24740 + Interview Questions in Mathematics

1.	ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in m2.
Answer» ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in $m^{2}$ .

1.

ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in m2.

Answer»

ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in $m^{2}$ .

2.	If dividend = x3+13x2+32x+20, divisor = x2+11x+10 remainder = 0. Find the quotient q(x)
Answer» If dividend = $x^{3} + 13 x^{2} + 32 x + 20$ , divisor = $x^{2} + 11 x + 10$ remainder = 0. Find the quotient q(x)

Discussion

3.	Factorise 32x4−500x
Answer» Factorise $32 x^{4} - 500 x$

Discussion

4.	Question 2 (v)Are the following statements ‘True’ or False’? Justify your answer.v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Answer» Question 2 (v) Are the following statements ‘True’ or False’? Justify your answer. v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

Discussion

5.	solve the following equatio for x: \|x-2\|/x-2>0
Answer» solve the following equatio for x: \|x-2\|/x-2>0

Discussion

6.	Find the mode and median of the data:13, 16, 12, 14, 19, 12, 14, 13, 14
Answer» Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14

Discussion

7.	Factorise: 10a3−11a2b−8ab2
Answer» Factorise: $10 a^{3} - 11 a^{2} b - 8 a b^{2}$

Discussion

8.	Thomas is a commercial farmer and purchase a square piece of land of dimension 100 m by 100 m. If the cost of 50 hectare of land is Rs. 250000, then find the rate of 1 square metre of the piece of land he purchased?
Answer» Thomas is a commercial farmer and purchase a square piece of land of dimension 100 m by 100 m. If the cost of 50 hectare of land is Rs. 250000, then find the rate of 1 square metre of the piece of land he purchased?

Discussion

9.	In a △ABC,if ∠A + ∠B = 150° and ∠B + ∠C = 75°, then ∠B =(a) 35°(b) 45°(c) 55°(d) 25°
Answer» In a △ABC,if ∠A + ∠B = 150° and ∠B + ∠C = 75°, then ∠B = (a) 35° (b) 45° (c) 55° (d) 25°

Discussion

10.	In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.
Answer» In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.

Discussion

11.	sin 60∘cos 45∘tan 45∘cot 60∘sec 30∘cosec 90∘
Answer» $s i n 60^{\circ} c o s 45^{\circ} t a n 45^{\circ} c o t 60^{\circ} s e c 30^{\circ} c o s e c 90^{\circ}$

Discussion

12.	Which of the following can always be a cyclic quadrilateral?
Answer» Which of the following can always be a cyclic quadrilateral?

Discussion

13.	In triangles ABC and PQR, if ∠A=∠R. ∠B=∠P and AB=RP, then which one of the following congruence condition applies:
Answer» In triangles ABC and PQR, if $∠ A = ∠ R .$ $∠ B = ∠ P a n d A B = R P, then which one of the following congruence condition applies:$

13.

In triangles ABC and PQR, if ∠A=∠R. ∠B=∠P and AB=RP, then which one of the following congruence condition applies:

Answer»

In triangles ABC and PQR, if $∠ A = ∠ R .$

$∠ B = ∠ P a n d A B = R P, then which one of the following congruence condition applies:$

Discussion

14.	What will be the value of x?
Answer» What will be the value of $x$ ?

Discussion

15.	Question 2 Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x)=2x3+x2−2x−1, g(x)=x+1 (ii) p(x)=x3+3x2+3x+1, g(x)=x+2 (iii) p(x)=x3−4x2+x+6, g(x)=x−3
Answer» Question 2 Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: $(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1$ $(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2$ $(i i i) p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3$

Discussion

16.	In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of(△BPC) equal to
Answer» In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of( $△$ BPC) equal to

16.

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of(△BPC) equal to

Answer»

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of( $△$ BPC) equal to

Discussion

17.	Question 3The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is:A) A rectangle of area 24 cm2B) A square of area 25 cm2C) A trapezium of area 24 cm2D) A rhombus of area 24 cm2
Answer» Question 3 The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is: A) A rectangle of area $24 c m^{2}$ B) A square of area $25 c m^{2}$ C) A trapezium of area $24 c m^{2}$ D) A rhombus of area $24 c m^{2}$

Discussion

18.	In the given figure, ABCD and AEFD are two parallelograms. Prove that(i) PE = FQ(ii) ar (Δ APE): ar (ΔPFA) = ar Δ (QFD) : ar (Δ PFD)(iii) ar (Δ PEA) = ar (Δ QFD).
Answer» In the given figure, ABCD and AEFD are two parallelograms. Prove that (i) PE = FQ (ii) ar (Δ APE): ar (ΔPFA) = ar Δ (QFD) : ar (Δ PFD) (iii) ar (Δ PEA) = ar (Δ QFD).

