24740 + Interview Questions in Mathematics Page 100 InterviewSolution

4951.	ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that(i) △ABE≅△ACF(ii) AB=AC, i.e., ABC is an isosceles triangle.
Answer» $A B C$ is a triangle in which altitudes $B E$ and $C F$ to sides $A C$ and $A B$ are equal (see the given figure). Show that (i) $△ A B E ≅ △ A C F$ (ii) $A B = A C,$ i.e., $A B C$ is an isosceles triangle.

4951.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that(i) △ABE≅△ACF(ii) AB=AC, i.e., ABC is an isosceles triangle.

Answer»

$A B C$ is a triangle in which altitudes $B E$ and $C F$ to sides $A C$ and $A B$ are equal (see the given figure). Show that

(i) $△ A B E ≅ △ A C F$

(ii) $A B = A C,$ i.e., $A B C$ is an isosceles triangle.

Discussion

4952.	Give difference and examples of random experiment and deterministic experiment
Answer» Give difference and examples of random experiment and deterministic experiment

Discussion

4953.	In the given figure, if ∠BCA=∠RPQ=15∘,then ∠PQR is .
Answer» In the given figure, if $∠ B C A = ∠ R P Q = 15^{\circ},$ then $∠ P Q R$ is .

Discussion

4954.	If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then AV(a) x2y2z2(b) 121xy+1yz+1zx(c) 1x+1y+1z(d) 1xyz
Answer» If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then $\frac{A}{V}$ (a) x²y²z² (b) $\frac{1}{2} (\frac{1}{x y} + \frac{1}{y z} + \frac{1}{z x})$ (c) $(\frac{1}{x} + \frac{1}{y} + \frac{1}{z})$ (d) $\frac{1}{x y z}$

Discussion

4955.	Which of the following is a binomial?
Answer» Which of the following is a binomial?

Discussion

4956.	Draw a rectangle of perimeter 17 cm and sides in the ratio of 5:3. Also, find the measure of the smallest side.
Answer» Draw a rectangle of perimeter 17 cm and sides in the ratio of 5:3. Also, find the measure of the smallest side.

Discussion

4957.	How many zeroes do the polynomialsP1(x)=x3+x2+x+1 andP2(x)=x2+1have in common?
Answer» How many zeroes do the polynomials $P_{1} (x) = x^{3} + x^{2} + x + 1$ and $P_{2} (x) = x^{2} + 1$ have in common?

Discussion

4958.	angle between the vectors \overrightarrow C and \overrightarrow D is θ then the value of the product (\overrightarrow C×\overrightarrow D).\overrightarrow D is equal to
Answer» angle between the vectors \overrightarrow C and \overrightarrow D is θ then the value of the product (\overrightarrow C×\overrightarrow D).\overrightarrow D is equal to

Discussion

4959.	Factorize a3+b3+a+b
Answer» Factorize $a^{3} + b^{3} + a + b$

Discussion

4960.	Points A and B are 90 km apart from each other on a highway. Car X starts from point A and another car Y starts from point B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in 97 hours. What is the speed of car X?
Answer» Points A and B are 90 km apart from each other on a highway. Car X starts from point A and another car Y starts from point B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in $\frac{9}{7}$ hours. What is the speed of car X?

Discussion

4961.	In a rhombus PQRS if PQ = 7.5 cm then find the length of QR. If ∠QPS=75∘ then find the measure of ∠PQR and ∠SRQ.
Answer» In a rhombus PQRS if PQ = 7.5 cm then find the length of QR. If $∠ Q P S = 75^{\circ}$ then find the measure of $∠ P Q R and ∠ S R Q .$

Discussion

4962.	In the given figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
Answer» In the given figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Discussion

4963.	Prove that the opposite sides of a quadrailateral circumscribing a circle subtend supplementary angles at the centre of the circl
Answer» Prove that the opposite sides of a quadrailateral circumscribing a circle subtend supplementary angles at the centre of the circl

Discussion

4964.	How to find the value of log 3 X 10^5
Answer» How to find the value of log 3 X 10^5

Discussion

4965.	Two opposite angles of a parallelogram are (3x−2)∘ and (63−2x)∘. Find all the angles of the parallelogram.
Answer» Two opposite angles of a parallelogram are $(3 x - 2)^{\circ}$ and $(63 - 2 x)^{\circ}$ . Find all the angles of the parallelogram.

Discussion

4966.

