24740 + Interview Questions in Mathematics Page 232 InterviewSolution

11551.	Question 18The product 3√2.4√2.12√32 equals toThinking processTake the LCM of indices of three irrational numbers. Then, convert all individually in the from whose index will be equal to LCM.A) √2B) 2C) 12√2D) 12√32
Answer» Question 18 The product $\sqrt[3]{2} . \sqrt[4]{2} . \sqrt[12]{32}$ equals to Thinking process Take the LCM of indices of three irrational numbers. Then, convert all individually in the from whose index will be equal to LCM. A) $\sqrt{2}$ B) $2$ C) $\sqrt[12]{2}$ D) $\sqrt[12]{32}$

Discussion

11552.	A father's age is thrice his son's age. The sum of their ages is 40 years. Find the son's age.
Answer» A father's age is thrice his son's age. The sum of their ages is 40 years. Find the son's age.

Discussion

11553.	In a parallelogram ABCD, if ∠A = 115o, then ∠B, ∠C and ∠D are
Answer» In a parallelogram ABCD, if ∠A = 115^o, then ∠B, ∠C and ∠D are

11553.

In a parallelogram ABCD, if ∠A = 115o, then ∠B, ∠C and ∠D are

Answer»

In a parallelogram ABCD, if ∠A = 115^o, then ∠B, ∠C and ∠D are

Discussion

11554.	Prove that “ The perpendicular from the centre of a circle to a chord bisects the chord”
Answer» Prove that “ The perpendicular from the centre of a circle to a chord bisects the chord”

Discussion

11555.	Without actually performing the long division, state whether 615 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

11556.	A circle has radius √2 cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in the major segment is 45∘.
Answer» A circle has radius $\sqrt{2}$ cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in the major segment is $45^{\circ}$ .

Discussion

11557.	Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.
Answer» Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

Discussion

11558.	The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if(a) ABCD is a Parallelogram(b) ABCD is rectangle(c) diagonals of ABCD are equal(d) diagonals of ABCD are perpendicular to each other.
Answer» The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if (a) ABCD is a Parallelogram (b) ABCD is rectangle (c) diagonals of ABCD are equal (d) diagonals of ABCD are perpendicular to each other.

Discussion

11559.	ABCD is a parallelogram, G is the point on AB such that AG = 2 GB, E is a point of DC such that CE = 2DE and F is the point of BC such that BF = 2FC. Prove that:(i) ar (ADEG) = ar (GBCE)(ii) ar (Δ EGB) = 16 ar (ABCD)(iii) ar (Δ EFC) = 12 ar (Δ EBF)(iv) ar (Δ EBG) = ar (Δ EFC)(v) Find what portion of the area of parallelogram is the area of Δ EFG
Answer» ABCD is a parallelogram, G is the point on AB such that AG = 2 GB, E is a point of DC such that CE = 2DE and F is the point of BC such that BF = 2FC. Prove that: (i) ar (ADEG) = ar (GBCE) (ii) ar (Δ EGB) = $\frac{1}{6}$ ar (ABCD) (iii) ar (Δ EFC) = $\frac{1}{2}$ ar (Δ EBF) (iv) ar (Δ EBG) = ar (Δ EFC) (v) Find what portion of the area of parallelogram is the area of Δ EFG

Discussion

11560.	The ___ co-ordinate of a point is the perpendicular distance of the point from the y axis.
Answer» The ___ co-ordinate of a point is the perpendicular distance of the point from the y axis.

11560.

The ___ co-ordinate of a point is the perpendicular distance of the point from the y axis.

Answer»

The

___

co-ordinate of a point is the perpendicular distance of the point from the y axis.

Discussion

11561.	In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE\|\|BP , then find the length of AE.
Answer» In the given figure, D is the mid-point of AB and $P C = \frac{1}{2} A P = 3$ cm. If $A D = D B = 4$ cm and $D E \| \| B P$ , then find the length of AE.

Discussion

11562.	What will be the probability that two friends have the same birthday date in a normal year ?
Answer» What will be the probability that two friends have the same birthday date in a normal year ?

