25365 + Interview Questions in Mathematics

1.	Let ABCD be a quadrilateral and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a parallelogram. (What extra result you need to prove this)?
Answer» Let ABCD be a quadrilateral and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a parallelogram. (What extra result you need to prove this)?

1.

Let ABCD be a quadrilateral and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a parallelogram. (What extra result you need to prove this)?

Answer»

Let ABCD be a quadrilateral and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a parallelogram. (What extra result you need to prove this)?

Discussion

2.	Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.
Answer» Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.

Discussion

3.	The sum of three consecutive multiples of 8 is 888. Find the multiple.
Answer» The sum of three consecutive multiples of 8 is 888. Find the multiple.

Discussion

4.	Locus of the foot of perpendicular drawn from a fixed point (10,0) on the x axis to any †an gent to the circle x2+y2=16 i
Answer» Locus of the foot of perpendicular drawn from a fixed point (10,0) on the x axis to any †an gent to the circle x2+y2=16 i

Discussion

5.	In the given figure, if ∠OAB = 30∘ and ∠OCB = 57∘ , then ∠BOC = _______ and ∠AOC = _________ .
Answer» In the given figure, if ∠OAB = 30^∘ and ∠OCB = 57^∘ , then ∠BOC = _______ and ∠AOC = _________ .

Discussion

6.	15.A sample of gas in a box is at pressure p^° and temp t^°. If number of molecules is doubled and KE of the gas is kept constant, then final temp and pressure will be
Answer» 15.A sample of gas in a box is at pressure p^° and temp t^°. If number of molecules is doubled and KE of the gas is kept constant, then final temp and pressure will be

Discussion

7.	Question 41(iii)Write the X-coordinate (abscissa) of the given point.(0,5)
Answer» Question 41(iii) Write the X-coordinate (abscissa) of the given point. (0,5)

Discussion

8.	Subtract the second polynomial from the first. (i) 5x2-2y + 9 ; 3x2 + 5y -7 (ii) 2x2 + 3x + 5 ; x 2 -2x + 3
Answer» Subtract the second polynomial from the first. (i) 5x² $-$ 2y + 9 ; 3x² + 5y $-$ 7 (ii) 2x²+ 3x + 5 ; x ² $-$ 2x + 3

Discussion

9.	what is concentrTion gradient
Answer» what is concentrTion gradient

Discussion

10.	Question 9 In which of the following expressions, prime factorization has been done: 24 = 2×3×4 56 = 7×2×2×2 70 = 2×5×7 54 = 2×3×9
Answer» Question 9 In which of the following expressions, prime factorization has been done: 24 = $2 \times 3 \times 4$ 56 = $7 \times 2 \times 2 \times 2$ 70 = $2 \times 5 \times 7$ 54 = $2 \times 3 \times 9$

10.

Question 9 In which of the following expressions, prime factorization has been done: 24 = 2×3×4 56 = 7×2×2×2 70 = 2×5×7 54 = 2×3×9

Answer»

Question 9

In which of the following expressions, prime factorization has been done:
24 = $2 \times 3 \times 4$
56 = $7 \times 2 \times 2 \times 2$
70 = $2 \times 5 \times 7$
54 = $2 \times 3 \times 9$

Discussion

11.	43. In triangle ABC, angle BAC=90 degree and AB=BC.seg AP is perpendicular on side BC. B-P-C.D is any point on side BC. prove that 2AD2=BD2+CD2
Answer» 43. In triangle ABC, angle BAC=90 degree and AB=BC.seg AP is perpendicular on side BC. B-P-C.D is any point on side BC. prove that 2AD2=BD2+CD2

Discussion

12.	The degree of the quotient when 6x3+3x is divided by 3x is ___
Answer» The degree of the quotient when $6 x^{3} + 3 x$ is divided by $3 x$ is ___

Discussion

13.	The following data set follows the equation y=10x. Use this information to find the missing entries A and B.
Answer» The following data set follows the equation $y = 10 x$ . Use this information to find the missing entries $A$ and $B$ .

Discussion

14.	If x2+y2=14 and xy=3, then find the value of 2(x+y)2−5(x−y)2.
Answer» $If x^{2} + y^{2} = 14 and x y = 3,$ then find the value of $2 (x + y)^{2} - 5 (x - y)^{2} .$

Discussion

15.	Aayan bought as many 25 paisa postal stamps as 50 paise stamps and paid Rs. 9 fir them. How many stamps of each denomination did he buy.
Answer» Aayan bought as many 25 paisa postal stamps as 50 paise stamps and paid Rs. 9 fir them. How many stamps of each denomination did he buy.

