24740 + Interview Questions in Mathematics Page 83 InterviewSolution

4101.	Question 4 (iii)Form the pair of linear equations for the following problem and find their solution (if they exist) by any algebraic method:Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?Assume Yash answered all the questions.
Answer» Question 4 (iii) Form the pair of linear equations for the following problem and find their solution (if they exist) by any algebraic method: Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? Assume Yash answered all the questions.

Discussion

4102.	In the given figure, ABC is isosceles triangle with AB=AC, ∠BCD=20∘. The measure of ∠ACB is equal to
Answer» In the given figure, ABC is isosceles triangle with $A B = A C, ∠ B C D = 20^{\circ} .$ The measure of $∠ A C B$ is equal to

Discussion

4103.	if m = ax , n=ay and a2 = (mynx)z then xyz =
Answer» if m = a^x , n=a^y and a² = (m^yn^x)^z then xyz =

Discussion

4104.	Refer to the following figure:D and C are equidistant from O.If any point P is located such that △ODP is congurent to △OCP, then P lies on the ________.
Answer» Refer to the following figure: D and C are equidistant from O. If any point P is located such that $△$ ODP is congurent to $△$ OCP, then P lies on the ________.

4104.

Refer to the following figure:D and C are equidistant from O.If any point P is located such that △ODP is congurent to △OCP, then P lies on the ________.

Answer»

Refer to the following figure:

D and C are equidistant from O.

If any point P is located such that $△$ ODP is congurent to $△$ OCP, then P lies on the ________.

Discussion

4105.	Two chords of a circle bisect each other. Then
Answer» Two chords of a circle bisect each other. Then

Discussion

4106.	If ABCD is a quadrilateral in which AB\parallel CD AND AD=BC .Prove that \angle A=\angle B
Answer» If ABCD is a quadrilateral in which AB\parallel CD AND AD=BC .Prove that \angle A=\angle B

Discussion

4107.	Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm in cm2.
Answer» Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm in ${c m}^{2}$ .

Discussion

4108.	An angle is double of its supplement. The measure of the angle is(a) 60°(b) 120°(c) 40°(d) 80°
Answer» An angle is double of its supplement. The measure of the angle is (a) 60° (b) 120° (c) 40° (d) 80°

Discussion

4109.	Question 2 (i)Write True or False. Give reasons for your answers.(i) Line segment joining the centre to any point on the circle is a radius of the circle
Answer» Question 2 (i) Write True or False. Give reasons for your answers. (i) Line segment joining the centre to any point on the circle is a radius of the circle

Discussion

4110.	Find the value of A:1250 = A100
Answer» Find the value of A: $\frac{12}{50} =$ $\frac{A}{100}$

Discussion

4111.	Find the measure of an angle of 37degree 42'34".
Answer» Find the measure of an angle of 37degree 42'34".

Discussion

4112.	Why is the sum of all the angles of a triangle 180 degree?
Answer» Why is the sum of all the angles of a triangle 180 degree?

Discussion

4113.	A non-terminating and non-recurring decimal number is known as a/an _________.
Answer» A non-terminating and non-recurring decimal number is known as a/an _________.

Discussion

4114.	Evaluate: limn→∞14+24+34+...+n4n5-limn→∞13+23+...+n3n5
Answer» Evaluate: $\lim_{n \to \infty} \frac{1^{4} + 2^{4} + 3^{4} + . . . + n^{4}}{n^{5}} - \lim_{n \to \infty} \frac{1^{3} + 2^{3} + . . . + n^{3}}{n^{5}}$

Discussion

4115.	Find p(0), p(1) and p(2) for each of the following polynomials:(i) p(y) = y2 − y + 1 (ii) p(t) = 2 + t + 2t2 − t3 (iii) p(x) = x3 (iv) p(x) = (x − 1) (x + 1)
Answer» Find p(0), p(1) and p(2) for each of the following polynomials: (i) p(y) = y² − y + 1 (ii) p(t) = 2 + t + 2t² − t³ (iii) p(x) = x³ (iv) p(x) = (x − 1) (x + 1)

4115.

