friend. If the can is 11 inches high and has a diameter of 7 inches, how many square inches of wrapping paper will be used?

Discussion

10905.	Two sides of a parallelogram are in the ratio 5 :3 If its perimeter is 64 cm, find the length of its sides.
Answer» Two sides of a parallelogram are in the ratio 5 :3 If its perimeter is 64 cm, find the length of its sides.

Discussion

10906.	A wooden box has inner dimensions l = 6 m, b = 8 m and h = 9 m and it has uniform thickness of 10 cm. The lateral surface of the outer side has to be painted at the rate of Rs. 50/m2. What is the cost of painting?
Answer» A wooden box has inner dimensions l = 6 m, b = 8 m and h = 9 m and it has uniform thickness of 10 cm. The lateral surface of the outer side has to be painted at the rate of Rs. 50/m². What is the cost of painting?

Discussion

10907.	Question 86 (i) Using suitable identities, evaluate the following: (52)2
Answer» Question 86 (i) Using suitable identities, evaluate the following: $(52)^{2}$

10907.

Question 86 (i) Using suitable identities, evaluate the following: (52)2

Answer»

Question 86 (i)

Using suitable identities, evaluate the following:

$(52)^{2}$

Discussion

10908.	Question 6 (iv)For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:2645
Answer» Question 6 (iv) For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained: 2645

10908.

Question 6 (iv)For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:2645

Answer»

Question 6 (iv)

For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:

2645

Discussion

10909.	How many interior angles does the following figure have?
Answer» How many interior angles does the following figure have?

Discussion

10910.	the solution of x∫_0^xy(t)dt=(x+1)∫_0^xt.y(t)dt,x>0,i
Answer» the solution of x∫_0^xy(t)dt=(x+1)∫_0^xt.y(t)dt,x>0,i

Discussion

10911.	Define an operation * on the set of all relational numbersas follows:r * s = r + s − (r × s),for any two rational numbers r, s. Answer the following with justification:(i) Is closed under the operation ?(ii) Is an associative operation on ?(iii) Is * a commutative operation on ?(iv) What is a * 1 for any a in (v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.
Answer» Define an operation * on the set of all relational numbersas follows: r * s = r + s − (r × s),for any two rational numbers r, s. Answer the following with justification: (i) Is closed under the operation ? (ii) Is an associative operation on ? (iii) Is * a commutative operation on ? (iv) What is a * 1 for any a in (v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.

10911.

Define an operation * on the set of all relational numbersas follows:r * s = r + s − (r × s),for any two rational numbers r, s. Answer the following with justification:(i) Is closed under the operation ?(ii) Is an associative operation on ?(iii) Is * a commutative operation on ?(iv) What is a * 1 for any a in (v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.

Answer»

Define an operation * on the set of all relational numbersas follows:

r * s = r + s − (r × s),for any two rational numbers r, s. Answer the following with justification:

(i) Is closed under the operation *?

(ii) Is * an associative operation on ?

(iii) Is * a commutative operation on ?

(iv) What is a * 1 for any a in

(v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.

Discussion

10912.	In a given rectangle ABCD, diagonals AD and BC intersect at O. If ∠COD=120∘, what is the value of ∠OBA?
Answer» In a given rectangle ABCD, diagonals AD and BC intersect at O. If $∠ C O D = 120^{\circ}$ , what is the value of $∠ O B A$ ?

Discussion

10913.	A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Answer» A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

Discussion

10914.	The area of the segment in a quarter of a circle of radius 8 inches isinches2
Answer» The area of the segment in a quarter of a circle of radius 8 inches is $i n c h e s^{2}$

Discussion

10915.	Observe the pictograph and answer the following question: How many students like blue colour?
Answer» Observe the pictograph and answer the following question: How many students like blue colour?

10915.

Observe the pictograph and answer the following question: How many students like blue colour?

Answer»

Observe the pictograph and answer the following question:

How many students like blue colour?

Discussion

10916.	On multiplying a decimal number by 100, we shift the decimal point (i) ______ places to the (ii) ______ and on dividing a decimal number by 100, we shift the decimal point, (iii)_______ places to the (iv) _______.
Answer» On multiplying a decimal number by $100$ , we shift the decimal point (i) ______ places to the (ii) ______ and on dividing a decimal number by $100$ , we shift the decimal point, (iii)_______ places to the (iv) _______.

