24740 + Interview Questions in Mathematics Page 31 InterviewSolution

1501.	Q. The height of a right circular cylinder is 6 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface . Find the radius of its base.
Answer» Q. The height of a right circular cylinder is 6 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface . Find the radius of its base.

Discussion

1502.	The sum of the incomes of Ramyani, Mac, and Ankit is ₹12,24,000. The percentage of their expenses are 80%, 85%, and 90%, respectively.If the ratio of their savings is 3:7:8 which is same as the ratio of their respective incomes, then find the annual saving of Mac and Ankit combined.
Answer» The sum of the incomes of Ramyani, Mac, and Ankit is ₹12,24,000. The percentage of their expenses are 80%, 85%, and 90%, respectively. If the ratio of their savings is 3:7:8 which is same as the ratio of their respective incomes, then find the annual saving of Mac and Ankit combined.

Discussion

1503.	If the vomume and the surface area of a sphere are numerically the same then its radius is(a) 1 unit (b) 2 units (c) 3 units (d) 4 units
Answer» $If the vomume and the surface area of a sphere are numerically the same then its radius is (a) 1 u n i t (b) 2 u n i t s (c) 3 u n i t s (d) 4 u n i t s$

Discussion

1504.	Write the converse theorem of angles opposite to equal sides of an equilateral triangle are equal.
Answer» Write the converse theorem of angles opposite to equal sides of an equilateral triangle are equal.

Discussion

1505.	Correct the following errors in Hari’s Books:(i) Credit sale of ₹ 132 to R. Krishan correctly entered in Sales Journal but posted to his account as ₹ 312.(ii) The total of the credit side of Ramesh’s Account was overcasted by ₹ 2,000.(iii) Total of the Purchases Journal of ₹ 5,250 has been posted to Purchases Account as ₹ 5,205.(iv) Printer purchased from R. Ltd. for ₹ 4,000 on credit was entered in the Purchases Book.(v) An item of ₹ 2,000 entered in the Sales Return Book was posted to the debit of Pandey who had returned the goods.
Answer» Correct the following errors in Hari’s Books: (i) Credit sale of ₹ 132 to R. Krishan correctly entered in Sales Journal but posted to his account as ₹ 312. (ii) The total of the credit side of Ramesh’s Account was overcasted by ₹ 2,000. (iii) Total of the Purchases Journal of ₹ 5,250 has been posted to Purchases Account as ₹ 5,205. (iv) Printer purchased from R. Ltd. for ₹ 4,000 on credit was entered in the Purchases Book. (v) An item of ₹ 2,000 entered in the Sales Return Book was posted to the debit of Pandey who had returned the goods.

Discussion

1506.	solve for x and y (a-b)x+(a+b)y=a2-2ab-b2 (a+b)(x+y)a2+b2
Answer» solve for x and y (a-b)x+(a+b)y=a2-2ab-b2 (a+b)(x+y)a2+b2

Discussion

1507.	ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =(a) 32AB(b) 2 AB(c) 3 AB(d) 54AB
Answer» ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF = (a) $\frac{3}{2} A B$ (b) 2 AB (c) 3 AB (d) $\frac{5}{4} A B$

Discussion

1508.	Prove that the sum of all interior angles of a triangle is 180°.
Answer» Prove that the sum of all interior angles of a triangle is 180°.

Discussion

1509.

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table. Weight (in kg) No. of students Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 Below 65 Below 70 0 24 78 183 294 408 543 621 674 685

Answer» Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Weight (in kg)	No. of students
Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 Below 65 Below 70	0 24 78 183 294 408 543 621 674 685

Discussion

1510.	If x2+1x2=79, find the value of x+1x
Answer» If $x^{2} + \frac{1}{x^{2}} = 79$ , find the value of $x + \frac{1}{x}$

Discussion

1511.	A normal at any point (x,y) to the curve y=f(x) cuts a triangle of unit area with the co-ordinate axes, then the differential equation of the curve is:
Answer» A normal at any point $(x, y)$ to the curve $y = f (x)$ cuts a triangle of unit area with the co-ordinate axes, then the differential equation of the curve is:

Discussion

1512.	If a=4^i+6^j and b=3^j+4^k, then the vector form of the component of a along b is
Answer» If $a = 4^i + 6^j$ and $b = 3^j + 4^k$ , then the vector form of the component of a along b is

Discussion

1513.	Question 11 Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.
Answer» Question 11 Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.

Discussion

1514.	Let m be the mid-point and u be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is __________.
Answer» Let m be the mid-point and u be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is __________.