Open a 'T' shape Cash Account with the following transactions: ₹ (i) Mohan started business with cash 40,000 (ii) Purchased Goods 20,000 (iii) Sold Goods 24,000 (iv) Paid Rent 400 (v) Paid salaries 600 (vi) Drew for personal use 1,000

Answer» Open a 'T' shape Cash Account with the following transactions:

		₹
(i)	Mohan started business with cash	40,000
(ii)	Purchased Goods	20,000
(iii)	Sold Goods	24,000
(iv)	Paid Rent	400
(v)	Paid salaries	600
(vi)	Drew for personal use	1,000

Discussion

4967.	Find(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.(ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.
Answer» Find (i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high. (ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.

4967.

Find(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.(ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.

Answer»

Find

(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

(ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.

Discussion

4968.	If the area of the top of a cylindrical vessel of height 2 cm is 154 cm2. Its volume is
Answer» If the area of the top of a cylindrical vessel of height 2 cm is 154 cm². Its volume is

Discussion

4969.	18. A variable chrod is drawn from the origin to the circle x2+y2-2gx=0.locus of centre of circle described on chrod as a diameter?
Answer» 18. A variable chrod is drawn from the origin to the circle x2+y2-2gx=0.locus of centre of circle described on chrod as a diameter?

Discussion

4970.	Express 0.357 7is termenatite in form of p÷q
Answer» Express 0.357 7is termenatite in form of p÷q

Discussion

4971.	A __________ is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them, with their widths usually placed on the x-axis and the frequency on the y-axis.
Answer» A __________ is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them, with their widths usually placed on the x-axis and the frequency on the y-axis.

Discussion

4972.	Given below is the data of the age of 9 children of a street. Find the median.5, 8, 7, 3, 4, 6, 2, 9, 1
Answer» Given below is the data of the age of 9 children of a street. Find the median. 5, 8, 7, 3, 4, 6, 2, 9, 1

Discussion

4973.	The radii of two similar right circular cylinders are 5 cm and 2.5 cm. What is the ratio of their altitudes?
Answer» The radii of two similar right circular cylinders are 5 cm and 2.5 cm. What is the ratio of their altitudes?

Discussion

4974.	In the given figure, the value of y is
Answer» In the given figure, the value of y is

4974.

In the given figure, the value of y is

Answer»

In the given figure, the value of y is

Discussion

4975.	Question 4(i)Factorisea4−b4
Answer» Question 4(i) Factorise $a^{4} - b^{4}$

Discussion

4976.	Match the following: Column AColumn B1. {x: x ∈ R, -5 < x ≤ 15 } A. 1 2.A=ThepowersetP(A)has––––––elements B.8 3.UniversasetofRationalNumbers&IrrationalNumbersC.RealNumbers4.No.ofelementsinPowerSetofA={a,b,c} D.Integers E.(−5,15] F.[−5,15)
Answer» Match the following: $\begin{matrix} Column A & Column B 1. {x: x \in R, -5 < x \leq 15 } & A. 1 2. A = T h e p o w e r s e t P (A) h a s - ---- - e l e m e n t s & B . 8 3. U n i v e r s a s e t o f R a t i o n a l N u m b e r s & I r r a t i o n a l N u m b e r s & C . R e a l N u m b e r s 4. N o . o f e l e m e n t s i n P o w e r S e t o f A = {a, b, c} & D . I n t e g e r s E . (- 5, 15] F . [- 5, 15) \end{matrix}$

4976.

Match the following: Column AColumn B1. {x: x ∈ R, -5 < x ≤ 15 } A. 1 2.A=ThepowersetP(A)has––––––elements B.8 3.UniversasetofRationalNumbers&IrrationalNumbersC.RealNumbers4.No.ofelementsinPowerSetofA={a,b,c} D.Integers E.(−5,15] F.[−5,15)

Answer»

Match the following:

$\begin{matrix} Column A & Column B 1. {x: x \in R, -5 < x \leq 15 } & A. 1 2. A = T h e p o w e r s e t P (A) h a s - ---- - e l e m e n t s & B . 8 3. U n i v e r s a s e t o f R a t i o n a l N u m b e r s & I r r a t i o n a l N u m b e r s & C . R e a l N u m b e r s 4. N o . o f e l e m e n t s i n P o w e r S e t o f A = {a, b, c} & D . I n t e g e r s E . (- 5, 15] F . [- 5, 15) \end{matrix}$

Discussion

4977.	how many significant figures in avogadro's number that is 6.02*1023 and why?
Answer» how many significant figures in avogadro's number that is 6.02*1023 and why?