Discussion

10917.	Let the opposite angular pts of a square be (3,4) and (1,-1). Find the coordinates of the remaining angular pts.
Answer» Let the opposite angular pts of a square be (3,4) and (1,-1). Find the coordinates of the remaining angular pts.

Discussion

10918.	∑ fx = 5x + 2, ∑ f = 12. If the mean of the distribution is 6, what is the value of x?
Answer» $\sum f_{x}$ = 5x + 2, $\sum f$ = 12. If the mean of the distribution is 6, what is the value of x?

Discussion

10919.	Find the number of elements in the set corresponding to common elements between set A and set B in the following venn diagram.3
Answer» Find the number of elements in the set corresponding to common elements between set A and set B in the following venn diagram. 3

Discussion

10920.	Simplify- (√7+√3)/(√27+√63-√28-√48)
Answer» Simplify- (√7+√3)/(√27+√63-√28-√48)

10920.

Simplify- (√7+√3)/(√27+√63-√28-√48)

Answer»

Simplify-

(√7+√3)/(√27+√63-√28-√48)

Discussion

10921.	53. ABCD is a quadrilateral.P, Q,R and S are mid points on its sides AB, BC ,CD and AD respectively. PQRS is a parallelogram. Prove that ar( \|\|gm PQRS)=1/2 ar(quad. ABCD)
Answer» 53. ABCD is a quadrilateral.P, Q,R and S are mid points on its sides AB, BC ,CD and AD respectively. PQRS is a parallelogram. Prove that ar( \|\|gm PQRS)=1/2 ar(quad. ABCD)

Discussion

10922.	How many zeroes will 190002 have at the end?
Answer» How many zeroes will $19000^{2}$ have at the end?

Discussion

10923.	The difference between the C.I. for a year payable half-yearly and the simple interest in a certain sum of money lent out at 10% for a year is Rs 12. Find the C.I.
Answer» The difference between the C.I. for a year payable half-yearly and the simple interest in a certain sum of money lent out at 10% for a year is Rs 12. Find the C.I.

Discussion

10924.	a flag staff of 5 m high stands on a building of 25 m height for an observer at a height of 30 m the flag staff & the building subtend equal angle the distance of the observer from the top of the flag staff is
Answer» a flag staff of 5 m high stands on a building of 25 m height for an observer at a height of 30 m the flag staff & the building subtend equal angle the distance of the observer from the top of the flag staff is

Discussion

10925.	The sum of the exponents of prime factors in the prime factorisation of 250 is _________.
Answer» The sum of the exponents of prime factors in the prime factorisation of 250 is _________.

Discussion

10926.	A student has to answer any 6 questions out of 10 questions came in the question paper. How many number of combinations of question are possible?
Answer» A student has to answer any $6$ questions out of $10$ questions came in the question paper. How many number of combinations of question are possible?

Discussion

10927.	What a relief when we reach home after crossing all the obstacles and jumping over the head of several toads and turtles! Here is a histogram which is made up of bricks. 1 brick = 10,500 CDs sold. Carefully observe the histogram and answer the questions that follow:What is the no. of CDs sold during the period 2008 - 2013?
Answer» What a relief when we reach home after crossing all the obstacles and jumping over the head of several toads and turtles! Here is a histogram which is made up of bricks. 1 brick = 10,500 CDs sold. Carefully observe the histogram and answer the questions that follow: What is the no. of CDs sold during the period 2008 - 2013?

10927.

What a relief when we reach home after crossing all the obstacles and jumping over the head of several toads and turtles! Here is a histogram which is made up of bricks. 1 brick = 10,500 CDs sold. Carefully observe the histogram and answer the questions that follow:What is the no. of CDs sold during the period 2008 - 2013?

Answer»

What a relief when we reach home after crossing all the obstacles and jumping over the head of several toads and turtles! Here is a histogram which is made up of bricks. 1 brick = 10,500 CDs sold. Carefully observe the histogram and answer the questions that follow:

What is the no. of CDs sold during the period 2008 - 2013?

Discussion

10928.	A certain company has 80 employees who are engineers. In this company, engineers constitute 40% of its work force. The number of people that are employed in the company is ___ .
Answer» A certain company has 80 employees who are engineers. In this company, engineers constitute $40 %$ of its work force. The number of people that are employed in the company is ___ .

Discussion

10929.	Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.
Answer» Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.