Discussion

1515.	The distance between Anshul's office and his house is 5.5 km. One day he went walking to office. While coming back, he walked for 2km and then took a cab. Find the total distance walked by Anshul in meters. [4 MARKS]
Answer» The distance between Anshul's office and his house is 5.5 km. One day he went walking to office. While coming back, he walked for 2km and then took a cab. Find the total distance walked by Anshul in meters. [4 MARKS]

Discussion

1516.	32. A square ABCD has each side 10 cm and two quadrant each of radius equal to side of square is inscribed in it such that some part overlap(shaded region). Find The area of shaded region (a) 2268 (b) 2520 (c) 2975 (d) 1560
Answer» 32. A square ABCD has each side 10 cm and two quadrant each of radius equal to side of square is inscribed in it such that some part overlap(shaded region). Find The area of shaded region (a) 2268 (b) 2520 (c) 2975 (d) 1560

Discussion

1517.	In a marathon of 5 km, Manish could run for 2 km. If Kushagra ran for 12 of the total length of the marathon, who covered more distance?
Answer» In a marathon of 5 km, Manish could run for 2 km. If Kushagra ran for $\frac{1}{2}$ of the total length of the marathon, who covered more distance?

Discussion

1518.	If the difference of two complementry angles is 40 degrees then find the angles.
Answer» If the difference of two complementry angles is 40 degrees then find the angles.

Discussion

1519.	What is Range?
Answer» What is Range?

Discussion

1520.	Explain the procedure of selecting a random sample of 3 students out of 10 in your class, by using random number tables.
Answer» Explain the procedure of selecting a random sample of 3 students out of 10 in your class, by using random number tables.

Discussion

1521.	In two triangles, two angles and one side of the first triangle are equal to the two angles and one side of the second triangle. Will these two triangles always be congruent?[3 MARKS]
Answer» In two triangles, two angles and one side of the first triangle are equal to the two angles and one side of the second triangle. Will these two triangles always be congruent?[3 MARKS]

Discussion

1522.	Evaluate the following:(ama−n)m−n×(ana−l)n−l×(ala−m)l−m
Answer» Evaluate the following: $(\frac{a^{m}}{a^{- n}})^{m - n} \times (\frac{a^{n}}{a^{- l}})^{n - l} \times (\frac{a^{l}}{a^{- m}})^{l - m}$

1522.

Evaluate the following:(ama−n)m−n×(ana−l)n−l×(ala−m)l−m

Answer»

Evaluate the following:

$(\frac{a^{m}}{a^{- n}})^{m - n} \times (\frac{a^{n}}{a^{- l}})^{n - l} \times (\frac{a^{l}}{a^{- m}})^{l - m}$

Discussion

1523.	In the above question, which of the following geometrical figures would help you in solving the problem?
Answer» In the above question, which of the following geometrical figures would help you in solving the problem?

Discussion

1524.	in the circle angle PQR = 100 where P, Q and R are the points on the circle with centre O then find angle OPR
Answer» in the circle angle PQR = 100 where P, Q and R are the points on the circle with centre O then find angle OPR

Discussion

1525.

The following data gives the number (in thousands) of applicants registered with an Year 1995 1996 1997 1998 1999 2000 Number of applicants registered (in thousands) 18 20 24 28 30 34 Construct a bar graph to represent the above data.

Answer» The following data gives the number (in thousands) of applicants registered with an

Year	1995	1996	1997	1998	1999	2000
Number of applicants registered (in thousands)	18	20	24	28	30	34

Construct a bar graph to represent the above data.

Discussion

1526.	In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.
Answer» In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.

Discussion

1527.	Write the value of the determinant x+yy+zz+xzxy-3-3-3.
Answer» Write the value of the determinant $\|\begin{matrix} x + y & y + z & z + x \\ z & x & y \\ - 3 & - 3 & - 3 \end{matrix}\|$ .

Discussion

1528.	If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.
Answer» If a² + b² + c² = 250 and ab + bc + ca = 3, find a + b + c.

Discussion

1529.	Without plotting the points indicate the quadrant in which they will lie ifi. the ordinate is 5 and abscissa is - 3.ii. the abscissa is - 5 and ordinate is - 3.
Answer» Without plotting the points indicate the quadrant in which they will lie if i. the ordinate is 5 and abscissa is - 3. ii. the abscissa is - 5 and ordinate is - 3.

Discussion

1530.	In which quadrant does the point (5, -6) lie?
Answer» In which quadrant does the point (5, -6) lie?

Discussion

1531.	I chapter 9 their is a theorem 1 known as parallelogram on the same Base and between the Same parallel are equal in area in ncert book of class 9 this theorem is proved by using ASA but in byjus it is proved by AAS which solution is right
Answer» I chapter 9 their is a theorem 1 known as parallelogram on the same Base and between the Same parallel are equal in area in ncert book of class 9 this theorem is proved by using ASA but in byjus it is proved by AAS which solution is right

Discussion

1532.	The base of an isosceles right triangle is 30cm. Its area is
Answer» The base of an isosceles right triangle is $30 c m$ . Its area is

Discussion

1533.	If a = 0.1039, then what is the value of 3a−√4a2−4a+1?
Answer» If a = 0.1039, then what is the value of $3 a - \sqrt{4 a^{2} - 4 a + 1}$ ?