Discussion

4978.	Dhoni won a game off the last ball by scoring 2 4 2 2 4 6 in the last over when 20 runs were required. If the scorecard for the last over was randomly rearranged, what is the probability that he finished the game with a six? [2 MARKS]
Answer» Dhoni won a game off the last ball by scoring 2 4 2 2 4 6 in the last over when 20 runs were required. If the scorecard for the last over was randomly rearranged, what is the probability that he finished the game with a six? [2 MARKS]

Discussion

4979.	If point P lies on the line y = 2, then what is its y-coordinate?
Answer» If point P lies on the line y = 2, then what is its y-coordinate?

Discussion

4980.	In △ABC, if AC > AB, then which of the following options is correct?
Answer» In $△ A B C$ , if AC $>$ AB, then which of the following options is correct?

Discussion

4981.	If the ratio of sides (taken in order) of a quadrilateral is a:b:a:b, then it is a
Answer» If the ratio of sides (taken in order) of a quadrilateral is a:b:a:b, then it is a

Discussion

4982.	O is the centre of the circle. The length of radius OS is 5 cm. What is the length of AB?
Answer» O is the centre of the circle. The length of radius OS is 5 cm. What is the length of AB?

Discussion

4983.	Find the circumference of the circle from the figure.(Use π=227)
Answer» Find the circumference of the circle from the figure. (Use $π = \frac{22}{7}$ )

Discussion

4984.	42. Find the eq of hyperbola whose centre (-4,1),vertex(2,1) and semi conjugate axis is equal to 4
Answer» 42. Find the eq of hyperbola whose centre (-4,1),vertex(2,1) and semi conjugate axis is equal to 4

Discussion

4985.	If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (ΔABC) : ar (ΔBDE).
Answer» If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (ΔABC) : ar (ΔBDE).

Discussion

4986.	Area of a square sheet is 300 cm2. The nearest whole number to which its side can be estimated is
Answer» Area of a square sheet is 300 cm². The nearest whole number to which its side can be estimated is

4986.

Area of a square sheet is 300 cm2. The nearest whole number to which its side can be estimated is

Answer»

Area of a square sheet is 300 cm². The nearest whole number to which its side can be estimated is

Discussion

4987.	When a circle circumscribes a regular hexagon, its radius is always equal to the ___ of the side of the hexagon.
Answer» When a circle circumscribes a regular hexagon, its radius is always equal to the ___ of the side of the hexagon.

Discussion

4988.	If sin17∘=xy, then what will be the value of sec17∘−sin73∘?
Answer» If $s i n 17^{\circ} = \frac{x}{y}$ , then what will be the value of $s e c 17^{\circ} - s i n 73^{\circ}$ ?

Discussion

4989.	If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Answer» If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

Discussion

4990.	Solve the following simultaneous liner equations by subsitution method mx-ny=m²+n² x+y=2m
Answer» Solve the following simultaneous liner equations by subsitution method mx-ny=m²+n² x+y=2m

4990.

Solve the following simultaneous liner equations by subsitution method mx-ny=m²+n² x+y=2m

Answer»

Solve the following simultaneous liner equations by subsitution method

mx-ny=m²+n²

x+y=2m

Discussion

4991.	For the linear equation in two variables: ax + by = c, the positive solutions lie in the ______ quadrant.
Answer» For the linear equation in two variables: ax + by = c, the positive solutions lie in the ______ quadrant.

Discussion

4992.

On 1st July, 2015, A Co. Ltd. purchases second-hand machinery for ₹ 20,000 and spends ₹ 3,000 on reconditioning and installing it. On 1st January, 2016, the firm purchases new machinery worth ₹ 12,000. On 30th June, 2017, the machinery purchased on 1st January, 2016, was sold for ₹ 8,000 and on 1st July, 2017, a fresh plant was installed.Payments for this plant was to be made as follows: 1st July, 2017 ₹ 5,000 30th June, 2018 ₹ 6,000 30th June, 2019 ₹ 5,500 Payments in 2018 and 2019 include interest of ₹ 1,000 and ₹ 500 respectively.The company writes off 10% p.a. on the original cost. The accounts are closed every year on 31st March. Show the Machinery Account for the year ended 31st March, 2018.

