24740 + Interview Questions in Mathematics

1.	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 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB \|\| CD, AB = 6 cm and CD = 8 cm. Determine PQ.

Discussion

2.	In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar(ΔABC) = ar(ΔABD)
Answer» In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar(ΔABC) = ar(ΔABD)

Discussion

3.

Alex played a shooting game. Shown below the marks of gun shots. Area of the shot Points Exterior of the circle 2 Interior of the circle 5 Boundary of the circle 10 Find the total points scored by Alex.

Answer» Alex played a shooting game. Shown below the marks of gun shots.

Area of the shot	Points
Exterior of the circle	2
Interior of the circle	5
Boundary of the circle	10

Find the total points scored by Alex.

Discussion

4.

The following table gives the distribution of IQ's (intelligence quotients) of 60 pupils of class V in a school: IQ's: 125.5 to 13.25 118.5 to 125.5 111.5 to 118.5 104.5 to 111.5 97.5 to 104.5 90.5 to 97.5 83.5 to 90.5 76.5 to 83.5 69.5 to 76.5 62.5 to 69.5 No. of pupils: 1 3 4 6 10 12 15 5 3 1 Draw a frequency polygon for the above data.

Answer» The following table gives the distribution of IQ's (intelligence quotients) of 60 pupils of class V in a school:

IQ's:	125.5 to 13.25	118.5 to 125.5	111.5 to 118.5	104.5 to 111.5	97.5 to 104.5	90.5 to 97.5	83.5 to 90.5	76.5 to 83.5	69.5 to 76.5	62.5 to 69.5
No. of pupils:	1	3	4	6	10	12	15	5	3	1

Draw a frequency polygon for the above data.

Discussion

5.	In the given figure, ∠PQR=∠PRQ, then prove that ∠PQS=∠PRT.
Answer» In the given figure, $∠ P Q R = ∠ P R Q$ , then prove that $∠ P Q S = ∠ P R T$ .

5.

In the given figure, ∠PQR=∠PRQ, then prove that ∠PQS=∠PRT.

Answer»

In the given figure, $∠ P Q R = ∠ P R Q$ , then prove that $∠ P Q S = ∠ P R T$ .

Discussion

6.	The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.
Answer» The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

Discussion

7.	The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-3, 0) then the distance of point B from the origin is ___ units.
Answer» The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-3, 0) then the distance of point B from the origin is ___ units.

Discussion

8.	WHAT IS AN ALLELE
Answer» WHAT IS AN ALLELE

Discussion

9.

Following are the ages of 360 patients getting medical treatment in a hospital on a day: Age (in years): 10-20 20-30 30-40 40-50 50-60 60-70 No.of Patients: 90 50 60 80 50 30 Construct a cumulative frequency distribution.

Answer» Following are the ages of 360 patients getting medical treatment in a hospital on a day:

Age (in years):	10-20	20-30	30-40	40-50	50-60	60-70
No.of Patients:	90	50	60	80	50	30

Construct a cumulative frequency distribution.

Discussion

10.	The amount of time allotted for various subjects is given. If the teacher wants to distribute the time equally, the time should be of the total time.
Answer» The amount of time allotted for various subjects is given. If the teacher wants to distribute the time equally, the time should be of the total time.

Discussion

11.	The image of the point (3, –5) in the x-axis has the coordinates __________.
Answer» The image of the point (3, –5) in the x-axis has the coordinates __________.

Discussion

12.	When are three or more points are said to be collinear?
Answer» When are three or more points are said to be collinear?

Discussion

13.	Write the value of argz+argz¯.
Answer» Write the value of $\arg (z) + \arg (\bar{z})$ .

Discussion

14.	Factorise: 10(3x+1x)2−(3x+1x)−3
Answer» Factorise: $10 (3 x + \frac{1}{x})^{2} - (3 x + \frac{1}{x}) - 3$

Discussion

15.	Consider the equation x(y + 1) = x + 3 . Check whether x is directly or inversely proportional to y. [3 MARKS]
Answer» Consider the equation x(y + 1) = x + 3 . Check whether x is directly or inversely proportional to y. [3 MARKS]

Discussion

16.	If the sides of a triangle is 5cm,7cm and 7cm.Find the perimeter of the triangle.
Answer» If the sides of a triangle is 5cm,7cm and 7cm.Find the perimeter of the triangle.

Discussion

17.	In the following figure, △ABC≅△ACD if ___.
Answer» In the following figure, $△ A B C ≅ △ A C D$ if ___.

17.

In the following figure, △ABC≅△ACD if ___.

Answer»

In the following figure, $△ A B C ≅ △ A C D$ if ___.