Find p(0), p(1) and p(2) for each of the following polynomials:(i) p(y) = y2 − y + 1 (ii) p(t) = 2 + t + 2t2 − t3 (iii) p(x) = x3 (iv) p(x) = (x − 1) (x + 1)

Answer»

Find p(0), p(1) and p(2) for each of the following polynomials:

(i) p(y) = y² − y + 1 (ii) p(t) = 2 + t + 2t² − t³

(iii) p(x) = x³ (iv) p(x) = (x − 1) (x + 1)

Discussion

4116.	The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:(a) 47 and 37(b) 37 and 47(c) 37.5 and 47.5(d) 47.5 and 37.5
Answer» The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are: (a) 47 and 37 (b) 37 and 47 (c) 37.5 and 47.5 (d) 47.5 and 37.5

Discussion

4117.	Question 3 (ii) Is 0.120120012000120000... 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 (ii) Is 0.120120012000120000... 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

4118.	Plot the given points on a graph sheet and check if they lie on a straight line. If not, name the shape they form when joined in the given order.(i) A (0, 2), B (0, 3.5), C (0, 5) and D (0, 6)(ii) P (1, 3), Q (1, 5), R (3, 3) and S (3, 5)(iii) E (4, 5), F (5, 5), G (5, 7) and H (6, 5)(iv) L (2, 0), M (2, 3), N (0, 3) and O (0, 0)(v) J (4, 3), K (6, 1), L (6, 5) and M (4, 7)
Answer» Plot the given points on a graph sheet and check if they lie on a straight line. If not, name the shape they form when joined in the given order. (i) A (0, 2), B (0, 3.5), C (0, 5) and D (0, 6) (ii) P (1, 3), Q (1, 5), R (3, 3) and S (3, 5) (iii) E (4, 5), F (5, 5), G (5, 7) and H (6, 5) (iv) L (2, 0), M (2, 3), N (0, 3) and O (0, 0) (v) J (4, 3), K (6, 1), L (6, 5) and M (4, 7)

Discussion

4119.	Question 10If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
Answer» Question 10 If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Discussion

4120.	Factorize:x3 − 2x2y + 3xy2 − 6y3
Answer» Factorize: x³ − 2x²y + 3xy² − 6y³

Discussion

4121.	The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the longest side is.
Answer» The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the longest side is.

Discussion

4122.	In Parallelogram PQRS, ∠Q=(4x−5)∘and ∠S=(3x+10)∘. Calculate: ∠Q and ∠R
Answer» In Parallelogram PQRS, $∠ Q = (4 x - 5)^{\circ} a n d ∠ S = (3 x + 10)^{\circ} .$ Calculate: $∠ Q a n d ∠ R$

Discussion

4123.	How many 5 digit numbers have atleast one even digit ? options: a)86875 b)88775 c)85625 d)87895
Answer» How many 5 digit numbers have atleast one even digit ? options: a)86875 b)88775 c)85625 d)87895

Discussion

4124.	In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =(a) 2 cm(b) 3 cm(c) 4 cm(d) 5 cm
Answer» In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD = (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm

Discussion

4125.	If (x−1) is a factor of ax3−bx2+cx, what is the value of a3−b3+c3?
Answer» If $(x - 1)$ is a factor of $a x^{3} - b x^{2} + c x$ , what is the value of $a^{3} - b^{3} + c^{3}$ ?

Discussion

4126.	Raghu needs to make a cylindrical aluminum tube. What will be the area of the aluminum sheet required to make the tube, if the length and radius of the tube should be 1 m and 3.5 cm respectively [Top and bottom of the tube are of another material]?(use π=227)
Answer» Raghu needs to make a cylindrical aluminum tube. What will be the area of the aluminum sheet required to make the tube, if the length and radius of the tube should be 1 $m$ and 3.5 $c m$ respectively [Top and bottom of the tube are of another material]? ( $u s e π = \frac{22}{7}$ )

Discussion

4127.	The boundary of the circle is called as the ___ of the circle.
Answer» The boundary of the circle is called as the ___ of the circle.