Discussion

10930.	Question 34The two digit number whose ten's digit is t and unit digit is u is ___ .
Answer» Question 34 The two digit number whose ten's digit is t and unit digit is u is ___ .

10930.

Question 34The two digit number whose ten's digit is t and unit digit is u is ___ .

Answer»

Question 34

The two digit number whose ten's digit is t and unit digit is u is ___ .

Discussion

10931.	Arti Limited invited applications for issuing 80,000 shares of Rs 10 each at a premium of Rs 4 per share. The amount was payable as follows: On Application Rs 5 per share. On Allotment Rs 9 per share (including premium ) Applications were received for 1,40,000 shares. Allotment was made on the following basis : (a) To applicants for 80,000 shares - 60,000 shares. (b) To applicants for 60,000 shares - 20,000 shares. Money overpaid on application was utilised towards sum due on allotment. Rajiv, who had applied for 1,200 shares was allotted shares under category (a), failed to pay his dues and his shares were forfeited. Later on forfeited shares were re-issued to Mr. Rakesh for Rs 12 per share. Pass Journal entries in the books of Arti Limited to record the above transactions. OR On 1st April, 2017, Logi-tech Ltd. was formed with an authorised capital of Rs 50,00,000 divided into 5,00,000 equity shares of Rs 10 each. The company issued prospectus inviting applications for 4,50,000 equity shares. The company received applications for 4,20,000 equity shares. During the first year Rs 8 per share were called. Amount called was as follows : On Applications Rs 2 per share; On Allotment Rs 4 per share and On first call Rs 2 per share. Alok holding 1,000 shares and Raju holding 2,000 shares did not pay the first call of Rs 2 per share. Raju's shares were forfeited after the first call and later on 1,500 of the forfeited shares were re-issued at Rs 6 per share, Rs 8 called up. Pass the necessary Journal entries.
Answer» Arti Limited invited applications for issuing 80,000 shares of Rs 10 each at a premium of Rs 4 per share. The amount was payable as follows: On Application Rs 5 per share. On Allotment Rs 9 per share (including premium ) Applications were received for 1,40,000 shares. Allotment was made on the following basis : (a) To applicants for 80,000 shares - 60,000 shares. (b) To applicants for 60,000 shares - 20,000 shares. Money overpaid on application was utilised towards sum due on allotment. Rajiv, who had applied for 1,200 shares was allotted shares under category (a), failed to pay his dues and his shares were forfeited. Later on forfeited shares were re-issued to Mr. Rakesh for Rs 12 per share. Pass Journal entries in the books of Arti Limited to record the above transactions. OR On 1st April, 2017, Logi-tech Ltd. was formed with an authorised capital of Rs 50,00,000 divided into 5,00,000 equity shares of Rs 10 each. The company issued prospectus inviting applications for 4,50,000 equity shares. The company received applications for 4,20,000 equity shares. During the first year Rs 8 per share were called. Amount called was as follows : On Applications Rs 2 per share; On Allotment Rs 4 per share and On first call Rs 2 per share. Alok holding 1,000 shares and Raju holding 2,000 shares did not pay the first call of Rs 2 per share. Raju's shares were forfeited after the first call and later on 1,500 of the forfeited shares were re-issued at Rs 6 per share, Rs 8 called up. Pass the necessary Journal entries.

10931.

Arti Limited invited applications for issuing 80,000 shares of Rs 10 each at a premium of Rs 4 per share. The amount was payable as follows: On Application Rs 5 per share. On Allotment Rs 9 per share (including premium ) Applications were received for 1,40,000 shares. Allotment was made on the following basis : (a) To applicants for 80,000 shares - 60,000 shares. (b) To applicants for 60,000 shares - 20,000 shares. Money overpaid on application was utilised towards sum due on allotment. Rajiv, who had applied for 1,200 shares was allotted shares under category (a), failed to pay his dues and his shares were forfeited. Later on forfeited shares were re-issued to Mr. Rakesh for Rs 12 per share. Pass Journal entries in the books of Arti Limited to record the above transactions. OR On 1st April, 2017, Logi-tech Ltd. was formed with an authorised capital of Rs 50,00,000 divided into 5,00,000 equity shares of Rs 10 each. The company issued prospectus inviting applications for 4,50,000 equity shares. The company received applications for 4,20,000 equity shares. During the first year Rs 8 per share were called. Amount called was as follows : On Applications Rs 2 per share; On Allotment Rs 4 per share and On first call Rs 2 per share. Alok holding 1,000 shares and Raju holding 2,000 shares did not pay the first call of Rs 2 per share. Raju's shares were forfeited after the first call and later on 1,500 of the forfeited shares were re-issued at Rs 6 per share, Rs 8 called up. Pass the necessary Journal entries.

