24740 + Interview Questions in Mathematics Page 135 InterviewSolution

6701.	Question 6Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Answer» Question 6 Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Discussion

6702.	Which figure comes next?
Answer» Which figure comes next?

6702.

Which figure comes next?

Answer»

Which figure comes next?

Discussion

6703.	Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
Answer» Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

Discussion

6704.	Let the area of parallelogram ABDC be p and the area of parallelogram ABFE be q. What is the relation between p and q? [Distance between AB and CD is equal to distance between AB and EF]
Answer» Let the area of parallelogram $A B D C$ be $p$ and the area of parallelogram $A B F E$ be $q$ . What is the relation between $p$ and $q$ ? [Distance between $A B$ and $C D$ is equal to distance between $A B$ and $E F$ ]

6704.

Let the area of parallelogram ABDC be p and the area of parallelogram ABFE be q. What is the relation between p and q? [Distance between AB and CD is equal to distance between AB and EF]

Answer»

Let the area of parallelogram $A B D C$ be $p$ and the area of parallelogram $A B F E$ be $q$ . What is the relation between $p$ and $q$ ? [Distance between $A B$ and $C D$ is equal to distance between $A B$ and $E F$ ]

Discussion

6705.	31 A particle goes from point P to point Q oncircular path of radius R. The distance travelled ingoing from P to Q isR0(2)2(1) R cos (3y R sin 0V4) RO
Answer» 31 A particle goes from point P to point Q oncircular path of radius R. The distance travelled ingoing from P to Q isR0(2)2(1) R cos (3y R sin 0V4) RO

Discussion

6706.	Zero of the polynomial p(x) = 2x + 5 is(a) -25(b) -52(c) 25(d) 52
Answer» Zero of the polynomial p(x) = 2x + 5 is (a) $\frac{- 2}{5}$ (b) $\frac{- 5}{2}$ (c) $\frac{2}{5}$ (d) $\frac{5}{2}$

Discussion

6707.	Question 3 Factorise the following using appropriate identities: (i) 9x2+6xy+y2 (ii) 4y2−4y+1 (iii) x2−y2100
Answer» Question 3 Factorise the following using appropriate identities: (i) $9 x^{2} + 6 x y + y^{2}$ (ii) $4 y^{2} - 4 y + 1$ (iii) $x^{2} - \frac{y^{2}}{100}$

Discussion

6708.	1.666666...... is a rational number and can be expressed in pq form. Then p + q is ______.
Answer» 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form. Then p + q is ______.

Discussion

6709.	If each side of a triangle is doubled,t hen find the ratio of area of the new triangle they formedand the original triangle
Answer» If each side of a triangle is doubled,t hen find the ratio of area of the new triangle they formedand the original triangle

Discussion

6710.	A roof is made by using 20 triangular rocks which are equally divided in 4 different colours.The sides of each piece are 2 m, 5 m and 5 m. What is the area covered by each colour?
Answer» A roof is made by using 20 triangular rocks which are equally divided in 4 different colours.The sides of each piece are 2 m, 5 m and 5 m. What is the area covered by each colour?

Discussion

6711.	The two numbers between 116,16 such that first three may be in G.P. and the last three in H.P. are respectively.
Answer» The two numbers between $\frac{1}{16}, \frac{1}{6}$ such that first three may be in G.P. and the last three in H.P. are respectively.

Discussion

6712.	If a+b+c=0 and △=∣∣∣∣abcbcacab∣∣∣∣, then which of the following is correct?
Answer» If $a + b + c = 0$ and $△ = ∣ ∣∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣∣ ∣,$ then which of the following is correct?

Discussion

6713.	In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]
Answer» In Fig. AC = AE, AB = AD and $∠$ BAD = $∠$ EAC. Prove that BC = DE. [2 MARKS]

6713.

In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]

Answer»

In Fig. AC = AE, AB = AD and $∠$ BAD = $∠$ EAC. Prove that BC = DE.
[2 MARKS]

Discussion

6714.	Find the roots of the equation: x−5=0
Answer» Find the roots of the equation: $x - 5 = 0$

Discussion

6715.	If 7x=1000 then, x=_____.
Answer» If $7^{x} = 1000$ then, x=_____.

Discussion

6716.	The distance between the points (1, 3) and (5, 6) is ___ units.
Answer» The distance between the points (1, 3) and (5, 6) is ___ units.

Discussion

6717.	If two equations intersect at one point, what do we call that system of equations?
Answer» If two equations intersect at one point, what do we call that system of equations?

Discussion

6718.	From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that ΔAPB is equilateral.
Answer» From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that $Δ A P B$ is equilateral.