Answer» On 1st July, 2015, A Co. Ltd. purchases second-hand machinery for ₹ 20,000 and spends ₹ 3,000 on reconditioning and installing it. On 1st January, 2016, the firm purchases new machinery worth ₹ 12,000. On 30th June, 2017, the machinery purchased on 1st January, 2016, was sold for ₹ 8,000 and on 1st July, 2017, a fresh plant was installed.

Payments for this plant was to be made as follows:

1st July, 2017	₹ 5,000
30th June, 2018	₹ 6,000
30th June, 2019	₹ 5,500

Payments in 2018 and 2019 include interest of ₹ 1,000 and ₹ 500 respectively.

The company writes off 10% p.a. on the original cost. The accounts are closed every year on 31st March. Show the Machinery Account for the year ended 31st March, 2018.

Discussion

4993.	(x2−4x−21)=? (a) (x−7)(x−3) (b) (x+7)(x−3) (c) (x−7)(x+3) (d) None of these
Answer» $(x^{2} - 4 x - 21)$ =? (a) $(x - 7) (x - 3)$ (b) $(x + 7) (x - 3)$ (c) $(x - 7) (x + 3)$ (d) None of these

4993.

(x2−4x−21)=? (a) (x−7)(x−3) (b) (x+7)(x−3) (c) (x−7)(x+3) (d) None of these

Answer»

$(x^{2} - 4 x - 21)$ =?

(a) $(x - 7) (x - 3)$

(b) $(x + 7) (x - 3)$

(c) $(x - 7) (x + 3)$

(d) None of these

Discussion

4994.	If U = {1, 2, 3, 4,5}, A = {2, 3, 4}, B = {1,4, 5}, then which of the following statements are true?
Answer» If U = {1, 2, 3, 4,5}, A = {2, 3, 4}, B = {1,4, 5}, then which of the following statements are true?

Discussion

4995.	The probability of guessing the correct answer to certain test questions is y4. If the probability of not guessing the correct answer to these questions is 34, then the value of y is:
Answer» The probability of guessing the correct answer to certain test questions is $\frac{y}{4}$ . If the probability of not guessing the correct answer to these questions is $\frac{3}{4}$ , then the value of y is:

Discussion

4996.	If z is any complex number satisfying \vert z-3-2i\vert≤2, then the minimum value of \vert2z-6+5i\vert is
Answer» If z is any complex number satisfying \vert z-3-2i\vert≤2, then the minimum value of \vert2z-6+5i\vert is

Discussion

4997.	Prove that the opposite angle of an isosceles trapezium are supplementary.
Answer» Prove that the opposite angle of an isosceles trapezium are supplementary.

Discussion

4998.	Rationalise 1√3+√2
Answer» Rationalise $\frac{1}{\sqrt{3} + \sqrt{2}}$

Discussion

4999.	State whether 10.064 is a rational or an irrational number. If it is a rational number, express it in the form p/q,where p and q are integers and q is not equal to 0
Answer» State whether 10.064 is a rational or an irrational number. If it is a rational number, express it in the form p/q,where p and q are integers and q is not equal to 0

Discussion

5000.	Question 6 The class marks of a continuous distribution are 1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64. Is it correct to say that last interval will be 1.55 - 1.73? Justify your answer.
Answer» Question 6 The class marks of a continuous distribution are 1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64. Is it correct to say that last interval will be 1.55 - 1.73? Justify your answer.

Discussion

Explore topic-wise InterviewSolutions in .

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that(i) △ABE≅△ACF(ii) AB=AC, i.e., ABC is an isosceles triangle.

Give difference and examples of random experiment and deterministic experiment

In the given figure, if ∠BCA=∠RPQ=15∘,then ∠PQR is .

If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then AV(a) x2y2z2(b) 121xy+1yz+1zx(c) 1x+1y+1z(d) 1xyz

Which of the following is a binomial?

Draw a rectangle of perimeter 17 cm and sides in the ratio of 5:3. Also, find the measure of the smallest side.

How many zeroes do the polynomialsP1(x)=x3+x2+x+1 andP2(x)=x2+1have in common?

angle between the vectors \overrightarrow C and \overrightarrow D is θ then the value of the product (\overrightarrow C×\overrightarrow D).\overrightarrow D is equal to

Factorize a3+b3+a+b

Points A and B are 90 km apart from each other on a highway. Car X starts from point A and another car Y starts from point B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in 97 hours. What is the speed of car X?