Discussion

19.	Question 6(iii)Using identities, evaluate:1022
Answer» Question 6(iii) Using identities, evaluate: $102^{2}$

Discussion

20.	If an event A cannot occur, then P(A) = ________.
Answer» If an event A cannot occur, then P(A) = ________.

Discussion

21.	Consider the following Bar Graph. i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______ ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm
Answer» Consider the following Bar Graph. i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______ ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm

21.

Consider the following Bar Graph. i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______ ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm

Answer»

Consider the following Bar Graph.

i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______

ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm

Discussion

22.	What do we mean by REAL zeroes of a polynomial ? Is there something called 'unreal zeroes' i.e zeroes which are not real ? If so what is the difference between the both??
Answer» What do we mean by REAL zeroes of a polynomial ? Is there something called 'unreal zeroes' i.e zeroes which are not real ? If so what is the difference between the both??

Discussion

23.	If x:y=2:3 and 2:x=1:2 then the value of y is______
Answer» If x:y=2:3 and 2:x=1:2 then the value of y is______

Discussion

24.	In an isoceles triangle one side is 12cm(other than the equal sides) and its perimeter is 26cm.Find the area of the triangle.
Answer» In an isoceles triangle one side is 12cm(other than the equal sides) and its perimeter is 26cm.Find the area of the triangle.

Discussion

25.	Divide 6x4−8x3+12x−4 by 2x2
Answer» Divide $6 x^{4} - 8 x^{3} + 12 x - 4$ by $2 x^{2}$

Discussion

26.	Two rational numbers between 23 and 53 are(a) 16 and 26(b) 12 and 21(c) 56 and 76(d) 23 and 43
Answer» Two rational numbers between $\frac{2}{3} and \frac{5}{3}$ are (a) $\frac{1}{6} and \frac{2}{6}$ (b) $\frac{1}{2} and \frac{2}{1}$ (c) $\frac{5}{6} and \frac{7}{6}$ (d) $\frac{2}{3} and \frac{4}{3}$

Discussion

27.	Construct aΔABC in which BC=4.5cm,∠B=45∘andAB+AC=8cmJustify your constructions.
Answer» $C o n s t r u c t a Δ A B C i n w h i c h B C = 4.5 c m, ∠ B = 45^{\circ} a n d A B + A C = 8 c m Justify your constructions.$

Discussion

28.	If AB\|\|CD\|\|FG and BC\|\|FE in the given figure, then the measure of reflex ∠DEF is
Answer» If AB\|\|CD\|\|FG and BC\|\|FE in the given figure, then the measure of reflex $∠ D E F$ is

Discussion

29.	What is the value of c when the equation 2y=5x+7 is written in the standard form ax+by+c=0?
Answer» What is the value of c when the equation $2 y = 5 x + 7$ is written in the standard form $a x + b y + c = 0 ?$

Discussion

30.	Question 1(a):From the figure, identify:The centre of circle.
Answer» Question 1(a): From the figure, identify: The centre of circle .

30.

Question 1(a):From the figure, identify:The centre of circle.

Answer»

Question 1(a):

From the figure, identify:

The centre of circle

.

Discussion

31.	Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR. Show that ΔABM ≅ ΔPQN
Answer» Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of $Δ$ PQR. Show that $Δ$ ABM $≅$ $Δ$ PQN

Discussion

32.	In the given triangle ABC, altitudes BD and CE to sides AC and AB are equal. Show that ΔABD ≅ ΔACE.
Answer» In the given triangle ABC, altitudes BD and CE to sides AC and AB are equal. Show that ΔABD ≅ ΔACE.

Discussion

33.	ABCD is a trapezium in which AB\|\| DC, DC=30cm and AB=50cm. If X and Y are respectively the mid-points of AD and BC, then prove that ar(DCYX)=7/9ar(XYBA)
Answer» ABCD is a trapezium in which AB\|\| DC, DC=30cm and AB=50cm. If X and Y are respectively the mid-points of AD and BC, then prove that ar(DCYX)=7/9ar(XYBA)

Discussion

34.	Factorize:x4 + x2y2 + y4
Answer» Factorize: x⁴+ x²y² + y⁴

Discussion

35.	The area of an isosceles triangle with sides 17 cm, 17 cm and 30 cm is
Answer» The area of an isosceles triangle with sides $17 c m, 17 c m a n d 30 c m$ is

Discussion

36.	If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
Answer» If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

Discussion

37.	Prove that. (x+y)³+(y+z)³+(z+x)³ —3(x+y)(y+z)(z+x)=2(x³+y³+z³—3xyz)
Answer» Prove that. (x+y)³+(y+z)³+(z+x)³ —3(x+y)(y+z)(z+x)=2(x³+y³+z³—3xyz)

Discussion

38.	Prove that, two lines which are both parallel to the same line, are parallel to each other.
Answer» Prove that, two lines which are both parallel to the same line, are parallel to each other.