Answer»

Arti Limited invited applications for issuing 80,000 shares of Rs 10 each at a premium of Rs 4 per share. The amount was payable as follows:
On Application Rs 5 per share.
On Allotment Rs 9 per share (including premium )

Applications were received for 1,40,000 shares.

Allotment was made on the following basis :

(a) To applicants for 80,000 shares - 60,000 shares.
(b) To applicants for 60,000 shares - 20,000 shares.

Money overpaid on application was utilised towards sum due on allotment. Rajiv, who had applied for 1,200 shares was allotted shares under category (a), failed to pay his dues and his shares were forfeited. Later on forfeited shares were re-issued to Mr. Rakesh for Rs 12 per share.
Pass Journal entries in the books of Arti Limited to record the above transactions.

OR

On 1st April, 2017, Logi-tech Ltd. was formed with an authorised capital of Rs 50,00,000 divided into 5,00,000 equity shares of Rs 10 each. The company issued prospectus inviting applications for 4,50,000 equity shares. The company received applications for 4,20,000 equity shares. During the first year Rs 8 per share were called. Amount called was as follows :
On Applications Rs 2 per share; On Allotment Rs 4 per share and On first call Rs 2 per share. Alok holding 1,000 shares and Raju holding 2,000 shares did not pay the first call of Rs 2 per share. Raju's shares were forfeited after the first call and later on 1,500 of the forfeited shares were re-issued at Rs 6 per share, Rs 8 called up. Pass the necessary Journal entries.

Discussion

10932.	Question 3 The numerical expression 38+(−5)7=−1956 shows that: (a) rational numbers are closed under addition. (b) rational numbers are not closed under addition. (c) rational numbers are closed under multiplication. (d) addition of rational numbers is not commutative.
Answer» Question 3 The numerical expression $\frac{3}{8} + \frac{(- 5)}{7} = \frac{- 19}{56}$ shows that: (a) rational numbers are closed under addition. (b) rational numbers are not closed under addition. (c) rational numbers are closed under multiplication. (d) addition of rational numbers is not commutative.

Discussion

10933.	Question 3In the given graph the coordinates of point P are(a) (0,2)(b) (2,3)(c) (3,2)(d) (3,0)
Answer» Question 3 In the given graph the coordinates of point P are (a) (0,2) (b) (2,3) (c) (3,2) (d) (3,0)

Discussion

10934.	The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest blood group among these student?
Answer» The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest blood group among these student?

Discussion

10935.	The midpoint of the line segment joining (A,3) and (4,B) is (3,5). What are the values of A and B?
Answer» The midpoint of the line segment joining $(A, 3)$ and $(4, B)$ is $(3, 5)$ . What are the values of $A$ and $B$ ?

Discussion

10936.	Test the divisibility of each of the following numers by 3:(i) 83(ii) 378(iii) 474(iv) 1693(v) 20345(vi) 67035(vii) 591282(viii) 903164(ix) 100002
Answer» Test the divisibility of each of the following numers by 3: (i) 83 (ii) 378 (iii) 474 (iv) 1693 (v) 20345 (vi) 67035 (vii) 591282 (viii) 903164 (ix) 100002

Discussion

10937.	If M is any set, then write M ∪ ϕ and M∩ ϕ .
Answer» If M is any set, then write M $\cup ϕ$ and M $\cap ϕ$ .

Discussion

10938.	If x2+1x2 = 51, find the value of x3-1x3
Answer» If $x^{2} + \frac{1}{x^{2}}$ = 51, find the value of $x^{3} - \frac{1}{x^{3}}$

Discussion

10939.	39. The diagonal of a rhombus are 24 cm and 10 cm, then find the side of rhombus? By applying correct formula.
Answer» 39. The diagonal of a rhombus are 24 cm and 10 cm, then find the side of rhombus? By applying correct formula.