Discussion

16.	Question 8Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.Which colour received 15 of the votes?(a) Red(b) Blue(c) Green(d) Yellow
Answer» Question 8 Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected. Which colour received $\frac{1}{5}$ of the votes? (a) Red (b) Blue (c) Green (d) Yellow

16.

Question 8Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.Which colour received 15 of the votes?(a) Red(b) Blue(c) Green(d) Yellow

Answer»

Question 8

Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.

Which colour received $\frac{1}{5}$ of the votes?

(a) Red

(b) Blue

(c) Green

(d) Yellow

Discussion

17.	The area of the base of a cuboid is 45cm2. It is height is 6 cm. Find the volume
Answer» The area of the base of a cuboid is 45cm2. It is height is 6 cm. Find the volume

Discussion

18.	Ratio 6:7 is equivalent to:
Answer» Ratio 6:7 is equivalent to:

Discussion

19.	42. An ellipse of eccentricity [{2×(root 2)}÷ 3] is inscribed in a circle and a point within the circle is chosen at random. The probability that this point lies outside the circle is____.
Answer» 42. An ellipse of eccentricity [{2×(root 2)}÷ 3] is inscribed in a circle and a point within the circle is chosen at random. The probability that this point lies outside the circle is____.

Discussion

20.	Find the speed of vehicles which cover:(a) A distance of 600 km in 8 hours.(b) A distance of 294 km in 7 hours.(c) A distance of 1368 m in 18 seconds.
Answer» Find the speed of vehicles which cover: (a) A distance of 600 km in 8 hours. (b) A distance of 294 km in 7 hours. (c) A distance of 1368 m in 18 seconds.

Discussion

21.	36. Parallelogram PQRS, given that PQ =6.5cmPS=3.4cm and the altitude PT from P is 2.5cm .Draw the altitude from R and measure it
Answer» 36. Parallelogram PQRS, given that PQ =6.5cmPS=3.4cm and the altitude PT from P is 2.5cm .Draw the altitude from R and measure it

Discussion

22.	Multiply (x2+x+1) by (1−x).
Answer» Multiply $(x^{2} + x + 1)$ by $(1 - x)$ .

Discussion

23.	75. If a triangle and a parallelogram on the same base and between the same parallels, then area of the triangleis equal to half that of the parallelogram
Answer» 75. If a triangle and a parallelogram on the same base and between the same parallels, then area of the triangleis equal to half that of the parallelogram

Discussion

24.	Suppose b is a positive integer such that is also an integer. What are the possible values of b?
Answer» Suppose b is a positive integer such that is also an integer. What are the possible values of b?

Discussion

25.	A family went to a restaurant for dinner. The bill of ₹3000 was handed which was not inclusive of the 4% Goods and Service Tax (GST). The final bill amount would be?
Answer» A family went to a restaurant for dinner. The bill of ₹3000 was handed which was not inclusive of the 4% Goods and Service Tax (GST). The final bill amount would be?

Discussion

26.	Locate the points A (1, 2), B (4, 2) and C (1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D in order to complete the rectangle ABCD.
Answer» Locate the points A (1, 2), B (4, 2) and C (1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D in order to complete the rectangle ABCD.

Discussion

27.	Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:1623512584810341228151176328596871412(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.
Answer» Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: $\begin{matrix} 1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12 \end{matrix}$ (i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.

Discussion

28.	5. Factorise }a^4x^2-2a^3x+a^2
Answer» 5. Factorise }a^4x^2-2a^3x+a^2

Discussion

29.	21 pirates collected 2720 gold coins yesterday. If they want to distribute the coins equally among themselves, how many coins will each pirate get?
Answer» 21 pirates collected 2720 gold coins yesterday. If they want to distribute the coins equally among themselves, how many coins will each pirate get?

Discussion

30.	Question 7A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
Answer» Question 7 A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.

Discussion

31.	Express the set in tabular and set builder form Set of positive integers
Answer» Express the set in tabular and set builder form Set of positive integers

31.

Express the set in tabular and set builder form Set of positive integers

Answer»

Express the set in tabular and set builder form

Set of positive integers

Discussion

32.	If a + b = 1, and a, b > 0, then prove that (a + 1/a)^2 + (b + 1/b)^2 >_ 25/2
Answer» If a + b = 1, and a, b > 0, then prove that (a + 1/a)^2 + (b + 1/b)^2 >_ 25/2

Discussion

33.	9. Find the domain and range of f(x)=1-\|x-3\|.
Answer» 9. Find the domain and range of f(x)=1-\|x-3\|.