Discussion

6719.	A hemispherical tank, of diameter 3m, is full of water. It is being emptied by a pipe at the rate of 347 litre per second. How much time will it take to make the tank half empty?
Answer» A hemispherical tank, of diameter 3m, is full of water. It is being emptied by a pipe at the rate of $3 \frac{4}{7}$ litre per second. How much time will it take to make the tank half empty?

Discussion

6720.	A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60∘. After some time, the angle of elevation reduces to 30∘. Find the distance traveled by the balloon during the interval.
Answer» A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$ . After some time, the angle of elevation reduces to $30^{\circ}$ . Find the distance traveled by the balloon during the interval.

Discussion

6721.	The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2?
Answer» The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m²?

Discussion

6722.	Tallys are usually marked in a bunch of(a) 3(b) 4(c) 5(d) 6
Answer» Tallys are usually marked in a bunch of (a) 3 (b) 4 (c) 5 (d) 6

Discussion

6723.	For any two sets A & B as shown in the diagram below, A△ B=
Answer» For any two sets $A & B$ as shown in the diagram below, $A △ B =$

Discussion

6724.	The simplest rationalising factor of 5003 is(a) 23(b) 53(c) 3(d) none of these
Answer» The simplest rationalising factor of $\sqrt[3]{500}$ is (a) $\sqrt[3]{2}$ (b) $\sqrt[3]{5}$ (c) $\sqrt{3}$ (d) none of these

Discussion

6725.	(i) What do you mean by convex and concave Quadrilaterals?(ii) The angles of a Quadrilateral ABCD are in the ratio of 3:4:5:6. Find the largest angle.
Answer» (i) What do you mean by convex and concave Quadrilaterals? (ii) The angles of a Quadrilateral ABCD are in the ratio of $3 : 4 : 5 : 6$ . Find the largest angle.

Discussion

6726.	Two poles of heights 8 m and 15 m stand vertically on a plane ground. If the distance between their feet is 24 m, then find the distance between their top ends.
Answer» Two poles of heights 8 m and 15 m stand vertically on a plane ground. If the distance between their feet is 24 m, then find the distance between their top ends.

Discussion

6727.	The volume of a hemisphere is 19404 cm3. Then, its total surface area is _____.
Answer» The volume of a hemisphere is $19404 c m^{3} .$ Then, its total surface area is _____.

Discussion

6728.	Sketch the graph \|y\|=\|1/(\|x\|+5)\|
Answer» Sketch the graph \|y\|=\|1/(\|x\|+5)\|

Discussion

6729.	Find the number of terms in the expression obtained by adding the following expressions:9x2−2yz and 2y+x2.
Answer» Find the number of terms in the expression obtained by adding the following expressions: $9 x^{2} - 2 yz and 2 y + x^{2} .$

Discussion

6730.	Match the following with the values of 'x'.
Answer» Match the following with the values of 'x'.

Discussion

6731.	Fill in the blank with the correct sign.The conjugate of 1+√2 is 1 √2.
Answer» $Fill in the blank with the correct sign . The conjugate of 1 + \sqrt{2} is 1$ $\sqrt{2} .$

Discussion

6732.	The square of a number is 2.25. Find the number.
Answer» The square of a number is $2.25.$ Find the number.

Discussion

6733.	Factorise:x2 + 20x – 69
Answer» Factorise: x² + 20x – 69

Discussion

6734.	Can you give me shortcut formulas to solve questions of compound interest, simple interest, profit and loss, percentage, ratio and proportion... Which can help me to save time in my examination Thanking you Regards
Answer» Can you give me shortcut formulas to solve questions of compound interest, simple interest, profit and loss, percentage, ratio and proportion... Which can help me to save time in my examination Thanking you Regards

6734.

Can you give me shortcut formulas to solve questions of compound interest, simple interest, profit and loss, percentage, ratio and proportion... Which can help me to save time in my examination Thanking you Regards

Answer»

Can you give me shortcut formulas to solve questions of compound interest, simple interest, profit and loss, percentage, ratio and proportion... Which can help me to save time in my examination

Thanking you

Regards

Discussion

6735.	Question 11 (i)By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.3x+y+4 = 0, 6x – 2y + 4 = 0
Answer» Question 11 (i) By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then. 3x+y+4 = 0, 6x – 2y + 4 = 0

Discussion

6736.	Correct the following errors in Mohan Lal’s Book:(i) A payment of ₹ 5,000 for salaries (to Mr. Ram) has been posted twice to the Salaries Account.(ii) ₹ 750 received from Rajesh are entered on the debit side of the Cash Book. No posting was done in Rajesh’s Account.(iii) Sales Book was overcasted by ₹ 3,000.(iv) Goods (Cost ₹ 2,000, Sales Price ₹ 2,500) distributed as samples among prospective customers were not recorded anywhere.(v) A sum of ₹ 1,500 written off as depreciation on furniture was not debited to Depreciation Account.
Answer» Correct the following errors in Mohan Lal’s Book: (i) A payment of ₹ 5,000 for salaries (to Mr. Ram) has been posted twice to the Salaries Account. (ii) ₹ 750 received from Rajesh are entered on the debit side of the Cash Book. No posting was done in Rajesh’s Account. (iii) Sales Book was overcasted by ₹ 3,000. (iv) Goods (Cost ₹ 2,000, Sales Price ₹ 2,500) distributed as samples among prospective customers were not recorded anywhere. (v) A sum of ₹ 1,500 written off as depreciation on furniture was not debited to Depreciation Account.