Discussion

11563.	if error in measurement of diameter of a circle is 4%, the error in measurement of radius of a circle is
Answer» if error in measurement of diameter of a circle is 4%, the error in measurement of radius of a circle is

Discussion

11564.	In the given figure, O is the centre of the circle and PR is a diameter. If angleSPQ=90∘ andPA=PQ, then the value of (a+b+c–d+e–f) is
Answer» In the given figure, O is the centre of the circle and PR is a diameter. If $a n g l e S P Q = 90^{\circ} a n d P A = P Q,$ then the value of $(a + b + c - d + e - f)$ is

Discussion

11565.	Find: cos 75∘sin 15∘+sin 12∘cos 78∘−cos 18∘sin 72∘= ______.
Answer» Find: $\frac{cos 75^{\circ}}{sin 15^{\circ}} + \frac{sin 12^{\circ}}{cos 78^{\circ}} - \frac{cos 18^{\circ}}{sin 72^{\circ}} =$ ______.

Discussion

11566.	In the adjacent figure, □ABCD is a trapezium AB \|\| DC . Points M and N are midpoints of diagonal AC and DB respectively then prove that MN \|\| AB .
Answer» In the adjacent figure, $□$ ABCD is a trapezium AB \|\| DC . Points M and N are midpoints of diagonal AC and DB respectively then prove that MN \|\| AB .

Discussion

11567.	If x2+1x2=51, find the value of x3−1x3.
Answer» If $x^{2} + \frac{1}{x^{2}} = 51$ , find the value of $x^{3} - \frac{1}{x^{3}}$ .

Discussion

11568.	AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.
Answer» AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.

Discussion

11569.	at what points does the graph of the linear equation x+y=5 meet a line which is parallel to the y axis , at a distance 2 units from the origin and in positive direction of x axis.
Answer» at what points does the graph of the linear equation x+y=5 meet a line which is parallel to the y axis , at a distance 2 units from the origin and in positive direction of x axis.

Discussion

11570.	In an isosceles triangle AB = AC and X and Y are midpoints of AB and AC respectively, then the relation between AX and YC is:
Answer» In an isosceles triangle AB = AC and X and Y are midpoints of AB and AC respectively, then the relation between AX and YC is:

Discussion

11571.	For which of the following can a perpendicular bisector be drawn?
Answer» For which of the following can a perpendicular bisector be drawn?

Discussion

11572.	Let f(x) denote a polynomial of degree 3. Suppose f(x+2)−f(x)=x2+4x+4 and f(1)=9. Find the value of f(3)
Answer» Let f(x) denote a polynomial of degree 3. Suppose $f (x + 2) - f (x) = x^{2} + 4 x + 4 a n d f (1) = 9.$ Find the value of f(3)

Discussion

11573.	What is mathematics at the beginning and what it means to us in simple language not in typical words?
Answer» What is mathematics at the beginning and what it means to us in simple language not in typical words?

Discussion

11574.	An unbiased dice is thrown. What is the probability of getting an even number or a multiple of 3?
Answer» An unbiased dice is thrown. What is the probability of getting an even number or a multiple of 3?