Discussion

4128.	In a triangle ABC, the median CM is perpendicular to angular bisector AL, M being on AB and L being on BC. Also CM/AL = n. Find cosA in terms of n. 1) (9+4n²)/(9-4n²)2) (9-4n²)/(9+4n²)3) (5-4n²)/(5+4n²)4) (9-n²)/(9+n²)
Answer» In a triangle ABC, the median CM is perpendicular to angular bisector AL, M being on AB and L being on BC. Also CM/AL = n. Find cosA in terms of n. 1) (9+4n²)/(9-4n²) 2) (9-4n²)/(9+4n²) 3) (5-4n²)/(5+4n²) 4) (9-n²)/(9+n²)

Discussion

4129.

From the following information supplied by Mr. D.H., prepare his Bank Reconciliation Statement as on 31st March, 2018: ₹ (i) Bank overdraft as per Pass Book. 33,000 (ii) Cheques issued but not presented for payment. 17,500 (iii) Cheques deposited but not collected. 21,000 (iv) Cheques recorded in the Cash Book but not sent to the bank for collection. 4,000 (v) Payment received from customers directly by the bank. 7,000 (vi) Bank charges debited in the Pass Book. 40 (vii) Premium of Life Insurance Policy of Mr. D.H. paid by the bank on standing instructions. 360 (viii) A bill for ₹ 6,000 dishonoured on 30th March, 2018 and bank paid Noting charges. This bill was discounted on 30th January, 2018. 20

Answer» From the following information supplied by Mr. D.H., prepare his Bank Reconciliation Statement as on 31st March, 2018:

		₹
(i)	Bank overdraft as per Pass Book.	33,000
(ii)	Cheques issued but not presented for payment.	17,500
(iii)	Cheques deposited but not collected.	21,000
(iv)	Cheques recorded in the Cash Book but not sent to the bank for collection.	4,000
(v)	Payment received from customers directly by the bank.	7,000
(vi)	Bank charges debited in the Pass Book.	40
(vii)	Premium of Life Insurance Policy of Mr. D.H. paid by the bank on standing instructions.	360
(viii)	A bill for ₹ 6,000 dishonoured on 30th March, 2018 and bank paid Noting charges. This bill was discounted on 30th January, 2018.	20

Discussion

4130.	Prove that 2+35 is an irrational number, given that 5 is an irrational number.
Answer» Prove that $(2 + 3 \sqrt{5})$ is an irrational number, given that $\sqrt{5}$ is an irrational number.

Discussion

4131.	The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is
Answer» The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is

Discussion

4132.	Unique point is obtained for the pair of equations a1x + b1y + c1 = 0 and a2x +b2y + c2 = 0 if __________ .
Answer» Unique point is obtained for the pair of equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 if __________ .

Discussion

4133.	Which of the following numbers can be represented as non-terminating, repeating decimals?(a) 3924(b) 316(c) 311(d) 13725
Answer» Which of the following numbers can be represented as non-terminating, repeating decimals? (a) $\frac{39}{24}$ (b) $\frac{3}{16}$ (c) $\frac{3}{11}$ (d) $\frac{137}{25}$

Discussion

4134.	Simplify(i) 11121114 .(ii) 712.812
Answer» Simplify (i) $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$ . (ii) $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

Discussion

4135.	A fraction becomes 45 if 1 is added to each of the numerator and denominator. However, if we subtract 5 from each, the fraction becomes 12. Find the fraction.
Answer» A fraction becomes $\frac{4}{5}$ if 1 is added to each of the numerator and denominator. However, if we subtract 5 from each, the fraction becomes $\frac{1}{2}$ . Find the fraction.

Discussion

4136.	A circle with centre O has a radius of 3.5 cm. If the distance between O and point P is 5 cm, where does P lie with respect to the circle?
Answer» A circle with centre O has a radius of $3.5$ cm. If the distance between O and point P is $5$ cm, where does P lie with respect to the circle?

Discussion

4137.	Question 49If pq is a rational number, then p cannot be equal to zero.
Answer» Question 49 If $\frac{p}{q}$ is a rational number, then p cannot be equal to zero.