Discussion

10940.	Question 1(iii)Find the cube root of each of the following numbers by prime factorization method:10648
Answer» Question 1(iii) Find the cube root of each of the following numbers by prime factorization method: 10648

Discussion

10941.	In Figure, AB=AD and ∠BAC = ∠DAC.(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.(ii) Complete each of the following, so as to make it true:(a) ∠ABC=(b) ∠ACD=(c) Line segment AC bisects ….. And ……..
Answer» In Figure, $A B = A D$ and $∠ B A C = ∠ D A C$ . (i) State in symbolic form the congruence of two triangles ABC and ADC that is true. (ii) Complete each of the following, so as to make it true: (a) $∠ A B C =$ (b) $∠ A C D =$ (c) Line segment AC bisects ….. And ……..

10941.

In Figure, AB=AD and ∠BAC = ∠DAC.(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.(ii) Complete each of the following, so as to make it true:(a) ∠ABC=(b) ∠ACD=(c) Line segment AC bisects ….. And ……..

Answer»

In Figure, $A B = A D$ and $∠ B A C = ∠ D A C$ .

(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.

(ii) Complete each of the following, so as to make it true:

(a) $∠ A B C =$

(b) $∠ A C D =$

(c) Line segment AC bisects ….. And ……..

Discussion

10942.	The ages (in years) of 360 patients treated in a hospital on a particular dayare given below.Age in years10−2020−3030−4040−5050−6060−70Number ofpatients9040602012030Draw a histogram and a frequency polygon on the same graph to represent the above data.
Answer» The ages (in years) of 360 patients treated in a hospital on a particular dayare given below. $\begin{matrix} Age in years & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 Number of patients & 90 & 40 & 60 & 20 & 120 & 30 \end{matrix}$ Draw a histogram and a frequency polygon on the same graph to represent the above data.

Discussion

10943.	Rahul makes a cuboid of plasticine of sides 5 cm,2 cm,5 cm. How many such cuboids will he need to form a cube?
Answer» Rahul makes a cuboid of plasticine of sides $5 c m, 2 c m, 5 c m$ . How many such cuboids will he need to form a cube?

Discussion

10944.	The sum of four consecutive multiples of 9 is 378. Find these multiples? [3 MARKS]
Answer» The sum of four consecutive multiples of 9 is 378. Find these multiples? [3 MARKS]

Discussion

10945.	What is the value of 7C2?
Answer» What is the value of $_{7} C_{2} ?$

Discussion

10946.	Suppose two adjacent angles are supplementary. Show that if one of them is an obtuse angle, then the other angle must be acute.
Answer» Suppose two adjacent angles are supplementary. Show that if one of them is an obtuse angle, then the other angle must be acute.

Discussion

10947.	Show that m -1 is a factor of m21 - 1 and m22 - 1.
Answer» Show that m $-$ 1 is a factor of m²¹ $-$ 1 and m²² $-$ 1.

Discussion

10948.	Which of the following polygons is uniquely determined when all the sides are given?
Answer» Which of the following polygons is uniquely determined when all the sides are given?

Discussion

10949.	The length of a rectangle is 15 cm and breadth is 8 cm. If the length is increased by 5 cm and breadth is increased by 2 cm, then the increase in area is equal to
Answer» The length of a rectangle is $15 c m$ and breadth is $8 c m .$ If the length is increased by $5 c m$ and breadth is increased by $2 c m,$ then the increase in area is equal to

Discussion

10950.	Question 4 Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.
Answer» Question 4 Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

Discussion

Explore topic-wise InterviewSolutions in .

Identify the region in which the elements are divisible by 6.

Fill in the blank to make statement true.Out of ___ faces of a rectangular pyramid ___ are triangles and the base is ___.

Draw the perpendicular bisector of a line segment which is 8 cm long.

Mary is wrapping a can of paint to gift it to a friend. If the can is 11 inches high and has a diameter of 7 inches, how many square inches of wrapping paper will be used?

Two sides of a parallelogram are in the ratio 5 :3 If its perimeter is 64 cm, find the length of its sides.

A wooden box has inner dimensions l = 6 m, b = 8 m and h = 9 m and it has uniform thickness of 10 cm. The lateral surface of the outer side has to be painted at the rate of Rs. 50/m2. What is the cost of painting?

Question 86 (i) Using suitable identities, evaluate the following: (52)2

Question 6 (iv)For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:2645

How many interior angles does the following figure have?

the solution of x∫_0^xy(t)dt=(x+1)∫_0^xt.y(t)dt,x>0,i

In a given rectangle ABCD, diagonals AD and BC intersect at O. If ∠COD=120∘, what is the value of ∠OBA?

