24740 + Interview Questions in Mathematics Page 108 InterviewSolution

5351.	Question 2In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to(A) 2 cm(B) 3 cm(C) 4 cm(D) 5 cm
Answer» Question 2 In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

Discussion

5352.	In a triangle with sides a, b and c, let s be the semiperimeter and p be the perimeter. The value of ps is ___.
Answer» In a triangle with sides a, b and c, let s be the semiperimeter and p be the perimeter. The value of $\frac{p}{s}$ is ___.

Discussion

5353.	If 2x−1=25=2a−4, then find the value of x and a.
Answer» If $2^{x - 1} = 2^{5} = 2^{a - 4}$ , then find the value of $x$ and $a$ .

Discussion

5354.	Question 8 (ii) Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: 1623512584810341228151176328596871412 (ii) How many children watched television for 15 or more hours a week?
Answer» Question 8 (ii) Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: $\begin{matrix} 1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12 \end{matrix}$ (ii) How many children watched television for 15 or more hours a week?

Discussion

5355.	In the given figure, arcs are drawn by taking vertices A,B and C of an equilateral triangle of side 10 cm, to intersect the sides BC,CA and AB at their respective mid-points D,E and F. Find the area of the shaded region.(Use π=3.14)
Answer» In the given figure, arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side 10 cm, to intersect the sides $B C, C A a n d A B$ at their respective mid-points $D, E a n d F$ . Find the area of the shaded region. $(U s e π = 3.14)$

Discussion

5356.	Factorise: x(a-5)+y(5-a)
Answer» Factorise: x(a-5)+y(5-a)

Discussion

5357.	In the adjoining figure, PQRS is a trapezium in which PQ \|\| SR and M is the midpoint of PS. A line segment MN \|\| PQ meets QR at N. Show that N is the midpoint of QR.
Answer» In the adjoining figure, PQRS is a trapezium in which PQ \|\| SR and M is the midpoint of PS. A line segment MN \|\| PQ meets QR at N. Show that N is the midpoint of QR.

5357.

In the adjoining figure, PQRS is a trapezium in which PQ || SR and M is the midpoint of PS. A line segment MN || PQ meets QR at N. Show that N is the midpoint of QR.

Answer»

In the adjoining figure, PQRS is a trapezium in which PQ || SR and M is the midpoint of PS. A line segment MN || PQ meets QR at N. Show that N is the midpoint of QR.

Discussion

5358.	if there are six straight lines in a plane,no two of which are parallel and no three of which pass through the same point,then find the number of points in which these lines intersect
Answer» if there are six straight lines in a plane,no two of which are parallel and no three of which pass through the same point,then find the number of points in which these lines intersect

Discussion

5359.	Water is discharged from a pipe of cross section area 3.2cm2 at a speed of 5m/s. Find the volume of water discharged in cm3 per second.
Answer» Water is discharged from a pipe of cross section area 3.2 $c m^{2}$ at a speed of 5m/s. Find the volume of water discharged in $c m^{3}$ per second.

Discussion

5360.	An iron tank with an open top is cylindrical in shape. It has a height 10m and radius 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it gets completely corroded is (Take pi=227)
Answer» An iron tank with an open top is cylindrical in shape. It has a height 10m and radius 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it gets completely corroded is (Take pi= $\frac{22}{7}$ )

Discussion

5361.	If the mean deviation of the numbers 1,1+d,1+2d,⋅,1+100d from their mean is 255, then d is equal to:
Answer» If the mean deviation of the numbers $1, 1 + d, 1 + 2 d, \cdot, 1 + 100 d$ from their mean is 255, then $d$ is equal to:

Discussion

5362.	If axn is a zero degree polynomial in x, what can be said about a?
Answer» If $a x^{n}$ is a zero degree polynomial in x, what can be said about a?

Discussion

5363.	If the average of a, b,c,d is the average of b and c, then the value of a – b – c + d is ___________.
Answer» If the average of a, b,c,d is the average of b and c, then the value of a – b – c + d is ___________.

Discussion

5364.	Question 1 (iv) Fill in the blanks: (iv) An arc is a __________ when its ends are the ends of a diameter.
Answer» Question 1 (iv) Fill in the blanks: (iv) An arc is a __________ when its ends are the ends of a diameter.

Discussion

5365.	Factorise: 27x3+y3+z3−9xyz
Answer» Factorise: $27 x^{3} + y^{3} + z^{3} - 9 x y z$

Discussion

5366.	Question 7(iii)Using a2−b2=(a+b)(a−b), find1533−1472
Answer» Question 7(iii) Using $a^{2} - b^{2} = (a + b) (a - b),$ find $153^{3} - 147^{2}$

Discussion

5367.	In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.
Answer» In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.