Discussion

1534.	If √2=1.414,√3=1.732,√5=2.236 and √6=2.449, find the value of 2+√32−√3+2−√32+√3+√3−1√3+1 .
Answer» If $\sqrt{2} = 1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236$ and $\sqrt{6} = 2.449,$ find the value of $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$ .

Discussion

1535.	The number of all possible pairs of integers (m,n) which satisfy the equation m2+2m−35=2n is
Answer» The number of all possible pairs of integers $(m, n)$ which satisfy the equation $m^{2} + 2 m - 35 = 2^{n}$ is

Discussion

1536.	If 2m+n2n-m=16, 3p3n=81 and a=21/10, thena2m+n-p(am-2n+2p)-1=(a) 2(b) 14(c) 9(d) 18
Answer» If $\frac{2^{m + n}}{2^{n - m}} = 16$ , $\frac{3^{p}}{3^{n}} = 81$ and $a = 2^{1 / 10}$ , then $\frac{a^{2 m + n - p}}{(a^{m - 2 n + 2 p})^{- 1}} =$ (a) 2 (b) $\frac{1}{4}$ (c) 9 (d) $\frac{1}{8}$

Discussion

1537.	Factorise: 4(√3)x2 + 5x - 2√3
Answer» Factorise: 4(√3)x² + 5x - 2√3

1537.

Factorise: 4(√3)x2 + 5x - 2√3

Answer»

Factorise:

4(√3)x² + 5x - 2√3

Discussion

1538.	Which of these pairs of lines are consistent?
Answer» Which of these pairs of lines are consistent?

Discussion

1539.	The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?
Answer» The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?

Discussion

1540.	Identify the solutions for the given equation 4x + y = 16.
Answer» Identify the solutions for the given equation 4x + y = 16.

Discussion

1541.	Question 11 (ii)By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.X – 2y = 6, 3x – 6y = 0
Answer» Question 11 (ii) By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then. X – 2y = 6, 3x – 6y = 0

Discussion

1542.	Out of the 10 apples that I had, 25 of them were spoilt. After selling off some of them, I was left with 13 of the fresh apples. Half of the remaining apples were eaten up by my friend. Then the number of apples left with me is ___.
Answer» Out of the 10 apples that I had, $\frac{2}{5}$ of them were spoilt. After selling off some of them, I was left with $\frac{1}{3}$ of the fresh apples. Half of the remaining apples were eaten up by my friend. Then the number of apples left with me is ___.

Discussion

1543.	If two sides of a triangle are equal, the angles opposite to these sides are
Answer» If two sides of a triangle are equal, the angles opposite to these sides are

1543.

If two sides of a triangle are equal, the angles opposite to these sides are

Answer»

If two sides of a triangle are equal, the angles opposite to these sides are

Discussion

1544.	12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is .
Answer» 12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is .

Discussion

1545.	The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.
Answer» The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 $m^{2} .$

Discussion

1546.	Assume that you are creating a document in Microsoft Word, now if you have to type an equation, how do you do it?
Answer» Assume that you are creating a document in Microsoft Word, now if you have to type an equation, how do you do it?

Discussion

1547.	In the given figure, if AB \|\| CD,∠APQ=50∘ and ∠PRD=127∘, the value of y is77
Answer» In the given figure, if $A B \| \| C D, ∠ A P Q = 50^{\circ}$ and $∠ P R D = 127^{\circ}$ , the value of y is 77

Discussion

1548.	The size of the interval in a data table depicting the entities contained in it is known as
Answer» The size of the interval in a data table depicting the entities contained in it is known as

Discussion

1549.	Of triangle ABC , AD,BE and CF be the internal angle bisector with D,E and F on the side BC ,CA and AB respectively.let AD,BE and CF are concurrent at I and B,D,I,F are concylic then find angle ifd
Answer» Of triangle ABC , AD,BE and CF be the internal angle bisector with D,E and F on the side BC ,CA and AB respectively.let AD,BE and CF are concurrent at I and B,D,I,F are concylic then find angle ifd

Discussion

1550.	Find the angle which is five times its supplement.
Answer» Find the angle which is five times its supplement.

Discussion

Explore topic-wise InterviewSolutions in .

Q. The height of a right circular cylinder is 6 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface . Find the radius of its base.