Discussion

4138.	The value of √3cosec20∘−sec20∘ is
Answer» The value of $\sqrt{3} cosec 20^{\circ} - sec 20^{\circ}$ is

Discussion

4139.	Question 37 Fill in the blanks to make the statement true. The number of cubes in are ___.
Answer» Question 37 Fill in the blanks to make the statement true. The number of cubes in are ___.

Discussion

4140.	by watching a graph of polynomial , how can be find the value of a , b ,c that they are less than 0 or greater than 0
Answer» by watching a graph of polynomial , how can be find the value of a , b ,c that they are less than 0 or greater than 0

Discussion

4141.	A is a point on the x axis with abscissa "-12" and B is a point on the y axis with ordinate 5. Find distance AB
Answer» A is a point on the x axis with abscissa "-12" and B is a point on the y axis with ordinate 5. Find distance AB

Discussion

4142.	Question 124Work out the surface area of the following shape.
Answer» Question 124 Work out the surface area of the following shape.

4142.

Question 124Work out the surface area of the following shape.

Answer»

Question 124

Work out the surface area of the following shape.

Discussion

4143.	Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Select all the correct options.
Answer» Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Select all the correct options.

4143.

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Select all the correct options.

Answer»

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all.

Select all the correct options.

Discussion

4144.	Question 7The coordinates of a point at a distance of 3 units from the X-axis and 6 units from the Y-axis are(a) (0,3)(b) (6,0)(c) (3,6)(d) (6,3)
Answer» Question 7 The coordinates of a point at a distance of 3 units from the X-axis and 6 units from the Y-axis are (a) (0,3) (b) (6,0) (c) (3,6) (d) (6,3)

Discussion

4145.	In a party there are 6 guests and if each other shake hand each other, how many shake hands occur in the party? Thank you..
Answer» In a party there are 6 guests and if each other shake hand each other, how many shake hands occur in the party? Thank you..

4145.

In a party there are 6 guests and if each other shake hand each other, how many shake hands occur in the party? Thank you..

Answer»

In a party there are 6 guests and if each other shake hand each other, how many shake hands occur in the party?

Thank you..

Discussion

4146.	Compare the given linear equation 2y=5x+7 with its standard form ax+by+c=0. What is the value of 'c' for the given equation?
Answer» Compare the given linear equation $2 y = 5 x + 7$ with its standard form $a x + b y + c = 0$ . What is the value of ' $c$ ' for the given equation?

Discussion

4147.	Find the diameter of the circle shown below if the perimeter of the square ABCD is 16 m.
Answer» Find the diameter of the circle shown below if the perimeter of the square ABCD is 16 m.

4147.

Find the diameter of the circle shown below if the perimeter of the square ABCD is 16 m.

Answer»

Find the diameter of the circle shown below if the perimeter of the square ABCD is 16 m.

Discussion

4148.	Find the curved surface area (m2) of a cylindrical concrete pillar whose radius and height are 70 cm and 10 m respectively.44
Answer» Find the curved surface area (m $^{2}$ ) of a cylindrical concrete pillar whose radius and height are 70 cm and 10 m respectively. 44

Discussion

4149.	Find the magnitude of angle A, if 2 sin A cos A - cos A -2 sin A + 1 = 0
Answer» Find the magnitude of angle A, if 2 sin A cos A - cos A -2 sin A + 1 = 0

4149.

Find the magnitude of angle A, if 2 sin A cos A - cos A -2 sin A + 1 = 0

Answer»

Find the magnitude of angle A, if

2 sin A cos A - cos A -2 sin A + 1 = 0

Discussion

4150.	If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
Answer» If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, ABC is isosceles triangle with AB=AC, ∠BCD=20∘. The measure of ∠ACB is equal to

if m = ax , n=ay and a2 = (mynx)z then xyz =

Refer to the following figure:D and C are equidistant from O.If any point P is located such that △ODP is congurent to △OCP, then P lies on the ________.