Discussion

11575.	On examining the Bank Statement of Green Ltd., it is found that the balance shown on 31st March, 2019, differs from the bank balance of ₹ 23,650 shown by the Cash Book on that date. From a detailed comparison of the entries it is found that:(i) ₹ 2,860 is entered in the Cash Book as paid into the bank on 31st March, 2019 but not credited by the bank until the following day.(ii) Bank charges of ₹ 70 on 31st March, 2019 are not entered in the Cash Book.(iii) A bill for ₹ 5,500 discounted with the bank is entered in the Cash Book without recording the discount charges of ₹ 270.(iv) Cheques totalling ₹ 16,720 were issued by the company and duly recorded in the Cash Book before 31st March, 2019 but had not been presented at the Bank for payment until after that date.(v) On 25th March, 2019, a debtor paid ₹ 1,000 into the Company's Bank in settlement of his account but no entry was made in the Cash Book of the company in respect of this.(vi) No entry has been made in the Cash Book to record the dishonour on 15th March, 2019, of a cheque for ₹ 550 received from Ram Babu.Prepare a Bank Reconciliation Statement as on 31st March, 2019.
Answer» On examining the Bank Statement of Green Ltd., it is found that the balance shown on 31st March, 2019, differs from the bank balance of ₹ 23,650 shown by the Cash Book on that date. From a detailed comparison of the entries it is found that: (i) ₹ 2,860 is entered in the Cash Book as paid into the bank on 31st March, 2019 but not credited by the bank until the following day. (ii) Bank charges of ₹ 70 on 31st March, 2019 are not entered in the Cash Book. (iii) A bill for ₹ 5,500 discounted with the bank is entered in the Cash Book without recording the discount charges of ₹ 270. (iv) Cheques totalling ₹ 16,720 were issued by the company and duly recorded in the Cash Book before 31st March, 2019 but had not been presented at the Bank for payment until after that date. (v) On 25th March, 2019, a debtor paid ₹ 1,000 into the Company's Bank in settlement of his account but no entry was made in the Cash Book of the company in respect of this. (vi) No entry has been made in the Cash Book to record the dishonour on 15th March, 2019, of a cheque for ₹ 550 received from Ram Babu. Prepare a Bank Reconciliation Statement as on 31st March, 2019.

Discussion

11576.	What is the type of lines given in the below pictures called?
Answer» What is the type of lines given in the below pictures called?

Discussion

11577.	Question 5Factorise: (i) x3−2x2−x+2(ii) x3−3x2−9x−5(iii) x3+13x2+32x+20(iv) 2y3+y2−2y−1
Answer» Question 5 Factorise: (i) $x^{3} - 2 x^{2} - x + 2$ (ii) $x^{3} - 3 x^{2} - 9 x - 5$ (iii) $x^{3} + 13 x^{2} + 32 x + 20$ (iv) $2 y^{3} + y^{2} - 2 y - 1$

Discussion

11578.	Question 1 (i)Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.
Answer» Question 1 (i) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Discussion

11579.	44. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.
Answer» 44. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

Discussion

11580.	The shape of the top surface of a table is a trapezium. Find its area if it's parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8 m. An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round? Remember, Circumference of a circle can be obtained by the expression c=2πr, where r is the radius of the circle.
Answer» The shape of the top surface of a table is a trapezium. Find its area if it's parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8 m. An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round? Remember, Circumference of a circle can be obtained by the expression c=2πr, where r is the radius of the circle.

Discussion

11581.	31. Prove that the sum of all three altitudes of a triangle is less than the sum of sides of triangle
Answer» 31. Prove that the sum of all three altitudes of a triangle is less than the sum of sides of triangle

Discussion

11582.	The area of tapazium is 475cm^2 and height is 19cm. Find the length of its parallel sides,if one side is 4cm greater than other
Answer» The area of tapazium is 475cm^2 and height is 19cm. Find the length of its parallel sides,if one side is 4cm greater than other

Discussion

11583.	Factorise 98(a+b)2−2
Answer» Factorise $98 (a + b)^{2} - 2$

Discussion

11584.	ntABCD is a parallelogram; P and Q are the mid points of the sides AB and DC respectively. Prove that DP and BQ trisect AC and are trisect by AC.n
Answer» ntABCD is a parallelogram; P and Q are the mid points of the sides AB and DC respectively. Prove that DP and BQ trisect AC and are trisect by AC.n

Discussion

11585.	A big iron boiler tank opened on top is cylindrical in shape. It's height is 10 m and radius is 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it totally gets corroded is (Take pi=227)
Answer» A big iron boiler tank opened on top is cylindrical in shape. It's height is 10 m and radius is 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it totally gets corroded is (Take pi= $\frac{22}{7}$ )

Discussion

11586.	A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Answer» A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Discussion

11587.	Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1.5 times the corresponding sides of the isosceles triangle.
Answer» Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1.5 times the corresponding sides of the isosceles triangle.