5367.

In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.

Answer»

In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.

Discussion

5368.	The number of decimal place after which the decimal expansion of the rational number 2322×5will terminate, is(a) 1(b) 2(c) 3(d) 4
Answer» The number of decimal place after which the decimal expansion of the rational number $\frac{23}{2^{2} \times 5}$ will terminate, is (a) 1 (b) 2 (c) 3 (d) 4

Discussion

5369.	ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = 12 ∠A.
Answer» ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = $\frac{1}{2}$ ∠A.

Discussion

5370.	Factorise:62x-3x2+72x-3x-20
Answer» Factorise: $6 {(2 x - \frac{3}{x})}^{2} + 7 (2 x - \frac{3}{x}) - 20$

Discussion

5371.	Find the following products:(i) (3x + 2y) (9x2 − 6xy + 4y2)(ii) (4x − 5y) (16x2 + 20xy + 25y2)(iii) (7p4 + q) (49p8 − 7p4q + q2)(iv) x2+2y x24-xy + 4y2(v) 3x-5y 9x2+25y2+15xy(vi) 3+5x 9-15x+25x2(vii) 2x+3x 4x2+9x2-6(viii) 3x-2x2 9x2+4x4-6x(ix) (1 − x) (1+ x + x2)(x) (1 + x) (1 − x + x2)(xi) (x2 − 1) (x4 + x2 + 1)(xii) (x3 + 1) (x6 − x3 + 1)
Answer» Find the following products: (i) (3x + 2y) (9x² − 6xy + 4y²) (ii) (4x − 5y) (16x² + 20xy + 25y²) (iii) (7p⁴ + q) (49p⁸ − 7p⁴q + q²) (iv) $(\frac{x}{2} + 2 y) (\frac{x^{2}}{4} - x y + 4 y^{2})$ (v) $(\frac{3}{x} - \frac{5}{y}) (\frac{9}{x^{2}} + \frac{25}{y^{2}} + \frac{15}{x y})$ (vi) $(3 + \frac{5}{x}) (9 - \frac{15}{x} + \frac{25}{x^{2}})$ (vii) $(\frac{2}{x} + 3 x) (\frac{4}{x^{2}} + 9 x^{2} - 6)$ (viii) $(\frac{3}{x} - 2 x^{2}) (\frac{9}{x^{2}} + 4 x^{4} - 6 x)$ (ix) (1 − x) (1+ x + x²) (x) (1 + x) (1 − x + x²) (xi) (x² − 1) (x⁴ + x² + 1) (xii) (x³ + 1) (x⁶ − x^{3 +}1)

Discussion

5372.	There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.
Answer» There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

5372.

There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

Answer»

There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

Discussion

5373.	The volume of a sphere is equal to ___ the volume of a cylinder of the same height and diameter.
Answer» The volume of a sphere is equal to ___ the volume of a cylinder of the same height and diameter.

Discussion

5374.	The number of workers for a job and the time needed to complete the job
Answer» The number of workers for a job and the time needed to complete the job

Discussion

5375.	In a triangle ABC ,D is any point on BC such that AD bisects angle A.Prove that AB>BD.
Answer» In a triangle ABC ,D is any point on BC such that AD bisects angle A.Prove that AB>BD.

Discussion

5376.	In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :(i)(ii)(iii)(iv)
Answer» In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following : (i) (ii) (iii) (iv)

Discussion

5377.	What is the value of x if the pair of linear equation x+3y=6 and 2x−3y=12 intersect at a point?6
Answer» What is the value of x if the pair of linear equation $x + 3 y = 6$ and $2 x - 3 y = 12$ intersect at a point? 6

Discussion

5378.	In the given figure, O is a point in the interior of square ABCD such that ΔOAB is an equilateral triangle.Show that ΔOCD is an isosceles triangle.
Answer» $In the given figure, O is a point in the interior of square ABCD such that Δ O A B is an equilateral triangle. Show that Δ O C D is an isosceles triangle.$

5378.

In the given figure, O is a point in the interior of square ABCD such that ΔOAB is an equilateral triangle.Show that ΔOCD is an isosceles triangle.

Answer»

$In the given figure, O is a point in the interior of square ABCD such that Δ O A B is an equilateral triangle. Show that Δ O C D is an isosceles triangle.$

Discussion

5379.	A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. Find acute angle between the diagonals.
Answer» A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$ . Find acute angle between the diagonals.

5379.

A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. Find acute angle between the diagonals.

Answer»

A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$ . Find acute angle between the diagonals.