Discussion

39.	If TanA = 125, then the value of (sinA+cosA) × secA is:
Answer» If TanA = $\frac{12}{5}$ , then the value of (sinA+cosA) $\times$ secA is:

Discussion

40.	Prove that the perimeter of a triangle is greater than the sum of its altitudes.
Answer» Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Discussion

41.	On the interval [0,1] the function x25(1−x)75 takes its maximum value at the point
Answer» On the interval $[0, 1]$ the function $x^{25} (1 - x)^{75}$ takes its maximum value at the point

Discussion

42.	There is a staircase as shown in the given figure, connecting points A and B. Measurements of steps are marked in the figure. Find the straight line distance between A and B.
Answer» There is a staircase as shown in the given figure, connecting points A and B. Measurements of steps are marked in the figure. Find the straight line distance between A and B.

Discussion

43.	(i) In ΔABC, ∠A=90∘. Which is its longest side?(ii)IN ΔABC, ∠A=∠B=45∘. Which is its longest side?(iii) In ΔABC, ∠A=100∘ and ∠C=50∘. Which is its shortest side?
Answer» $(i) In Δ A B C, ∠ A = 90^{\circ} . Which is its longest side? (ii)IN Δ A B C, ∠ A = ∠ B = 45^{\circ} . Which is its longest side? (iii) In Δ A B C, ∠ A = 100^{\circ} a n d ∠ C = 50^{\circ} . Which is its shortest side?$

Discussion

44.	Which of the following is not an irrational number?(i) √2(ii) π(iii) √3(iv) 4.8
Answer» Which of the following is not an irrational number? (i) $\sqrt{2}$ (ii) $π$ (iii) $\sqrt{3}$ (iv) 4.8

Discussion

45.	A circle of diameter 13 cm has two chords of length 12 cm and 5 cm. If both the chords lie in the same semi-circle, what is the distance between the chords?
Answer» A circle of diameter 13 cm has two chords of length 12 cm and 5 cm. If both the chords lie in the same semi-circle, what is the distance between the chords?

Discussion

46.	How much water is present in a 4000 ml measuring cylinder if it is filled to half its capacity?
Answer» How much water is present in a 4000 ml measuring cylinder if it is filled to half its capacity?

Discussion

47.	x3 − 12x(x − 4) − 64
Answer» x³ − 12x(x − 4) − 64

Discussion

48.	Finds the capacity in litres of a conical vessel with: (i) radius 7 cm, slant height 25 cm, (ii) height 12 cm, slant height 13 cm.
Answer» Finds the capacity in litres of a conical vessel with: (i) radius 7 cm, slant height 25 cm, (ii) height 12 cm, slant height 13 cm.

48.

Finds the capacity in litres of a conical vessel with: (i) radius 7 cm, slant height 25 cm, (ii) height 12 cm, slant height 13 cm.

Answer»

Finds the capacity in litres of a conical vessel with:

(i) radius 7 cm, slant height 25 cm,

(ii) height 12 cm, slant height 13 cm.

Discussion

49.	ABCD is a parallelogram whose diagonals intersect at O. IF P is any point on BO, prove that (i) ar(△ADO)=ar(△CDO)(ii)ar(△ABP)=ar(△CBP)
Answer» ABCD is a parallelogram whose diagonals intersect at O. IF P is any point on BO, prove that (i) $a r (△ A D O) = a r (△ C D O) (i i) a r (△ A B P) = a r (△ C B P)$

Discussion

50.	Sheela and Meena have a certain number of coins which adds upto 30. If Sheela gives 5 coins to Meena ,Meena will have double the number of coins Sheela has. How many coins does sheela have?
Answer» Sheela and Meena have a certain number of coins which adds upto 30. If Sheela gives 5 coins to Meena ,Meena will have double the number of coins Sheela has. How many coins does sheela have?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in m2.

If dividend = x3+13x2+32x+20, divisor = x2+11x+10 remainder = 0. Find the quotient q(x)

Factorise 32x4−500x

Question 2 (v)Are the following statements ‘True’ or False’? Justify your answer.v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

solve the following equatio for x: |x-2|/x-2>0

Find the mode and median of the data:13, 16, 12, 14, 19, 12, 14, 13, 14

Factorise: 10a3−11a2b−8ab2

Thomas is a commercial farmer and purchase a square piece of land of dimension 100 m by 100 m. If the cost of 50 hectare of land is Rs. 250000, then find the rate of 1 square metre of the piece of land he purchased?