Two chords of a circle bisect each other. Then

If ABCD is a quadrilateral in which AB\parallel CD AND AD=BC .Prove that \angle A=\angle B

Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm in cm2.​

An angle is double of its supplement. The measure of the angle is(a) 60°(b) 120°(c) 40°(d) 80°

Question 2 (i)Write True or False. Give reasons for your answers.(i) Line segment joining the centre to any point on the circle is a radius of the circle

Find the value of A:1250 = A100

Find the measure of an angle of 37degree 42'34".

Why is the sum of all the angles of a triangle 180 degree?

A non-terminating and non-recurring decimal number is known as a/an _________.

Evaluate: limn→∞14+24+34+...+n4n5-limn→∞13+23+...+n3n5

Find p(0), p(1) and p(2) for each of the following polynomials:(i) p(y) = y2 − y + 1 (ii) p(t) = 2 + t + 2t2 − t3 (iii) p(x) = x3 (iv) p(x) = (x − 1) (x + 1)

The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:(a) 47 and 37(b) 37 and 47(c) 37.5 and 47.5(d) 47.5 and 37.5

Question 3 (ii) Is 0.120120012000120000... rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

Question 10If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Factorize:x3 − 2x2y + 3xy2 − 6y3

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the longest side is.

In Parallelogram PQRS, ∠Q=(4x−5)∘and ∠S=(3x+10)∘. Calculate: ∠Q and ∠R

How many 5 digit numbers have atleast one even digit ? options: a)86875 b)88775 c)85625 d)87895

In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =(a) 2 cm(b) 3 cm(c) 4 cm(d) 5 cm

If (x−1) is a factor of ax3−bx2+cx, what is the value of a3−b3+c3?

Raghu needs to make a cylindrical aluminum tube. What will be the area of the aluminum sheet required to make the tube, if the length and radius of the tube should be 1 m and 3.5 cm respectively [Top and bottom of the tube are of another material]?(use π=227)

The boundary of the circle is called as the ___ of the circle.

In a triangle ABC, the median CM is perpendicular to angular bisector AL, M being on AB and L being on BC. Also CM/AL = n. Find cosA in terms of n. 1) (9+4n²)/(9-4n²)2) (9-4n²)/(9+4n²)3) (5-4n²)/(5+4n²)4) (9-n²)/(9+n²)

Prove that 2+35 is an irrational number, given that 5 is an irrational number.

The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is

Unique point is obtained for the pair of equations a1x + b1y + c1 = 0 and a2x +b2y + c2 = 0 if __________ .

Which of the following numbers can be represented as non-terminating, repeating decimals?(a) 3924(b) 316(c) 311(d) 13725

Simplify(i) 11121114 .(ii) 712.812

A fraction becomes 45 if 1 is added to each of the numerator and denominator. However, if we subtract 5 from each, the fraction becomes 12. Find the fraction.

A circle with centre O has a radius of 3.5 cm. If the distance between O and point P is 5 cm, where does P lie with respect to the circle?

Question 49If pq is a rational number, then p cannot be equal to zero.

The value of √3cosec20∘−sec20∘ is

Question 37 Fill in the blanks to make the statement true. The number of cubes in are ___.

by watching a graph of polynomial , how can be find the value of a , b ,c that they are less than 0 or greater than 0

A is a point on the x axis with abscissa "-12" and B is a point on the y axis with ordinate 5. Find distance AB

Question 124Work out the surface area of the following shape.

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Select all the correct options.

Question 7The coordinates of a point at a distance of 3 units from the X-axis and 6 units from the Y-axis are(a) (0,3)(b) (6,0)(c) (3,6)(d) (6,3)

In a party there are 6 guests and if each other shake hand each other, how many shake hands occur in the party? Thank you..

Compare the given linear equation 2y=5x+7 with its standard form ax+by+c=0. What is the value of 'c' for the given equation?

Find the diameter of the circle shown below if the perimeter of the square ABCD is 16 m.

Find the curved surface area (m2) of a cylindrical concrete pillar whose radius and height are 70 cm and 10 m respectively.44

Find the magnitude of angle A, if 2 sin A cos A - cos A -2 sin A + 1 = 0

If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm in cm2.