Discussion

5380.	40. A circle of radius 2 cm is divided in to two segment by a chord of length 2cm, than the angle subtended by the chord at a point in major segment is
Answer» 40. A circle of radius 2 cm is divided in to two segment by a chord of length 2cm, than the angle subtended by the chord at a point in major segment is

Discussion

5381.	Solve the following equation for A (1) 2 sin A =1 (2) root 3 tan A = 1
Answer» Solve the following equation for A (1) 2 sin A =1 (2) root 3 tan A = 1

Discussion

5382.	In ∆PQR, PQ = 10 cm, QR = 12 cm, PR = 8 cm. Find out the greatest and the smallest angle of the triangle.
Answer» In $∆$ PQR, PQ = 10 cm, QR = 12 cm, PR = 8 cm. Find out the greatest and the smallest angle of the triangle.

Discussion

5383.	Q: PQRS is a rectangle incribed in quadrant of a circle of radius 13 cm. A is any point on PQ. If PS =5 cm, then ar(triangle RAS) is?
Answer» Q: PQRS is a rectangle incribed in quadrant of a circle of radius 13 cm. A is any point on PQ. If PS =5 cm, then ar(triangle RAS) is?

Discussion

5384.	If the volume of a sphere is 38808cm3 then its radius is = ___ cm.
Answer» If the volume of a sphere is $38808 {c m}^{3}$ then its radius is = ___ cm.

Discussion

5385.	Plz explain me the process of sloving simultaneous equations with help of cross multiplication
Answer» Plz explain me the process of sloving simultaneous equations with help of cross multiplication

Discussion

5386.	Mark the correct alternative in each of the following:If all the three angles of a triangle are equal, then each one of them is equal to(a) 90°(b) 45°(c) 60°(d) 30°
Answer» Mark the correct alternative in each of the following: If all the three angles of a triangle are equal, then each one of them is equal to (a) 90° (b) 45° (c) 60° (d) 30°

Discussion

5387.	Question 84 (vii) Simplify(x2−4)+(x2+4)+16
Answer» Question 84 (vii) Simplify $(x^{2} - 4) + (x^{2} + 4) + 16$

5387.

Question 84 (vii) Simplify(x2−4)+(x2+4)+16

Answer»

Question 84 (vii)

Simplify

$(x^{2} - 4) + (x^{2} + 4) + 16$

Discussion

5388.	The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.
Answer» The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Discussion

5389.	In fig., DE ∥ AC and DC ∥ AP. Prove that BEBC = BCCP.
Answer» In fig., DE $∥$ AC and DC $∥$ AP. Prove that $\frac{B E}{B C}$ = $\frac{B C}{C P}$ .

Discussion

5390.	What is the irrational number between 3/7 and 9/13
Answer» What is the irrational number between 3/7 and 9/13

Discussion

5391.	What is the value of 53 - 13(without solving cube)?
Answer» What is the value of 5³- 1³(without solving cube)?

Discussion

5392.	For an equilateral triangle of side 6cm, find the area of the triangle without using heron's formula.
Answer» For an equilateral triangle of side 6cm, find the area of the triangle without using heron's formula.

Discussion

5393.	Question 197Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O=120∘,∠R=105∘ and ∠A=135∘? If not, why?
Answer» Question 197 Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, $∠ O = 120^{\circ}, ∠ R = 105^{\circ}$ and $∠ A = 135^{\circ}$ ? If not, why?

Discussion

5394.	Question 2 (a) How many diagonals does each of the following have? (a) A convex quadrilateral
Answer» Question 2 (a) How many diagonals does each of the following have? (a) A convex quadrilateral

Discussion

5395.	Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.
Answer» Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

5395.

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

Answer»

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

Discussion

5396.	FIND THE VALUE OF a IF x-a IS A FACTOR OF x3 - ax2 - 2x + a-1
Answer» FIND THE VALUE OF a IF x-a IS A FACTOR OF x³ - ax² - 2x + a-1

Discussion

5397.	M is the mid point of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L.Then which of the following is correct?
Answer» M is the mid point of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Then which of the following is correct?

Discussion

5398.	If a2 + b2 + c2 − ab − bc − ca =0, then(a) a + b + c(b) b + c = a(c) c + a = b(d) a = b = c
Answer» If a² + b² + c² − ab − bc − ca =0, then (a) a + b + c (b) b + c = a (c) c + a = b (d) a = b = c

Discussion

5399.	Upper limit of class interval 75 - 85 is ______.
Answer» Upper limit of class interval 75 - 85 is ______.

Discussion

5400.	If 2x−3y = 10 and xy=16; find the value of 8x3−27y3
Answer» If $2 x - 3 y$ = 10 and $x y = 16$ ; find the value of $8 x^{3} - 27 y^{3}$

Discussion

Explore topic-wise InterviewSolutions in .