Discussion

6737.	1) A point O is taken inside a rhombus ABCD such that OB=OD. Prove that the points A, O and C are collinear points.
Answer» 1) A point O is taken inside a rhombus ABCD such that OB=OD. Prove that the points A, O and C are collinear points.

Discussion

6738.	Fill in the blanks(i) The centre of a circle lies in __________ of the circle. (exterior/ interior)(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)(iii) The longest chord of a circle is a __________ of the circle.(iv) An arc is a __________ when its ends are the ends of a diameter.(v) Segment of a circle is the region between an arc and __________ of the circle.(vi) A circle divides the plane, on which it lies, in __________ parts.
Answer» Fill in the blanks (i) The centre of a circle lies in __________ of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior) (iii) The longest chord of a circle is a __________ of the circle. (iv) An arc is a __________ when its ends are the ends of a diameter. (v) Segment of a circle is the region between an arc and __________ of the circle. (vi) A circle divides the plane, on which it lies, in __________ parts.

6738.

Fill in the blanks(i) The centre of a circle lies in of the circle. (exterior/ interior)(ii) A point, whose distance from the centre of a circle is greater than its radius lies in of the circle. (exterior/ interior)(iii) The longest chord of a circle is a of the circle.(iv) An arc is a when its ends are the ends of a diameter.(v) Segment of a circle is the region between an arc and of the circle.(vi) A circle divides the plane, on which it lies, in parts.

Answer»

Fill in the blanks

(i) The centre of a circle lies in __________ of the circle. (exterior/ interior)

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

(iii) The longest chord of a circle is a __________ of the circle.

(iv) An arc is a __________ when its ends are the ends of a diameter.

(v) Segment of a circle is the region between an arc and __________ of the circle.

(vi) A circle divides the plane, on which it lies, in __________ parts.

Discussion

6739.

The marks scored by 55 students in a test are given below: Marks: 0-5 5-10 10-15 15-20 20-25 25-30 30-35 No. of students 2 6 13 17 11 4 2 Prepare a cumulative frequency table.

Answer» The marks scored by 55 students in a test are given below:

Marks:	0-5	5-10	10-15	15-20	20-25	25-30	30-35
No. of students	2	6	13	17	11	4	2

Prepare a cumulative frequency table.

Discussion

6740.	O is the centre of the circle of radius 5 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB\|\|CD, AB=6 cm and CD=8 cm. Determine PQ.
Answer» $O$ is the centre of the circle of radius $5 c m, O P$ is perpendicular to $A B, O Q$ is perpendicular to $C D, A B \| \| C D, A B = 6 c m$ and $C D = 8 c m .$ Determine $P Q .$

Discussion

6741.	If 49a2−b=(7a+12)(7a−12),then the value of b is
Answer» If $49 a^{2} - b = (7 a + \frac{1}{2}) (7 a - \frac{1}{2}),$ then the value of b is

Discussion

6742.	Reduce thefollowing fractions to simplest form:(a) (b) (c) (d) (e)
Answer» Reduce the following fractions to simplest form: (a) (b) (c) (d) (e)

6742.

Reduce thefollowing fractions to simplest form:(a) (b) (c) (d) (e)

Answer»

Reduce the
following fractions to simplest form:

(a) (b)

(c) (d)

(e)

Discussion

6743.	26. If the arc of the same length in two circles subtend angles 60 and 110 degree at centre find ratio of their radii
Answer» 26. If the arc of the same length in two circles subtend angles 60 and 110 degree at centre find ratio of their radii

Discussion

6744.	In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ∠1, ∠2 and ∠3.
Answer» In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ∠1, ∠2 and ∠3.

Discussion

6745.	Question 6 (i)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(i) ar(DOC) = ar(AOB)
Answer» Question 6 (i) In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (i) ar(DOC) = ar(AOB)

Discussion

6746.	In the figure, if AB=AC and ∠B=∠C. Prove that BQ = CP.
Answer» In the figure, if $A B = A C a n d ∠ B = ∠ C .$ Prove that BQ = CP.

6746.

In the figure, if AB=AC and ∠B=∠C. Prove that BQ = CP.