The sum of the incomes of Ramyani, Mac, and Ankit is ₹12,24,000. The percentage of their expenses are 80%, 85%, and 90%, respectively.If the ratio of their savings is 3:7:8 which is same as the ratio of their respective incomes, then find the annual saving of Mac and Ankit combined.

If the vomume and the surface area of a sphere are numerically the same then its radius is(a) 1 unit (b) 2 units (c) 3 units (d) 4 units

Write the converse theorem of angles opposite to equal sides of an equilateral triangle are equal.

solve for x and y (a-b)x+(a+b)y=a2-2ab-b2 (a+b)(x+y)a2+b2

ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =(a) 32AB(b) 2 AB(c) 3 AB(d) 54AB

Prove that the sum of all interior angles of a triangle is 180°.

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table. Weight (in kg) No. of students Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 Below 65 Below 70 0 24 78 183 294 408 543 621 674 685

If x2+1x2=79, find the value of x+1x

A normal at any point (x,y) to the curve y=f(x) cuts a triangle of unit area with the co-ordinate axes, then the differential equation of the curve is:

If a=4^i+6^j and b=3^j+4^k, then the vector form of the component of a along b is

Question 11 Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.

Let m be the mid-point and u be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is __________.

The distance between Anshul's office and his house is 5.5 km. One day he went walking to office. While coming back, he walked for 2km and then took a cab. Find the total distance walked by Anshul in meters. [4 MARKS]

32. A square ABCD has each side 10 cm and two quadrant each of radius equal to side of square is inscribed in it such that some part overlap(shaded region). Find The area of shaded region (a) 2268 (b) 2520 (c) 2975 (d) 1560

In a marathon of 5 km, Manish could run for 2 km. If Kushagra ran for 12 of the total length of the marathon, who covered more distance?

If the difference of two complementry angles is 40 degrees then find the angles.

What is Range?

Explain the procedure of selecting a random sample of 3 students out of 10 in your class, by using random number tables.

In two triangles, two angles and one side of the first triangle are equal to the two angles and one side of the second triangle. Will these two triangles always be congruent?[3 MARKS]

Evaluate the following:(ama−n)m−n×(ana−l)n−l×(ala−m)l−m

In the above question, which of the following geometrical figures would help you in solving the problem?

in the circle angle PQR = 100 where P, Q and R are the points on the circle with centre O then find angle OPR

The following data gives the number (in thousands) of applicants registered with an Year 1995 1996 1997 1998 1999 2000 Number of applicants registered (in thousands) 18 20 24 28 30 34 Construct a bar graph to represent the above data.

In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.

Write the value of the determinant x+yy+zz+xzxy-3-3-3.

If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.

Without plotting the points indicate the quadrant in which they will lie ifi. the ordinate is 5 and abscissa is - 3.ii. the abscissa is - 5 and ordinate is - 3.

In which quadrant does the point (5, -6) lie?

I chapter 9 their is a theorem 1 known as parallelogram on the same Base and between the Same parallel are equal in area in ncert book of class 9 this theorem is proved by using ASA but in byjus it is proved by AAS which solution is right

The base of an isosceles right triangle is 30cm. Its area is

If a = 0.1039, then what is the value of 3a−√4a2−4a+1?

If √2=1.414,√3=1.732,√5=2.236 and √6=2.449, find the value of 2+√32−√3+2−√32+√3+√3−1√3+1 .

The number of all possible pairs of integers (m,n) which satisfy the equation m2+2m−35=2n is

If 2m+n2n-m=16, 3p3n=81 and a=21/10, thena2m+n-p(am-2n+2p)-1=(a) 2(b) 14(c) 9(d) 18

Factorise: 4(√3)x2 + 5x - 2√3

Which of these pairs of lines are consistent?

The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?

Identify the solutions for the given equation 4x + y = 16.

Question 11 (ii)By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.X – 2y = 6, 3x – 6y = 0

Out of the 10 apples that I had, 25 of them were spoilt. After selling off some of them, I was left with 13 of the fresh apples. Half of the remaining apples were eaten up by my friend. Then the number of apples left with me is ___.

If two sides of a triangle are equal, the angles opposite to these sides are

12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is .

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.

Assume that you are creating a document in Microsoft Word, now if you have to type an equation, how do you do it?

In the given figure, if AB || CD,∠APQ=50∘ and ∠PRD=127∘, the value of y is77

The size of the interval in a data table depicting the entities contained in it is known as

Of triangle ABC , AD,BE and CF be the internal angle bisector with D,E and F on the side BC ,CA and AB respectively.let AD,BE and CF are concurrent at I and B,D,I,F are concylic then find angle ifd

Find the angle which is five times its supplement.