Question 2In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to(A) 2 cm(B) 3 cm(C) 4 cm(D) 5 cm

In a triangle with sides a, b and c, let s be the semiperimeter and p be the perimeter. The value of ps is ___.

If 2x−1=25=2a−4, then find the value of x and a.

Question 8 (ii) Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: 1623512584810341228151176328596871412 (ii) How many children watched television for 15 or more hours a week?

In the given figure, arcs are drawn by taking vertices A,B and C of an equilateral triangle of side 10 cm, to intersect the sides BC,CA and AB at their respective mid-points D,E and F. Find the area of the shaded region.(Use π=3.14)

Factorise: x(a-5)+y(5-a)

In the adjoining figure, PQRS is a trapezium in which PQ || SR and M is the midpoint of PS. A line segment MN || PQ meets QR at N. Show that N is the midpoint of QR.

if there are six straight lines in a plane,no two of which are parallel and no three of which pass through the same point,then find the number of points in which these lines intersect

Water is discharged from a pipe of cross section area 3.2cm2 at a speed of 5m/s. Find the volume of water discharged in cm3 per second.

An iron tank with an open top is cylindrical in shape. It has a height 10m and radius 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it gets completely corroded is (Take pi=227)

If the mean deviation of the numbers 1,1+d,1+2d,⋅,1+100d from their mean is 255, then d is equal to:

If axn is a zero degree polynomial in x, what can be said about a?

If the average of a, b,c,d is the average of b and c, then the value of a – b – c + d is ___________.

Question 1 (iv) Fill in the blanks: (iv) An arc is a __________ when its ends are the ends of a diameter.

Factorise: 27x3+y3+z3−9xyz

Question 7(iii)Using a2−b2=(a+b)(a−b), find1533−1472

In the figure, a is greater than b by one third of a right-angle. Find the values of a and b.

The number of decimal place after which the decimal expansion of the rational number 2322×5will terminate, is(a) 1(b) 2(c) 3(d) 4

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = 12 ∠A.

Factorise:62x-3x2+72x-3x-20

There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

The volume of a sphere is equal to ___ the volume of a cylinder of the same height and diameter.

The number of workers for a job and the time needed to complete the job

In a triangle ABC ,D is any point on BC such that AD bisects angle A.Prove that AB>BD.

In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :(i)(ii)(iii)(iv)

What is the value of x if the pair of linear equation x+3y=6 and 2x−3y=12 intersect at a point?6

In the given figure, O is a point in the interior of square ABCD such that ΔOAB is an equilateral triangle.Show that ΔOCD is an isosceles triangle.

A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. Find acute angle between the diagonals.

40. A circle of radius 2 cm is divided in to two segment by a chord of length 2cm, than the angle subtended by the chord at a point in major segment is

Solve the following equation for A (1) 2 sin A =1 (2) root 3 tan A = 1

In ∆PQR, PQ = 10 cm, QR = 12 cm, PR = 8 cm. Find out the greatest and the smallest angle of the triangle.

Q: PQRS is a rectangle incribed in quadrant of a circle of radius 13 cm. A is any point on PQ. If PS =5 cm, then ar(triangle RAS) is?

If the volume of a sphere is 38808cm3 then its radius is = ___ cm.

Plz explain me the process of sloving simultaneous equations with help of cross multiplication

Mark the correct alternative in each of the following:If all the three angles of a triangle are equal, then each one of them is equal to(a) 90°(b) 45°(c) 60°(d) 30°

Question 84 (vii) Simplify(x2−4)+(x2+4)+16

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

In fig., DE ∥ AC and DC ∥ AP. Prove that BEBC = BCCP.

What is the irrational number between 3/7 and 9/13

What is the value of 53 - 13(without solving cube)?

For an equilateral triangle of side 6cm, find the area of the triangle without using heron's formula.

Question 197Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O=120∘,∠R=105∘ and ∠A=135∘? If not, why?

Question 2 (a) How many diagonals does each of the following have? (a) A convex quadrilateral

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

FIND THE VALUE OF a IF x-a IS A FACTOR OF x​​​​​​3 - ax​​​​​2 - 2x + a-1

M is the mid point of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L.Then which of the following is correct?

If a2 + b2 + c2 − ab − bc − ca =0, then(a) a + b + c(b) b + c = a(c) c + a = b(d) a = b = c

Upper limit of class interval 75 - 85 is ______.

If 2x−3y = 10 and xy=16; find the value of 8x3−27y3

FIND THE VALUE OF a IF x-a IS A FACTOR OF x3 - ax2 - 2x + a-1