Answer»

In the figure, if $A B = A C a n d ∠ B = ∠ C .$

Prove that BQ = CP.

Discussion

6747.	A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surfaced of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
Answer» A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surfaced of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Discussion

6748.	A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of cylinder to cone is 4:3, then the ratio of their volumes is
Answer» A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of cylinder to cone is $4 : 3,$ then the ratio of their volumes is

Discussion

6749.	Find the mean of the first ten prime numbers.
Answer» Find the mean of the first ten prime numbers.

Discussion

6750.	212+213+214110×25×1256 is equal to:
Answer» $\frac{2 \frac{1}{2} + 2 \frac{1}{3} + 2 \frac{1}{4}}{\frac{1}{10} \times \frac{2}{5} \times \frac{125}{6}}$ is equal to:

Discussion

Explore topic-wise InterviewSolutions in .

Question 6Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Which figure comes next?

Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.

Let the area of parallelogram ABDC be p and the area of parallelogram ABFE be q. What is the relation between p and q? [Distance between AB and CD is equal to distance between AB and EF]

31 A particle goes from point P to point Q oncircular path of radius R. The distance travelled ingoing from P to Q isR0(2)2(1) R cos (3y R sin 0V4) RO

Zero of the polynomial p(x) = 2x + 5 is(a) -25(b) -52(c) 25(d) 52

Question 3 Factorise the following using appropriate identities: (i) 9x2+6xy+y2 (ii) 4y2−4y+1 (iii) x2−y2100

1.666666...... is a rational number and can be expressed in pq form. Then p + q is ______.

If each side of a triangle is doubled,t hen find the ratio of area of the new triangle they formedand the original triangle

A roof is made by using 20 triangular rocks which are equally divided in 4 different colours.The sides of each piece are 2 m, 5 m and 5 m. What is the area covered by each colour?

The two numbers between 116,16 such that first three may be in G.P. and the last three in H.P. are respectively.

If a+b+c=0 and △=∣∣∣∣abcbcacab∣∣∣∣, then which of the following is correct?

In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]

Find the roots of the equation: x−5=0

If 7x=1000 then, x=_____.

The distance between the points (1, 3) and (5, 6) is ___ units.

If two equations intersect at one point, what do we call that system of equations?

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that ΔAPB is equilateral.

A hemispherical tank, of diameter 3m, is full of water. It is being emptied by a pipe at the rate of 347 litre per second. How much time will it take to make the tank half empty?

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2?

Tallys are usually marked in a bunch of(a) 3(b) 4(c) 5(d) 6

For any two sets A &amp; B as shown in the diagram below, A△ B=

The simplest rationalising factor of 5003 is(a) 23(b) 53(c) 3(d) none of these

(i) What do you mean by convex and concave Quadrilaterals?(ii) The angles of a Quadrilateral ABCD are in the ratio of 3:4:5:6. Find the largest angle.

Two poles of heights 8 m and 15 m stand vertically on a plane ground. If the distance between their feet is 24 m, then find the distance between their top ends.

The volume of a hemisphere is 19404 cm3. Then, its total surface area is _____.

Sketch the graph |y|=|1/(|x|+5)|

Find the number of terms in the expression obtained by adding the following expressions:9x2−2yz and 2y+x2.

Match the following with the values of 'x'.

Fill in the blank with the correct sign.The conjugate of 1+√2 is 1 √2.

The square of a number is 2.25. Find the number.

Factorise:x2 + 20x – 69

Can you give me shortcut formulas to solve questions of compound interest, simple interest, profit and loss, percentage, ratio and proportion... Which can help me to save time in my examination Thanking you Regards

Question 11 (i)By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.3x+y+4 = 0, 6x – 2y + 4 = 0

1) A point O is taken inside a rhombus ABCD such that OB=OD. Prove that the points A, O and C are collinear points.

The marks scored by 55 students in a test are given below: Marks: 0-5 5-10 10-15 15-20 20-25 25-30 30-35 No. of students 2 6 13 17 11 4 2 Prepare a cumulative frequency table.

O is the centre of the circle of radius 5 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB||CD, AB=6 cm and CD=8 cm. Determine PQ.

If 49a2−b=(7a+12)(7a−12),then the value of b is

Reduce thefollowing fractions to simplest form:(a) (b) (c) (d) (e)

26. If the arc of the same length in two circles subtend angles 60 and 110 degree at centre find ratio of their radii

In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ∠1, ∠2 and ∠3.

Question 6 (i)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(i) ar(DOC) = ar(AOB)

In the figure, if AB=AC and ∠B=∠C. Prove that BQ = CP.

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surfaced of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of cylinder to cone is 4:3, then the ratio of their volumes is

Find the mean of the first ten prime numbers.

212+213+214110×25×1256 is equal to:

For any two sets A & B as shown in the diagram below, A△ B=