Discussion

34.	In ΔABC,∠A=30∘,∠B=40∘and ∠C=110∘In ΔPQR,∠P=30∘,∠Q=40∘and ∠R=110∘A student says that ΔABC≅ΔPQR by AAA congruence criterion. Is he justified? Why or why not?
Answer» In $Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}$ In $Δ P Q R, ∠ P = 30^{\circ}, ∠ Q = 40^{\circ} a n d ∠ R = 110^{\circ}$ A student says that $Δ A B C ≅ Δ P Q R$ by AAA congruence criterion. Is he justified? Why or why not?

Discussion

35.	A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find out the number of rows if 71 students were left out after the arrangement.
Answer» A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find out the number of rows if 71 students were left out after the arrangement.

Discussion

36.	a pirateship 560m from a fort defending a harbour entrance. a defence canon, located at sea level, fires a ball at initial speed 82ms^{-1} what is the maximum range of the cannon balls
Answer» a pirateship 560m from a fort defending a harbour entrance. a defence canon, located at sea level, fires a ball at initial speed 82ms^{-1} what is the maximum range of the cannon balls

Discussion

37.	Question 93 Solve the following question: Using distributive law, find the squares of a) 101 b) 72
Answer» Question 93 Solve the following question: Using distributive law, find the squares of a) 101 b) 72

37.

Question 93 Solve the following question: Using distributive law, find the squares of a) 101 b) 72

Answer»

Question 93

Solve the following question:

Using distributive law, find the squares of
a) 101
b) 72

Discussion

38.	In a company, the weighted average salary of the employees is $500. The average salary of 25 employees is $800, while the average salary of the remaining employees is $600. What is the total number of employees in the company?
Answer» In a company, the weighted average salary of the employees is $$ 500$ . The average salary of $25$ employees is $$ 800$ , while the average salary of the remaining employees is $$ 600$ . What is the total number of employees in the company?

Discussion

39.	In the figure, if AB = DC and ∠ABO = 35o. What is the value of ∠DCO?
Answer» In the figure, if AB = DC and ∠ABO = $35^{o}$ . What is the value of ∠DCO?

Discussion

40.	Find the sum of cube of -2 and cube of 5. [2 MARKS]
Answer» Find the sum of cube of -2 and cube of 5. [2 MARKS]

Discussion

41.	Fifteen workers take 8 hours to build a wall. How many hours will 12 workers need to build the same wall?
Answer» Fifteen workers take 8 hours to build a wall. How many hours will 12 workers need to build the same wall?

Discussion

42.	For what value of a and b, the algebraic expression a3 + b3 - 3ab(a + b) equals 37.
Answer» For what value of a and b, the algebraic expression a³+ b³ - 3ab(a + b) equals 37.

Discussion

43.	is analyser made of nicole prism set
Answer» is analyser made of nicole prism set

Discussion

44.	Formulas related to selling and cost price
Answer» Formulas related to selling and cost price

Discussion

45.	Find the next two terms of the sequence: 6,2,12,4,24,...
Answer» Find the next two terms of the sequence: $6, 2, 12, 4, 24, . . .$

Discussion

46.	40+3x-x² factorise the following
Answer» 40+3x-x² factorise the following

Discussion

47.	If you know that side of a square is 4cm, you also know:
Answer» If you know that side of a square is 4cm, you also know:

Discussion

48.	Question 50If a diagonal of a quadrilateral bisects both the angles, then it is aa) Kiteb) Parallelogramc) Rhombusd) Rectangle
Answer» Question 50 If a diagonal of a quadrilateral bisects both the angles, then it is a a) Kite b) Parallelogram c) Rhombus d) Rectangle

Discussion

49.	Factorise : ax+2bx+3cx−3a−6b−9c
Answer» Factorise : $a x + 2 b x + 3 c x - 3 a - 6 b - 9 c$

Discussion

50.	The number 98754256 is divisible by:
Answer» The number 98754256 is divisible by:

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let ABCD be a quadrilateral and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a parallelogram. (What extra result you need to prove this)?

Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.

The sum of three consecutive multiples of 8 is 888. Find the multiple.

Locus of the foot of perpendicular drawn from a fixed point (10,0) on the x axis to any †an gent to the circle x2+y2=16 i

In the given figure, if ∠OAB = 30∘ and ∠OCB = 57∘ , then ∠BOC = _______ and ∠AOC = _________ .