Discussion

11588.	FInd x : 174×172=17x
Answer» FInd x : $17^{4} \times 17^{2} = 17^{x}$

Discussion

11589.	Construct a trapezium ABCD, in which AD∥BC, AD = 3 cm, AB = 2.5 cm, BC = 5 cm, and CD = 2.8 cm.
Answer» Construct a trapezium ABCD, in which $A D ∥ B C$ , AD = 3 cm, AB = 2.5 cm, BC = 5 cm, and CD = 2.8 cm.

Discussion

11590.	If Sin A +Cosec A= 2 Then sin2A + cosec2A=__
Answer» If Sin A +Cosec A= 2 Then $s i n^{2}$ A + $c o s e c^{2}$ A=__

11590.

If Sin A +Cosec A= 2 Then sin2A + cosec2A=__

Answer»

If Sin A +Cosec A= 2

Then $s i n^{2}$ A + $c o s e c^{2}$ A=__

Discussion

11591.	The point C (–1,2) divides the lines segment AB in the ratio 3:4, the coordinates of A are (2, 5). The coordinates of B are:
Answer» The point C (–1,2) divides the lines segment AB in the ratio 3:4, the coordinates of A are (2, 5). The coordinates of B are:

Discussion

11592.	Question 6 (ii)Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 112 Years if the interest is:(ii) Compounded half yearly.
Answer» Question 6 (ii) Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after $1 \frac{1}{2}$ Years if the interest is: (ii) Compounded half yearly.

Discussion

11593.	If x=210-8 and y=210+22, then (x-y)2=____________.
Answer» If $x = \frac{2}{\sqrt{10} - \sqrt{8}} and y = \frac{2}{\sqrt{10} + 2 \sqrt{2}}, then {(x - y)}^{2} =____________.$

Discussion

11594.	In a ΔABC,∠C=3∠B=2(∠A+∠B). Find the angles.
Answer» In a $Δ A B C, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B)$ . Find the angles.

Discussion

11595.	Marks of students of a Class are represented in the frequency polygon shown below. How many students got marks less than 20?39
Answer» Marks of students of a Class are represented in the frequency polygon shown below. How many students got marks less than 20? 39

Discussion

11596.	In the given Fig arcs have been drawn with radii 14 cm each and with centres P, Q and R. find the area of the shaded region if PQR is an equilateral triangle of side 35cm. [3 MARKS]
Answer» In the given Fig arcs have been drawn with radii 14 cm each and with centres P, Q and R. find the area of the shaded region if PQR is an equilateral triangle of side 35cm. [3 MARKS]

11596.

In the given Fig arcs have been drawn with radii 14 cm each and with centres P, Q and R. find the area of the shaded region if PQR is an equilateral triangle of side 35cm. [3 MARKS]

Answer»

In the given Fig arcs have been drawn with radii 14 cm each and with centres P, Q and R. find the area of the shaded region if PQR is an equilateral triangle of side 35cm. [3 MARKS]

Discussion

11597.	If the altitude of the triangle are equal, then prove that it is the equilateral triangle
Answer» If the altitude of the triangle are equal, then prove that it is the equilateral triangle

Discussion

11598.	Lines AC and BD intersect at point P. m∠APD = 47° .Find the measures of ∠APB, ∠BPC, ∠CPD.
Answer» Lines AC and BD intersect at point P. m∠APD = 47^° .Find the measures of ∠APB, ∠BPC, ∠CPD.

Discussion

11599.	How many circles can be drawn passing through three collinear points?
Answer» How many circles can be drawn passing through three collinear points?

Discussion

11600.	Without actually calculating the cubes find the value of (9.8)3-(11.3)3+(1.5)3
Answer» Without actually calculating the cubes find the value of (9.8)³-(11.3)³+(1.5)³

Discussion

Explore topic-wise InterviewSolutions in .

Question 18The product 3√2.4√2.12√32 equals toThinking processTake the LCM of indices of three irrational numbers. Then, convert all individually in the from whose index will be equal to LCM.A) √2B) 2C) 12√2D) 12√32

A father's age is thrice his son's age. The sum of their ages is 40 years. Find the son's age.