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

The area of the segment in a quarter of a circle of radius 8 inches isinches2

Observe the pictograph and answer the following question: How many students like blue colour?

On multiplying a decimal number by 100, we shift the decimal point (i) ______ places to the (ii) ______ and on dividing a decimal number by 100, we shift the decimal point, (iii)_______ places to the (iv) _______.

Let the opposite angular pts of a square be (3,4) and (1,-1). Find the coordinates of the remaining angular pts.

∑ fx = 5x + 2, ∑ f = 12. If the mean of the distribution is 6, what is the value of x?

Find the number of elements in the set corresponding to common elements between set A and set B in the following venn diagram.3

Simplify- (√7+√3)/(√27+√63-√28-√48)

53. ABCD is a quadrilateral.P, Q,R and S are mid points on its sides AB, BC ,CD and AD respectively. PQRS is a parallelogram. Prove that ar( ||gm PQRS)=1/2 ar(quad. ABCD)

How many zeroes will 190002 have at the end?

The difference between the C.I. for a year payable half-yearly and the simple interest in a certain sum of money lent out at 10% for a year is Rs 12. Find the C.I.

a flag staff of 5 m high stands on a building of 25 m height for an observer at a height of 30 m the flag staff & the building subtend equal angle the distance of the observer from the top of the flag staff is​

The sum of the exponents of prime factors in the prime factorisation of 250 is _________.

A student has to answer any 6 questions out of 10 questions came in the question paper. How many number of combinations of question are possible?

A certain company has 80 employees who are engineers. In this company, engineers constitute 40% of its work force. The number of people that are employed in the company is ___ .

Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.

Question 34The two digit number whose ten's digit is t and unit digit is u is ___ .

Question 3 The numerical expression 38+(−5)7=−1956 shows that: (a) rational numbers are closed under addition. (b) rational numbers are not closed under addition. (c) rational numbers are closed under multiplication. (d) addition of rational numbers is not commutative.

Question 3In the given graph the coordinates of point P are(a) (0,2)(b) (2,3)(c) (3,2)(d) (3,0)

The midpoint of the line segment joining (A,3) and (4,B) is (3,5). What are the values of A and B?

Test the divisibility of each of the following numers by 3:(i) 83(ii) 378(iii) 474(iv) 1693(v) 20345(vi) 67035(vii) 591282(viii) 903164(ix) 100002

If M is any set, then write M ∪ ϕ and M∩ ϕ .

If x2+1x2 = 51, find the value of x3-1x3

39. The diagonal of a rhombus are 24 cm and 10 cm, then find the side of rhombus? By applying correct formula.

Question 1(iii)Find the cube root of each of the following numbers by prime factorization method:10648

In Figure, AB=AD and ∠BAC = ∠DAC.(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.(ii) Complete each of the following, so as to make it true:(a) ∠ABC=(b) ∠ACD=(c) Line segment AC bisects ….. And ……..

The ages (in years) of 360 patients treated in a hospital on a particular dayare given below.Age in years10−2020−3030−4040−5050−6060−70Number ofpatients9040602012030Draw a histogram and a frequency polygon on the same graph to represent the above data.

Rahul makes a cuboid of plasticine of sides 5 cm,2 cm,5 cm. How many such cuboids will he need to form a cube?

The sum of four consecutive multiples of 9 is 378. Find these multiples? [3 MARKS]

What is the value of 7C2?

Suppose two adjacent angles are supplementary. Show that if one of them is an obtuse angle, then the other angle must be acute.

Show that m -1 is a factor of m21 - 1 and m22 - 1.

Which of the following polygons is uniquely determined when all the sides are given?

The length of a rectangle is 15 cm and breadth is 8 cm. If the length is increased by 5 cm and breadth is increased by 2 cm, then the increase in area is equal to

Question 4 Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

Fill in the blank to make statement true.Out of _ faces of a rectangular pyramid _ are triangles and the base is ___.

On multiplying a decimal number by 100, we shift the decimal point (i) __ places to the (ii) and on dividing a decimal number by 100, we shift the decimal point, (iii)_ places to the (iv) ___.

a flag staff of 5 m high stands on a building of 25 m height for an observer at a height of 30 m the flag staff & the building subtend equal angle the distance of the observer from the top of the flag staff is