15.A sample of gas in a box is at pressure p^° and temp t^°. If number of molecules is doubled and KE of the gas is kept constant, then final temp and pressure will be

Question 41(iii)Write the X-coordinate (abscissa) of the given point.(0,5)

Subtract the second polynomial from the first. (i) 5x2-2y + 9 ; 3x2 + 5y -7 (ii) 2x2 + 3x + 5 ; x 2 -2x + 3

what is concentrTion gradient

Question 9 In which of the following expressions, prime factorization has been done: 24 = 2×3×4 56 = 7×2×2×2 70 = 2×5×7 54 = 2×3×9

43. In triangle ABC, angle BAC=90 degree and AB=BC.seg AP is perpendicular on side BC. B-P-C.D is any point on side BC. prove that 2AD2=BD2+CD2

The degree of the quotient when 6x3+3x is divided by 3x is ___

The following data set follows the equation y=10x. Use this information to find the missing entries A and B.

If x2+y2=14 and xy=3, then find the value of 2(x+y)2−5(x−y)2.

Aayan bought as many 25 paisa postal stamps as 50 paise stamps and paid Rs. 9 fir them. How many stamps of each denomination did he buy.

Question 8Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.Which colour received 15 of the votes?(a) Red(b) Blue(c) Green(d) Yellow

The area of the base of a cuboid is 45cm2. It is height is 6 cm. Find the volume

Ratio 6:7 is equivalent to:

42. An ellipse of eccentricity [{2×(root 2)}÷ 3] is inscribed in a circle and a point within the circle is chosen at random. The probability that this point lies outside the circle is____.

Find the speed of vehicles which cover:(a) A distance of 600 km in 8 hours.(b) A distance of 294 km in 7 hours.(c) A distance of 1368 m in 18 seconds.

36. Parallelogram PQRS, given that PQ =6.5cmPS=3.4cm and the altitude PT from P is 2.5cm .Draw the altitude from R and measure it

Multiply (x2+x+1) by (1−x).

75. If a triangle and a parallelogram on the same base and between the same parallels, then area of the triangleis equal to half that of the parallelogram

Suppose b is a positive integer such that is also an integer. What are the possible values of b?

A family went to a restaurant for dinner. The bill of ₹3000 was handed which was not inclusive of the 4% Goods and Service Tax (GST). The final bill amount would be?

Locate the points A (1, 2), B (4, 2) and C (1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D in order to complete the rectangle ABCD.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:1623512584810341228151176328596871412(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.

5. Factorise }a^4x^2-2a^3x+a^2

21 pirates collected 2720 gold coins yesterday. If they want to distribute the coins equally among themselves, how many coins will each pirate get?

Question 7A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.

Express the set in tabular and set builder form Set of positive integers

If a + b = 1, and a, b > 0, then prove that (a + 1/a)^2 + (b + 1/b)^2 >_ 25/2

9. Find the domain and range of f(x)=1-|x-3|.

In ΔABC,∠A=30∘,∠B=40∘and ∠C=110∘In ΔPQR,∠P=30∘,∠Q=40∘and ∠R=110∘A student says that ΔABC≅ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find out the number of rows if 71 students were left out after the arrangement.

a pirateship 560m from a fort defending a harbour entrance. a defence canon, located at sea level, fires a ball at initial speed 82ms^{-1} what is the maximum range of the cannon balls

Question 93 Solve the following question: Using distributive law, find the squares of a) 101 b) 72

In a company, the weighted average salary of the employees is $500. The average salary of 25 employees is $800, while the average salary of the remaining employees is $600. What is the total number of employees in the company?

In the figure, if AB = DC and ∠ABO = 35o. What is the value of ∠DCO?

Find the sum of cube of -2 and cube of 5. [2 MARKS]

Fifteen workers take 8 hours to build a wall. How many hours will 12 workers need to build the same wall?

For what value of a and b, the algebraic expression a3 + b3 - 3ab(a + b) equals 37.

is analyser made of nicole prism set

Formulas related to selling and cost price

Find the next two terms of the sequence: 6,2,12,4,24,...

40+3x-x² factorise the following

If you know that side of a square is 4cm, you also know:

Question 50If a diagonal of a quadrilateral bisects both the angles, then it is aa) Kiteb) Parallelogramc) Rhombusd) Rectangle

Factorise : ax+2bx+3cx−3a−6b−9c

The number 98754256 is divisible by:

In the given figure, if ∠OAB = 30∘ and ∠OCB = 57∘ , then ∠BOC = _ and ∠AOC = ___ .