In a parallelogram ABCD, if ∠A = 115o, then ∠B, ∠C and ∠D are

Prove that “ The perpendicular from the centre of a circle to a chord bisects the chord”

Without actually performing the long division, state whether 615 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

A circle has radius √2 cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in the major segment is 45∘.

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if(a) ABCD is a Parallelogram(b) ABCD is rectangle(c) diagonals of ABCD are equal(d) diagonals of ABCD are perpendicular to each other.

The ___ co-ordinate of a point is the perpendicular distance of the point from the y axis.

In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE||BP , then find the length of AE.

What will be the probability that two friends have the same birthday date in a normal year ?

if error in measurement of diameter of a circle is 4%, the error in measurement of radius of a circle is

In the given figure, O is the centre of the circle and PR is a diameter. If angleSPQ=90∘ andPA=PQ, then the value of (a+b+c–d+e–f) is

Find: cos 75∘sin 15∘+sin 12∘cos 78∘−cos 18∘sin 72∘= ______.

In the adjacent figure, □ABCD is a trapezium AB || DC . Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB .

If x2+1x2=51, find the value of x3−1x3.

AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.

at what points does the graph of the linear equation x+y=5 meet a line which is parallel to the y axis , at a distance 2 units from the origin and in positive direction of x axis.

In an isosceles triangle AB = AC and X and Y are midpoints of AB and AC respectively, then the relation between AX and YC is:

For which of the following can a perpendicular bisector be drawn?

Let f(x) denote a polynomial of degree 3. Suppose f(x+2)−f(x)=x2+4x+4 and f(1)=9. Find the value of f(3)

What is mathematics at the beginning and what it means to us in simple language not in typical words?

An unbiased dice is thrown. What is the probability of getting an even number or a multiple of 3?

What is the type of lines given in the below pictures called?

Question 5Factorise: (i) x3−2x2−x+2(ii) x3−3x2−9x−5(iii) x3+13x2+32x+20(iv) 2y3+y2−2y−1

Question 1 (i)Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

44. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

31. Prove that the sum of all three altitudes of a triangle is less than the sum of sides of triangle

The area of tapazium is 475cm^2 and height is 19cm. Find the length of its parallel sides,if one side is 4cm greater than other

Factorise 98(a+b)2−2

ntABCD is a parallelogram; P and Q are the mid points of the sides AB and DC respectively. Prove that DP and BQ trisect AC and are trisect by AC.n

A big iron boiler tank opened on top is cylindrical in shape. It's height is 10 m and radius is 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it totally gets corroded is (Take pi=227)

A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1.5 times the corresponding sides of the isosceles triangle.

FInd x : 174×172=17x

Construct a trapezium ABCD, in which AD∥BC, AD = 3 cm, AB = 2.5 cm, BC = 5 cm, and CD = 2.8 cm.

If Sin A +Cosec A= 2 Then sin2A + cosec2A=__

The point C (–1,2) divides the lines segment AB in the ratio 3:4, the coordinates of A are (2, 5). The coordinates of B are:

Question 6 (ii)Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 112 Years if the interest is:(ii) Compounded half yearly.

If x=210-8 and y=210+22, then (x-y)2=____________.

In a ΔABC,∠C=3∠B=2(∠A+∠B). Find the angles.

Marks of students of a Class are represented in the frequency polygon shown below. How many students got marks less than 20?39

In the given Fig arcs have been drawn with radii 14 cm each and with centres P, Q and R. find the area of the shaded region if PQR is an equilateral triangle of side 35cm. [3 MARKS]

If the altitude of the triangle are equal, then prove that it is the equilateral triangle

Lines AC and BD intersect at point P. m∠APD = 47° .Find the measures of ∠APB, ∠BPC, ∠CPD.

How many circles can be drawn passing through three collinear points?

Without actually calculating the cubes find the value of (9.8)3-(11.3)3+(1.5)3