In a rhombus PQRS if PQ = 7.5 cm then find the length of QR. If ∠QPS=75∘ then find the measure of ∠PQR and ∠SRQ.

In the given figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Prove that the opposite sides of a quadrailateral circumscribing a circle subtend supplementary angles at the centre of the circl

How to find the value of log 3 X 10^5

Two opposite angles of a parallelogram are (3x−2)∘ and (63−2x)∘. Find all the angles of the parallelogram.

Open a 'T' shape Cash Account with the following transactions: ₹ (i) Mohan started business with cash 40,000 (ii) Purchased Goods 20,000 (iii) Sold Goods 24,000 (iv) Paid Rent 400 (v) Paid salaries 600 (vi) Drew for personal use 1,000

Find(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.(ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.

If the area of the top of a cylindrical vessel of height 2 cm is 154 cm2. Its volume is

18. A variable chrod is drawn from the origin to the circle x2+y2-2gx=0.locus of centre of circle described on chrod as a diameter?

Express 0.357 7is termenatite in form of p÷q

A __________ is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them, with their widths usually placed on the x-axis and the frequency on the y-axis.

Given below is the data of the age of 9 children of a street. Find the median.5, 8, 7, 3, 4, 6, 2, 9, 1

The radii of two similar right circular cylinders are 5 cm and 2.5 cm. What is the ratio of their altitudes?

In the given figure, the value of y is

Question 4(i)Factorisea4−b4

Match the following: Column AColumn B1. {x: x ∈ R, -5 &lt; x ≤ 15 } A. 1 2.A=ThepowersetP(A)has––––––elements B.8 3.UniversasetofRationalNumbers&amp;IrrationalNumbersC.RealNumbers4.No.ofelementsinPowerSetofA={a,b,c} D.Integers E.(−5,15] F.[−5,15)

how many significant figures in avogadro's number that is 6.02*1023 and why?

Dhoni won a game off the last ball by scoring 2 4 2 2 4 6 in the last over when 20 runs were required. If the scorecard for the last over was randomly rearranged, what is the probability that he finished the game with a six? [2 MARKS]

If point P lies on the line y = 2, then what is its y-coordinate?

In △ABC, if AC &gt; AB, then which of the following options is correct?

If the ratio of sides (taken in order) of a quadrilateral is a:b:a:b, then it is a

O is the centre of the circle. The length of radius OS is 5 cm. What is the length of AB?

Find the circumference of the circle from the figure.(Use π=227)

42. Find the eq of hyperbola whose centre (-4,1),vertex(2,1) and semi conjugate axis is equal to 4

If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (ΔABC) : ar (ΔBDE).

Area of a square sheet is 300 cm2. The nearest whole number to which its side can be estimated is

When a circle circumscribes a regular hexagon, its radius is always equal to the ___ of the side of the hexagon.

If sin17∘=xy, then what will be the value of sec17∘−sin73∘?

If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.

Solve the following simultaneous liner equations by subsitution method mx-ny=m²+n² x+y=2m

For the linear equation in two variables: ax + by = c, the positive solutions lie in the ______ quadrant.

(x2−4x−21)=? (a) (x−7)(x−3) (b) (x+7)(x−3) (c) (x−7)(x+3) (d) None of these

If U = {1, 2, 3, 4,5}, A = {2, 3, 4}, B = {1,4, 5}, then which of the following statements are true?

The probability of guessing the correct answer to certain test questions is y4. If the probability of not guessing the correct answer to these questions is 34, then the value of y is:

If z is any complex number satisfying \vert z-3-2i\vert≤2, then the minimum value of \vert2z-6+5i\vert is

Prove that the opposite angle of an isosceles trapezium are supplementary.

Rationalise 1√3+√2

State whether 10.064 is a rational or an irrational number. If it is a rational number, express it in the form p/q,where p and q are integers and q is not equal to 0

Question 6 The class marks of a continuous distribution are 1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64. Is it correct to say that last interval will be 1.55 - 1.73? Justify your answer.

Match the following: Column AColumn B1. {x: x ∈ R, -5 < x ≤ 15 } A. 1 2.A=ThepowersetP(A)has––––––elements B.8 3.UniversasetofRationalNumbers&IrrationalNumbersC.RealNumbers4.No.ofelementsinPowerSetofA={a,b,c} D.Integers E.(−5,15] F.[−5,15)

In △ABC, if AC > AB, then which of the following options is correct?