Discussion

18.	If the ratio of the number of diagonals to number of interior angles in a polygon is 7, then the number of sides of the polygon is:
Answer» If the ratio of the number of diagonals to number of interior angles in a polygon is 7, then the number of sides of the polygon is:

Discussion

19.	Question 19The value of 4√(81)−2 isA) 19B) 13C) 9D) 181
Answer» Question 19 The value of $\sqrt[4]{(81)^{- 2}}$ is A) $\frac{1}{9}$ B) $\frac{1}{3}$ C) $9$ D) $\frac{1}{81}$

Discussion

20.	What is the value of (a+b)(a–b)?
Answer» What is the value of $(a + b) (a - b) ?$

Discussion

21.	In ΔABC, if ∠C>∠B, then(a) BC>AC (b) AB>AC (c) AB<AC (d) BC<AC
Answer» $I n Δ A B C, i f ∠ C > ∠ B, t h e n (a) B C > A C (b) A B > A C (c) A B < A C (d) B C < A C$

Discussion

22.	The line l is tangent to the circle S at the point A; B and C are points on 'i' on opposite sides of A and the other tangents from B, C to S intersect at a point P. If B,C vary along 'i' in such a way that the product of AB.AC is constant, find the locus of P.
Answer» The line l is tangent to the circle S at the point A; B and C are points on 'i' on opposite sides of A and the other tangents from B, C to S intersect at a point P. If B,C vary along 'i' in such a way that the product of AB.AC is constant, find the locus of P.

Discussion

23.	Q 9/15 Express in terms of four significant figues"6.608543"
Answer» Q 9/15 Express in terms of four significant figues"6.608543"

Discussion

24.	Let set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {1, 3, 5, 7, 9}. Prove that (A ∩ B)’ = A’ ∪ B.’
Answer» Let set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {1, 3, 5, 7, 9}. Prove that (A $\cap$ B)’ = A’ $\cup$ B.’

Discussion

25.	A set S has 7 elements. How many subsets having at most 5 elements does it have?
Answer» A set S has 7 elements. How many subsets having at most 5 elements does it have?

Discussion

26.	Let ABC be a triangle in which AB = AC . Let I be its incentre . Suppose that BC =AB+AI . Find angle BAC
Answer» Let ABC be a triangle in which AB = AC . Let I be its incentre . Suppose that BC =AB+AI . Find angle BAC

Discussion

27.	In the figure given below, find the measure of the angles denoted by x,y,z,p,q and r.
Answer» In the figure given below, find the measure of the angles denoted by $x, y, z, p, q$ and $r$ .

Discussion

28.	The value of 2 tan 30∘1 −tan2 30∘ is _______.
Answer» The value of $\frac{2 t a n 30^{\circ}}{1 - t a n^{2} 30^{\circ}}$ is _______.

Discussion

29.	If p(x) = 2x3 + ax2 − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?
Answer» If p(x) = 2x³ + ax² − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?

29.

If p(x) = 2x3 + ax2 − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?

Answer»

If p(x) = 2x³ + ax² − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?

Discussion

30.	Question 10 Write True or False and justify your answer : In the figure, if AOB is a diameter and ∠ADC=120∘, then ∠CAB=30∘.
Answer» Question 10 Write True or False and justify your answer : In the figure, if AOB is a diameter and $∠ A D C = 120^{\circ}, t h e n ∠ C A B = 30^{\circ}$ .

Discussion

31.	Let →a=2→i+^j+^k, →b=^i+2^j−^k and a unit vector →c be coplanar. If →c is perpendicular to →a, then →c is equal to
Answer» Let $\to a = 2 \to i +^j +^k, \to b =^i + 2^j -^k$ and a unit vector $\to c$ be coplanar. If $\to c$ is perpendicular to $\to a,$ then $\to c$ is equal to

Discussion

32.	In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___ ∘.
Answer» In the given figure, if $∠$ ACB = $30^{\circ}$ , the value of $∠$ ACD is ___ $^{\circ}$ .

32.

In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___ ∘.

Answer»

In the given figure, if $∠$ ACB = $30^{\circ}$ , the value of $∠$ ACD is ___ $^{\circ}$ .

Discussion

33.	In the adjoining figure, if BE^ AC, ∠EBC = 40o and ∠DAC = 30o, find and .
Answer» In the adjoining figure, if BE^ AC, ∠EBC = 40^o and ∠DAC = 30^o, find and .

33.

In the adjoining figure, if BE^ AC, ∠EBC = 40o and ∠DAC = 30o, find and .

Answer»

In the adjoining figure, if BE^ AC, ∠EBC = 40^o and ∠DAC = 30^o, find and .

Discussion

34.	A loan of ