32581 + Interview Questions in Mathematics

1.	period of cos[\|sinx\| - \|cosx\|]
Answer» period of cos[\|sinx\| - \|cosx\|]

Discussion

2.	Through the vertex A of paralle\log ram ABCD ,a line AEF is drawn to meet BC at E And DC produced at F.Show that triangle BEF and DCE are equal in are
Answer» Through the vertex A of paralle\log ram ABCD ,a line AEF is drawn to meet BC at E And DC produced at F.Show that triangle BEF and DCE are equal in are

Discussion

3.	given : M=[5−3−24] Find its transopose Matrix M ' If possible, find: (i) M + M ' (ii) M - M '
Answer» given : $M = [\begin{matrix} 5 & - 3 - 2 & 4 \end{matrix}]$ Find its transopose Matrix M ' If possible, find: (i) M + M ' (ii) M - M '

Discussion

4.	If one root is 6 times the other.Find the value of pxsquare-14x+8=0
Answer» If one root is 6 times the other.Find the value of pxsquare-14x+8=0

Discussion

5.	What is true dip angle and apparent dip angle formula in relation with cos theta?
Answer» What is true dip angle and apparent dip angle formula in relation with cos theta?

Discussion

6.	Refer to the following figure:∠BCA = ∠EFD. Find EF.
Answer» Refer to the following figure: ∠BCA = ∠EFD. Find EF.

6.

Refer to the following figure:∠BCA = ∠EFD. Find EF.

Answer»

Refer to the following figure:

∠BCA = ∠EFD. Find EF.

Discussion

7.	In a right triangle ABC, right angled at B, which of the following is true about the other two angles A and C?
Answer» In a right triangle ABC, right angled at B, which of the following is true about the other two angles A and C?

Discussion

8.	If √3 tanA = 3 sinA Then prove that:- sin2A – cos2A= 1/3
Answer» If √3 tanA = 3 sinA Then prove that:- sin²A – cos²A= 1/3

Discussion

9.	The set of value(s) of m for which vectors 2x^i−x^j−^k and −x^i+m^j+2^k makes obtuse angle for all values of x∈R, is
Answer» The set of value(s) of $m$ for which vectors $2 x^i - x^j -^k$ and $- x^i + m^j + 2^k$ makes obtuse angle for all values of $x \in R,$ is

Discussion

10.	Divide 29 into two parts so that the sum of the squares of the parts is 425.
Answer» Divide 29 into two parts so that the sum of the squares of the parts is 425.

Discussion

11.	The points A x1,y1 , Bx2,y2 , Cx3,y3 are the vertices of ∆ ABC .(i) The median from A meets BC at D . Find the coordinates of the point D.(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.(iii) Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.(iv) What are the coordinates of the centropid of the triangle ABC ?
Answer» The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})$ are the vertices of $∆$ ABC . (i) The median from A meets BC at D . Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1. (iii) Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1. (iv) What are the coordinates of the centropid of the triangle ABC ?

Discussion

12.	The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is
Answer» The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is

Discussion

13.	Draw a circle of radius 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q. [CBSE 2017]
Answer» Draw a circle of radius 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q. [CBSE 2017]

Discussion

14.	21. If the standard deviation of a variable X is sigma. Then the standard deviation of variable is (aX+b) /c is
Answer» 21. If the standard deviation of a variable X is sigma. Then the standard deviation of variable is (aX+b) /c is

Discussion

15.	The length of the shadow of a tower standing on level plane is found to be '2y' metres longers when the sun's altitude is 30∘ than when it is 60∘. The height of the tower is m
Answer» The length of the shadow of a tower standing on level plane is found to be '2y' metres longers when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$ . The height of the tower is m

Discussion

16.	Which of the following polynomials below is identical to the polynomial (x2−1)(x2−4)?
Answer» Which of the following polynomials below is identical to the polynomial $(x^{2} - 1) (x^{2} - 4)$ ?

Discussion

17.	The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of bucket is 5390 cm3, then find the value of r. [CBSE 2011]
Answer» The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of bucket is 5390 cm³, then find the value of r. [CBSE 2011]

Discussion

18.	Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and ∠A=75o.Find a point P (i) inside the triangle ABC; (ii) outside the triangle ABC; equidistant from B and C; and at a distance of 1.2 cm from BC.
Answer» Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and $∠ A = 75^{o}$ .Find a point P (i) inside the triangle ABC; (ii) outside the triangle ABC; equidistant from B and C; and at a distance of 1.2 cm from BC.

18.

Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and ∠A=75o.Find a point P (i) inside the triangle ABC; (ii) outside the triangle ABC; equidistant from B and C; and at a distance of 1.2 cm from BC.

Answer»

Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and $∠ A = 75^{o}$ .Find a point P

(i) inside the triangle ABC;

(ii) outside the triangle ABC;

equidistant from B and C; and at a distance of 1.2 cm from BC.

Discussion

19.	A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face and (iii) the queen of diamonds.
Answer» A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face and (iii) the queen of diamonds.

Discussion

20.	Find out the wrong number in the series given below :1,2,8,33,148,760,4626
Answer» Find out the wrong number in the series given below : $1, 2, 8, 33, 148, 760, 4626$

Discussion

21.	Question 8 (iii)The distance (in km) of 40 engineers from their residence to their place of work were found as follows.5310202511137123119101217181132171627978351215183121429615157612What is the empirical probability that an engineer lives: within 12 km from her place of work?
Answer» Question 8 (iii) The distance (in km) of 40 engineers from their residence to their place of work were found as follows. $\begin{matrix} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 & 31 19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 & 2 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 & 3 12 & 14 & 2 & 9 & 6 & 15 & 15 & 7 & 6 & 12 \end{matrix}$ What is the empirical probability that an engineer lives: within $\frac{1}{2}$ km from her place of work?

Discussion

22.	If the lengths of the three unequal edges of a rectangular solid block are in G.P., volume of the block is 216 cm3 and its total surface area is 252 cm2, then the length of the longest edge (in cm) is equal to
Answer» If the lengths of the three unequal edges of a rectangular solid block are in G.P., volume of the block is $216$ ${cm}^{3}$ and its total surface area is $252 {cm}^{2},$ then the length of the longest edge (in cm) is equal to

Discussion

23.	Find the points on the X-axis which are at a distance of 2√5 from the point (7, -4).
Answer» Find the points on the X-axis which are at a distance of $2 \sqrt{5}$ from the point (7, -4).

Discussion

24.	21. If each side of a cube is increased by 50%, thenthe surface area of the cube increases by (1) 50%(2) 100%(3) 125%(4) 150%
Answer» 21. If each side of a cube is increased by 50%, thenthe surface area of the cube increases by (1) 50%(2) 100%(3) 125%(4) 150%

Discussion

25.	A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin(i) Will be a 50 p coin?(ii) Will not be a Rs.5 coin?
Answer» A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) Will be a 50 p coin? (ii) Will not be a Rs.5 coin?

25.

A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin(i) Will be a 50 p coin?(ii) Will not be a Rs.5 coin?

Answer»

A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) Will be a 50 p coin?

(ii) Will not be a Rs.5 coin?

Discussion

26.	In △ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of cos R is .
Answer» In $△$ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of cos R is .

Discussion

27.	IN AN EQUILATERAL TRIANGLE, PROVE THAT THE CENTRROID AND THE CIRCUMCENTER OF A TRIANGLE COINCIDES.
Answer» IN AN EQUILATERAL TRIANGLE, PROVE THAT THE CENTRROID AND THE CIRCUMCENTER OF A TRIANGLE COINCIDES.

Discussion

28.	In Fig.2, PQ and PR are two tangents to a circle with centre O. If ∠QPR=46∘, then ∠QOR equals :
Answer» In Fig.2, PQ and PR are two tangents to a circle with centre O. If $∠ Q P R = 46^{\circ}$ , then $∠ Q O R$ equals :

Discussion

29.	Determine the line containing the point (2,3)
Answer» Determine the line containing the point (2,3)

Discussion

30.	If a, b, c, d, e, f are in AP, then (d -b) is equal to
Answer» If a, b, c, d, e, f are in AP, then (d -b) is equal to

Discussion

31.	A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of ∆PQR is 336 cm2, find the sides PQ and PR. [CBSE 2014]
Answer» A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of ∆PQR is 336 cm², find the sides PQ and PR. [CBSE 2014]

Discussion

32.	a two digit number is such that the product of its digits is 20. if 9 is added to the number the digits interchange their places?find the number
Answer» a two digit number is such that the product of its digits is 20. if 9 is added to the number the digits interchange their places?find the number

Discussion

33.	What is the maximum value of the sum of the AP 50, 48, 46, 44, ... ? [2 MARKS]
Answer» What is the maximum value of the sum of the AP 50, 48, 46, 44, ... ? [2 MARKS]

Discussion

34.	A company with 10000 shares of ₹ 100 each, declares an annual dividend of 5 % (i) What is the total amount of dividend paid by the company(ii) What would be the annual income of a man, who has 72 shares , in the company(iii) If he received only 4 % on his investment , find the price he paid for each share
Answer» A company with 10000 shares of ₹ 100 each, declares an annual dividend of 5 % (i) What is the total amount of dividend paid by the company (ii) What would be the annual income of a man, who has 72 shares , in the company (iii) If he received only 4 % on his investment , find the price he paid for each share

34.

A company with 10000 shares of ₹ 100 each, declares an annual dividend of 5 % (i) What is the total amount of dividend paid by the company(ii) What would be the annual income of a man, who has 72 shares , in the company(iii) If he received only 4 % on his investment , find the price he paid for each share

Answer»

A company with 10000 shares of ₹ 100 each, declares an annual dividend of 5 %

(i) What is the total amount of dividend paid by the company

(ii) What would be the annual income of a man, who has 72 shares , in the company

(iii) If he received only 4 % on his investment , find the price he paid for each share

Discussion

35.	A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
Answer» A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Discussion

36.	In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?
Answer» In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

Discussion

37.	Question 4 A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π=3.14)
Answer» Question 4 A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. $(U s e π = 3.14)$

Discussion

38.	a^(1/a)=b^(1/b)=c^(1/c)anda^(bc)+b^(ca)+c^(ab)=729 then find value of b^(1/b)
Answer» a^(1/a)=b^(1/b)=c^(1/c)anda^(bc)+b^(ca)+c^(ab)=729 then find value of b^(1/b)

Discussion

39.	write down the values of (X'+X) and (X\ast X') in boolean alge bra
Answer» write down the values of (X'+X) and (X\ast X') in boolean alge bra

Discussion

40.	For what integer value/s of m, the quadratic equation x2−mx+5m=0 has real and distinct roots.
Answer» For what integer value/s of m, the quadratic equation $x^{2} - m x + 5 m = 0$ has real and distinct roots.

Discussion

41.	Value of cosec 110 and way to find it in terms of sec
Answer» Value of cosec 110 and way to find it in terms of sec

Discussion

42.	If sinθ=12, then write the value of 3cot2θ+3. CBSE 2009
Answer» $If \sin θ = \frac{1}{2}, then write the value of (3 \cot^{2} θ + 3) . [CBSE 2009]$

Discussion

43.	A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then find the algebra for the distance from the starting point to the ball after 't' seconds.
Answer» A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then find the algebra for the distance from the starting point to the ball after 't' seconds.

Discussion

44.	Question 15O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with ABIIDC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.
Answer» Question 15 O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with ABIIDC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.

Discussion

45.	A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.
Answer» A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

Discussion

46.

Pass entries in the books of Mr. Roopani of Gujarat assuming CGST 9% and SGST9%. (i) Purchased goods for ₹ 2,00,000 from Suryakant of Jaipur (Rajasthan) on Credit. (ii) Sold goods for ₹ 1,50,000 to Mr. Pawar of Mumbai (Maharashtra) and the cheque received was sent to bank. (iii) Sold goods for ₹ 2,50,000 within the state on credit. (iv) Paid insurance premium of 20,000 by cheque. (v) Purchased furniture for office for ₹ 60,000 by cheque.

Answer» Pass entries in the books of Mr. Roopani of Gujarat assuming CGST 9% and SGST9%.

(i)	Purchased goods for ₹ 2,00,000 from Suryakant of Jaipur (Rajasthan) on Credit.
(ii)	Sold goods for ₹ 1,50,000 to Mr. Pawar of Mumbai (Maharashtra) and the cheque received was sent to bank.
(iii)	Sold goods for ₹ 2,50,000 within the state on credit.
(iv)	Paid insurance premium of 20,000 by cheque.
(v)	Purchased furniture for office for ₹ 60,000 by cheque.

Discussion

47.	A man buys 20 shares (per value rs.10) of a company which pays 9%dividend at such a price that he gets 12% on his money. Find the market value of each share. Plz solve it using the formulas of shares and dividends and not by unitary method so that I can understand 🙏🙏🙏
Answer» A man buys 20 shares (per value rs.10) of a company which pays 9%dividend at such a price that he gets 12% on his money. Find the market value of each share. Plz solve it using the formulas of shares and dividends and not by unitary method so that I can understand 🙏🙏🙏

Discussion

48.	If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c. [CBSE 2014]
Answer» If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c. [CBSE 2014]

Discussion

49.

Calculate mode from the following data: Marks (more than) 0-9 10-19 20-29 30-39 40-49 50-59 No of students 2 5 15 25 10 3

Answer» Calculate mode from the following data:

Marks (more than)	0-9	10-19	20-29	30-39	40-49	50-59
No of students	2	5	15	25	10	3

Discussion

50.

Question 138 Fill in the blank to make the statement true. The number of factors of a prime number is...........

Answer»

Question 138

Fill in the blank to make the statement true.

The number of factors of a prime number is...........

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

period of cos[|sinx| - |cosx|]

Through the vertex A of paralle\log ram ABCD ,a line AEF is drawn to meet BC at E And DC produced at F.Show that triangle BEF and DCE are equal in are

given : M=[5−3−24] Find its transopose Matrix M ' If possible, find: (i) M + M ' (ii) M - M '

If one root is 6 times the other.Find the value of pxsquare-14x+8=0

What is true dip angle and apparent dip angle formula in relation with cos theta?

Refer to the following figure:∠BCA = ∠EFD. Find EF.

In a right triangle ABC, right angled at B, which of the following is true about the other two angles A and C?

If √3 tanA = 3 sinA Then prove that:- sin2A – cos2A= 1/3

The set of value(s) of m for which vectors 2x^i−x^j−^k and −x^i+m^j+2^k makes obtuse angle for all values of x∈R, is

Divide 29 into two parts so that the sum of the squares of the parts is 425.

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is

Draw a circle of radius 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q. [CBSE 2017]

21. If the standard deviation of a variable X is sigma. Then the standard deviation of variable is (aX+b) /c is

The length of the shadow of a tower standing on level plane is found to be '2y' metres longers when the sun's altitude is 30∘ than when it is 60∘. The height of the tower is m

Which of the following polynomials below is identical to the polynomial (x2−1)(x2−4)?

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of bucket is 5390 cm3, then find the value of r. [CBSE 2011]

Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and ∠A=75o.Find a point P (i) inside the triangle ABC; (ii) outside the triangle ABC; equidistant from B and C; and at a distance of 1.2 cm from BC.

A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face and (iii) the queen of diamonds.

Find out the wrong number in the series given below :1,2,8,33,148,760,4626

Question 8 (iii)The distance (in km) of 40 engineers from their residence to their place of work were found as follows.5310202511137123119101217181132171627978351215183121429615157612What is the empirical probability that an engineer lives: within 12 km from her place of work?

If the lengths of the three unequal edges of a rectangular solid block are in G.P., volume of the block is 216 cm3 and its total surface area is 252 cm2, then the length of the longest edge (in cm) is equal to

Find the points on the X-axis which are at a distance of 2√5 from the point (7, -4).

21. If each side of a cube is increased by 50%, thenthe surface area of the cube increases by (1) 50%(2) 100%(3) 125%(4) 150%

A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin(i) Will be a 50 p coin?(ii) Will not be a Rs.5 coin?

In △ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of cos R is .

IN AN EQUILATERAL TRIANGLE, PROVE THAT THE CENTRROID AND THE CIRCUMCENTER OF A TRIANGLE COINCIDES.

In Fig.2, PQ and PR are two tangents to a circle with centre O. If ∠QPR=46∘, then ∠QOR equals :

Determine the line containing the point (2,3)

If a, b, c, d, e, f are in AP, then (d -b) is equal to

A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of ∆PQR is 336 cm2, find the sides PQ and PR. [CBSE 2014]

a two digit number is such that the product of its digits is 20. if 9 is added to the number the digits interchange their places?find the number

What is the maximum value of the sum of the AP 50, 48, 46, 44, ... ? [2 MARKS]

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

Question 4 A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π=3.14)

a^(1/a)=b^(1/b)=c^(1/c)anda^(bc)+b^(ca)+c^(ab)=729 then find value of b^(1/b)

write down the values of (X'+X) and (X\ast X') in boolean alge bra

For what integer value/s of m, the quadratic equation x2−mx+5m=0 has real and distinct roots.

Value of cosec 110 and way to find it in terms of sec

If sinθ=12, then write the value of 3cot2θ+3. CBSE 2009

A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then find the algebra for the distance from the starting point to the ball after 't' seconds.

Question 15O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with ABIIDC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

A man buys 20 shares (per value rs.10) of a company which pays 9%dividend at such a price that he gets 12% on his money. Find the market value of each share. Plz solve it using the formulas of shares and dividends and not by unitary method so that I can understand 🙏🙏🙏

If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c. [CBSE 2014]

Calculate mode from the following data: Marks (more than) 0-9 10-19 20-29 30-39 40-49 50-59 No of students 2 5 15 25 10 3

Question 138 Fill in the blank to make the statement true. The number of factors of a prime number is...........