In a △ABC,if ∠A + ∠B = 150° and ∠B + ∠C = 75°, then ∠B =(a) 35°(b) 45°(c) 55°(d) 25°

In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.

sin 60∘cos 45∘tan 45∘cot 60∘sec 30∘cosec 90∘

Which of the following can always be a cyclic quadrilateral?

In triangles ABC and PQR, if ∠A=∠R. ∠B=∠P and AB=RP, then which one of the following congruence condition applies:

What will be the value of x?

Question 2 Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x)=2x3+x2−2x−1, g(x)=x+1 (ii) p(x)=x3+3x2+3x+1, g(x)=x+2 (iii) p(x)=x3−4x2+x+6, g(x)=x−3

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of(△BPC) equal to

Question 3The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is:A) A rectangle of area 24 cm2B) A square of area 25 cm2C) A trapezium of area 24 cm2D) A rhombus of area 24 cm2

In the given figure, ABCD and AEFD are two parallelograms. Prove that(i) PE = FQ(ii) ar (Δ APE): ar (ΔPFA) = ar Δ (QFD) : ar (Δ PFD)(iii) ar (Δ PEA) = ar (Δ QFD).

Question 6(iii)Using identities, evaluate:1022

If an event A cannot occur, then P(A) = ________.

Consider the following Bar Graph. i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______ ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm

What do we mean by REAL zeroes of a polynomial ? Is there something called 'unreal zeroes' i.e zeroes which are not real ? If so what is the difference between the both??

If x:y=2:3 and 2:x=1:2 then the value of y is______

In an isoceles triangle one side is 12cm(other than the equal sides) and its perimeter is 26cm.Find the area of the triangle.

Divide 6x4−8x3+12x−4 by 2x2

Two rational numbers between 23 and 53 are(a) 16 and 26(b) 12 and 21(c) 56 and 76(d) 23 and 43

Construct aΔABC in which BC=4.5cm,∠B=45∘andAB+AC=8cmJustify your constructions.

If AB||CD||FG and BC||FE in the given figure, then the measure of reflex ∠DEF is

What is the value of c when the equation 2y=5x+7 is written in the standard form ax+by+c=0?

Question 1(a):From the figure, identify:The centre of circle.

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR. Show that ΔABM ≅ ΔPQN

In the given triangle ABC, altitudes BD and CE to sides AC and AB are equal. Show that ΔABD ≅ ΔACE.

ABCD is a trapezium in which AB|| DC, DC=30cm and AB=50cm. If X and Y are respectively the mid-points of AD and BC, then prove that ar(DCYX)=7/9ar(XYBA)

Factorize:x4 + x2y2 + y4

The area of an isosceles triangle with sides 17 cm, 17 cm and 30 cm is

If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

Prove that. (x+y)³+(y+z)³+(z+x)³ —3(x+y)(y+z)(z+x)=2(x³+y³+z³—3xyz)

Prove that, two lines which are both parallel to the same line, are parallel to each other.

If TanA = 125, then the value of (sinA+cosA) × secA is:

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

On the interval [0,1] the function x25(1−x)75 takes its maximum value at the point

There is a staircase as shown in the given figure, connecting points A and B. Measurements of steps are marked in the figure. Find the straight line distance between A and B.

(i) In ΔABC, ∠A=90∘. Which is its longest side?(ii)IN ΔABC, ∠A=∠B=45∘. Which is its longest side?(iii) In ΔABC, ∠A=100∘ and ∠C=50∘. Which is its shortest side?

Which of the following is not an irrational number?(i) √2(ii) π(iii) √3(iv) 4.8

A circle of diameter 13 cm has two chords of length 12 cm and 5 cm. If both the chords lie in the same semi-circle, what is the distance between the chords?

How much water is present in a 4000 ml measuring cylinder if it is filled to half its capacity?

x3 − 12x(x − 4) − 64

Finds the capacity in litres of a conical vessel with: (i) radius 7 cm, slant height 25 cm, (ii) height 12 cm, slant height 13 cm.

ABCD is a parallelogram whose diagonals intersect at O. IF P is any point on BO, prove that (i) ar(△ADO)=ar(△CDO)(ii)ar(△ABP)=ar(△CBP)

Sheela and Meena have a certain number of coins which adds upto 30. If Sheela gives 5 coins to Meena ,Meena will have double the number of coins Sheela has. How many coins does sheela have?