24740 + Interview Questions in Mathematics

1.	Question 4 Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle. TriangleGiven measurements4.Δ LMNm∠L=60∘m∠N=120∘LM=5cm
Answer» Question 4 Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle. $\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 4. & Δ L M N & m ∠ L = 60^{\circ} & m ∠ N = 120^{\circ} & L M = 5 c m \end{matrix}$

Discussion

2.	Find the value of (x-a)3 + (x-b)3 + (x-c)3 - 3(x-a)(x-b)(x-c) If a + b + c = 3x
Answer» Find the value of (x-a)³ + (x-b)³+ (x-c)³ - 3(x-a)(x-b)(x-c) If a + b + c = 3x

2.

Find the value of (x-a)3 + (x-b)3 + (x-c)3 - 3(x-a)(x-b)(x-c) If a + b + c = 3x

Answer»

Find the value of

(x-a)³ + (x-b)³+ (x-c)³ - 3(x-a)(x-b)(x-c)

If a + b + c = 3x

Discussion

3.	For 2 sets A and B, which of the following is/are true always?
Answer» For 2 sets A and B, which of the following is/are true always?

Discussion

4.	The polynomials (2x3+x2−ax+2) and (2x3−3x2−3x+a) when divided by (x -2) leave the same remainder. Find the value of a.
Answer» The polynomials $(2 x^{3} + x^{2} - a x + 2)$ and $(2 x^{3} - 3 x^{2} - 3 x + a)$ when divided by (x -2) leave the same remainder. Find the value of a.

Discussion

5.	What special name can be given to a quadrilateral whose all angles are equal?
Answer» What special name can be given to a quadrilateral whose all angles are equal?

Discussion

6.	In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60∘,calculate ∠CDE.
Answer» In the adjoining figure, $D E$ is a chord parallel to diameter $A C$ of the circle with centre $O$ . If $∠ C B D = 60^{\circ}$ ,calculate $∠ C D E .$

6.

In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60∘,calculate ∠CDE.

Answer»

In the adjoining figure, $D E$ is a chord parallel to diameter $A C$ of the circle with centre $O$ . If $∠ C B D = 60^{\circ}$ ,calculate $∠ C D E .$

Discussion

7.	If the length of a diagonal of a cube is 8√3 cm, then its surface area is
Answer» If the length of a diagonal of a cube is $8 \sqrt{3} c m,$ then its surface area is

Discussion

8.	In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55∘ and ∠BAC=45∘, find ∠BCD.
Answer» In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $∠ D B C = 55^{\circ} a n d ∠ B A C = 45^{\circ},$ find $∠ B C D$ .

8.

In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55∘ and ∠BAC=45∘, find ∠BCD.

Answer»

In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $∠ D B C = 55^{\circ} a n d ∠ B A C = 45^{\circ},$ find $∠ B C D$ .

Discussion

9.	If three sides of a triangle are a , √3 a and √2 a, then the measure of the angle opposite to the longest side is:
Answer» If three sides of a triangle are a , $\sqrt{3}$ a and $\sqrt{2}$ a, then the measure of the angle opposite to the longest side is:

Discussion

10.	In the figure, two congruent circles with centre O and O' intersect at A and B. If ∠AO′B=50o, then find ∠APB.
Answer» In the figure, two congruent circles with centre O and O' intersect at A and B. If ∠AO′B=50o, then find ∠APB.

10.

In the figure, two congruent circles with centre O and O' intersect at A and B. If ∠AO′B=50o, then find ∠APB.

Answer»

In the figure, two congruent circles with centre O and O' intersect at A and B. If ∠AO′B=50o, then find ∠APB.

Discussion

11.	Find the mode of the following data. Class/space interval0−100100−200200−300300−400400−500Frequency7111598 ___
Answer» Find the mode of the following data. $\begin{matrix} Class/space interval & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 Frequency & 7 & 11 & 15 & 9 & 8 \end{matrix}$ ___

11.

Find the mode of the following data. Class/space interval0−100100−200200−300300−400400−500Frequency7111598 ___

Answer»

Find the mode of the following data.

$\begin{matrix} Class/space interval & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 Frequency & 7 & 11 & 15 & 9 & 8 \end{matrix}$

___

Discussion

12.	If the probability of winning a game is 0.3, what is the probability of losing it ?
Answer» If the probability of winning a game is 0.3, what is the probability of losing it ?

Discussion

13.	What is 34743−5?
Answer» What is $\frac{{\frac{3}{4}}^{7}}{{\frac{4}{3}}^{- 5}}$ ?

Discussion

14.	Where does the point (–2, 0) lie?
Answer» Where does the point (–2, 0) lie?

Discussion

15.	The radius and height of a cylinder are in the ratio 5:7 and it's volume is 550 cm3. Find its radius.
Answer» The radius and height of a cylinder are in the ratio $5 : 7$ and it's volume is $550 c m^{3} .$ Find its radius.

Discussion

16.	If the points (0,1) and (1,0) lie on the graph of the equation y=mx+c, then find the values of m and c.
Answer» If the points (0,1) and (1,0) lie on the graph of the equation y=mx+c, then find the values of m and c.

Discussion

17.	If ab = cd , then which of the following is true
Answer» If $\frac{a}{b}$ = $\frac{c}{d}$ , then which of the following is true

17.

If ab = cd , then which of the following is true

Answer»

If $\frac{a}{b}$ = $\frac{c}{d}$ , then which of the following is true

Discussion

18.	What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?
Answer» What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

Discussion

19.	Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.
Answer» Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of $R s 30 p e r m^{3}$ .

Discussion

20.	In a survey, out of 200 students, it is observed that 125 students like mathematics. What is the probability of the students who do not like mathematics?
Answer» In a survey, out of 200 students, it is observed that 125 students like mathematics. What is the probability of the students who do not like mathematics?

Discussion

21.	The greatest coefficent in the expansion of (1−x)20 is
Answer» The greatest coefficent in the expansion of $(1 - x)^{20}$ is

Discussion

22.	The mean of 15 observations is 14. If the mean of first 7 observations is 12 and that of last 7 observations is 16, find the middle term.
Answer» The mean of 15 observations is 14. If the mean of first 7 observations is 12 and that of last 7 observations is 16, find the middle term.

Discussion

23.	Solve for y : log9y = 3
Answer» Solve for y : log₉y = 3

Discussion

24.	Question 6 Refer to Q.5. Draw the less than type and more than type ogive for the data and use them to find the median weight.
Answer» Question 6 Refer to Q.5. Draw the less than type and more than type ogive for the data and use them to find the median weight.

Discussion

25.	ABCD is rhombus with ∠ABC = 30°. The measure of ∠ACD is:
Answer» ABCD is rhombus with ∠ABC = 30°. The measure of ∠ACD is:

Discussion

26.	Find the measure (in degrees) of the exterior angle of a regular octagon.45
Answer» Find the measure (in degrees) of the exterior angle of a regular octagon. 45

Discussion

27.	Question 1 (ii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?
Answer» Question 1 (ii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?

Discussion

28.	If log10 3=0.477, then the value of log10340 is approximately:
Answer» If $l o g_{10} 3 = 0.477$ , then the value of $l o g_{10} 3^{40}$ is approximately:

Discussion

29.	Question 12 Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class Height(in cm)FrequencyCumulative frequency150−15512a155−160b25160−16510c165−170d43170−175e48175−1802fTotal50
Answer» Question 12 Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class $\begin{matrix} H e i g h t (i n c m) & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 150 - 155 & 12 & a 155 - 160 & b & 25 160 - 165 & 10 & c 165 - 170 & d & 43 170 - 175 & e & 48 175 - 180 & 2 & f T o t a l & 50 \end{matrix}$

Discussion

30.	The co-ordinates of the point on x-axis which is equidistant from the points A(5, 4) and B(– 2, 3) is:
Answer» The co-ordinates of the point on x-axis which is equidistant from the points A(5, 4) and B(– 2, 3) is:

Discussion

31.	In a circle of radius 5 cm, AB and AC are two chords such that AB=AC=6 cm. Find the length of the chord BC.
Answer» In a circle of radius 5 cm, $A B$ and $A C$ are two chords such that $A B = A C = 6 c m .$ Find the length of the chord $B C$ .

31.

In a circle of radius 5 cm, AB and AC are two chords such that AB=AC=6 cm. Find the length of the chord BC.

Answer»

In a circle of radius 5 cm, $A B$ and $A C$ are two chords such that $A B = A C = 6 c m .$ Find the length of the chord $B C$ .

Discussion

32.	Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?
Answer» Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

Discussion

33.	If twice the age of the daughter is added to age of her mother, the result is 56. But if twice the age of the mother is added to the age of the daughter, the result is 82. What is the present age of the mother and her daughter?
Answer» If twice the age of the daughter is added to age of her mother, the result is 56. But if twice the age of the mother is added to the age of the daughter, the result is 82. What is the present age of the mother and her daughter?

Discussion

34.	If a + 2b is equal to 5 then show that a raise to power 3 + 8b to the power 3 + 30ab is equal to 125
Answer» If a + 2b is equal to 5 then show that a raise to power 3 + 8b to the power 3 + 30ab is equal to 125

Discussion

35.	Statement1: cosec2A - cot2A = 1 Statement2: 1 + tan2A = sec2A
Answer» Statement1: $c o s e c^{2} A$ - $c o t^{2} A$ = 1 Statement2: 1 + $t a n^{2} A$ = $s e c^{2} A$

35.

Statement1: cosec2A - cot2A = 1 Statement2: 1 + tan2A = sec2A

Answer»

Statement1: $c o s e c^{2} A$ - $c o t^{2} A$ = 1

Statement2: 1 + $t a n^{2} A$ = $s e c^{2} A$

Discussion

36.	The area of a rectangle is 96 cm2 and its length is 12 cm. The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.
Answer» The area of a rectangle is $96 c m^{2}$ and its length is $12 c m$ . The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.

Discussion

37.	A discount of 15% on one article is the same as a discount of 20% on another article. Find the ratio of the cost price of the two articles.
Answer» A discount of $15 %$ on one article is the same as a discount of $20 %$ on another article. Find the ratio of the cost price of the two articles.

Discussion

38.	A quadrilateral ABCD is drawn in which the mid- points of sides AB, BC, CD, and AD are P, Q, R and S respectively. If quadrilateral ABCD is a parallelogram, what can you say about quadrilateral PQRS?
Answer» A quadrilateral ABCD is drawn in which the mid- points of sides AB, BC, CD, and AD are P, Q, R and S respectively. If quadrilateral ABCD is a parallelogram, what can you say about quadrilateral PQRS?

Discussion

39.	The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.
Answer» The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$ . Find the fraction.

Discussion

40.	Simplify: (3pq+3qr)2−18pq2r.
Answer» Simplify: ${(3 p q + 3 q r)}^{2} - 18 p q^{2} r$ .

Discussion

41.	___ is the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.
Answer» ___ is the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.

Discussion

42.	AE \|\| BC and D is the midpoint of BC. If area △ABC = 84 square cm, what is the area of △BDE?
Answer» AE \|\| BC and D is the midpoint of BC. If area $△ A B C$ = 84 square cm, what is the area of $△ B D E$ ?

42.

AE || BC and D is the midpoint of BC. If area △ABC = 84 square cm, what is the area of △BDE?

Answer»

AE || BC and D is the midpoint of BC. If area $△ A B C$ = 84 square cm, what is the area of $△ B D E$ ?

Discussion

43.	Respected sir /madam I just wanted to ask that can I please ask the doubts of the concept of logarithm?? I am very much interested in the subject and have recently solved some questions.i have doubt in Se of them. Sir/madam it would be very good if you answer those questions. Please answer them Thankyou very much
Answer» Respected sir /madam I just wanted to ask that can I please ask the doubts of the concept of logarithm?? I am very much interested in the subject and have recently solved some questions.i have doubt in Se of them. Sir/madam it would be very good if you answer those questions. Please answer them Thankyou very much

43.

Respected sir /madam I just wanted to ask that can I please ask the doubts of the concept of logarithm?? I am very much interested in the subject and have recently solved some questions.i have doubt in Se of them. Sir/madam it would be very good if you answer those questions. Please answer them Thankyou very much

Answer»

Respected sir /madam

I just wanted to ask that can I please ask the doubts of the concept of logarithm??

I am very much interested in the subject and have recently solved some questions.i have doubt in Se of them.

Sir/madam it would be very good if you answer those questions.

Please answer them

Thankyou very much

Discussion

44.	If 2352=2p×3q×7r, frind the values of p,q and r
Answer» If $2352 = 2^{p} \times 3^{q} \times 7^{r}$ , frind the values of $p, q a n d r$

Discussion

45.	(5a+2/3)² - (2a-1/3)²
Answer» (5a+2/3)² - (2a-1/3)²

Discussion

46.	Factories: x3+1/x3-2
Answer» Factories: x³+1/x³-2

Discussion

47.	A sum of Rs 100 is compounded annually at the rate of 10% for two years. The equivalent rate of simple interest to earn the same interest is
Answer» A sum of Rs 100 is compounded annually at the rate of 10% for two years. The equivalent rate of simple interest to earn the same interest is

Discussion

48.	Calculate the surface area of a sphere who's volume is 485cm
Answer» Calculate the surface area of a sphere who's volume is 485cm

Discussion

49.	Half the perimeter of a rectangular garden, whose length is 4 m more than it's breadth, is 16 m, then the dimensions of the garden are .
Answer» Half the perimeter of a rectangular garden, whose length is 4 m more than it's breadth, is 16 m, then the dimensions of the garden are .

Discussion

50.	Question 7 (i) To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table. OpinionNumber of studentslike135dislike65 Find the probability that a student chosen at random (i) likes statistics
Answer» Question 7 (i) To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table. $\begin{matrix} O p i n i o n & N u m b e r o f s t u d e n t s l i k e & 135 d i s l i k e & 65 \end{matrix}$ Find the probability that a student chosen at random (i) likes statistics

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 4 Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle. TriangleGiven measurements4.Δ LMNm∠L=60∘m∠N=120∘LM=5cm

Find the value of (x-a)3 + (x-b)3 + (x-c)3 - 3(x-a)(x-b)(x-c) If a + b + c = 3x

For 2 sets A and B, which of the following is/are true always?

The polynomials (2x3+x2−ax+2) and (2x3−3x2−3x+a) when divided by (x -2) leave the same remainder. Find the value of a.

What special name can be given to a quadrilateral whose all angles are equal?

In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60∘,calculate ∠CDE.

If the length of a diagonal of a cube is 8√3 cm, then its surface area is

In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55∘ and ∠BAC=45∘, find ∠BCD.

If three sides of a triangle are a , √3 a and √2 a, then the measure of the angle opposite to the longest side is:

In the figure, two congruent circles with centre O and O' intersect at A and B. If ∠AO′B=50o, then find ∠APB.

Find the mode of the following data. Class/space interval0−100100−200200−300300−400400−500Frequency7111598 ___

If the probability of winning a game is 0.3, what is the probability of losing it ?

What is 34743−5?

Where does the point (–2, 0) lie?

The radius and height of a cylinder are in the ratio 5:7 and it's volume is 550 cm3. Find its radius.

If the points (0,1) and (1,0) lie on the graph of the equation y=mx+c, then find the values of m and c.

If ab = cd , then which of the following is true

What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

In a survey, out of 200 students, it is observed that 125 students like mathematics. What is the probability of the students who do not like mathematics?

The greatest coefficent in the expansion of (1−x)20 is

The mean of 15 observations is 14. If the mean of first 7 observations is 12 and that of last 7 observations is 16, find the middle term.

Solve for y : log9y = 3

Question 6 Refer to Q.5. Draw the less than type and more than type ogive for the data and use them to find the median weight.

ABCD is rhombus with ∠ABC = 30°. The measure of ∠ACD is:

Find the measure (in degrees) of the exterior angle of a regular octagon.45

Question 1 (ii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?

If log10 3=0.477, then the value of log10340 is approximately:

Question 12 Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class Height(in cm)FrequencyCumulative frequency150−15512a155−160b25160−16510c165−170d43170−175e48175−1802fTotal50

The co-ordinates of the point on x-axis which is equidistant from the points A(5, 4) and B(– 2, 3) is:

In a circle of radius 5 cm, AB and AC are two chords such that AB=AC=6 cm. Find the length of the chord BC.

Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

If twice the age of the daughter is added to age of her mother, the result is 56. But if twice the age of the mother is added to the age of the daughter, the result is 82. What is the present age of the mother and her daughter?

If a + 2b is equal to 5 then show that a raise to power 3 + 8b to the power 3 + 30ab is equal to 125

Statement1: cosec2A - cot2A = 1 Statement2: 1 + tan2A = sec2A

The area of a rectangle is 96 cm2 and its length is 12 cm. The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.

A discount of 15% on one article is the same as a discount of 20% on another article. Find the ratio of the cost price of the two articles.

A quadrilateral ABCD is drawn in which the mid- points of sides AB, BC, CD, and AD are P, Q, R and S respectively. If quadrilateral ABCD is a parallelogram, what can you say about quadrilateral PQRS?

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.​

Simplify: (3pq+3qr)2−18pq2r.

___ is the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.

AE || BC and D is the midpoint of BC. If area △ABC = 84 square cm, what is the area of △BDE?

If 2352=2p×3q×7r, frind the values of p,q and r

(5a+2/3)² - (2a-1/3)²

Factories: x​​​​​​3+1/x​​​​​​3​​​​​-2

A sum of Rs 100 is compounded annually at the rate of 10% for two years. The equivalent rate of simple interest to earn the same interest is

Calculate the surface area of a sphere who's volume is 485cm

Half the perimeter of a rectangular garden, whose length is 4 m more than it's breadth, is 16 m, then the dimensions of the garden are .

Question 7 (i) To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table. OpinionNumber of studentslike135dislike65 Find the probability that a student chosen at random (i) likes statistics

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.

Factories: x3+1/x3-2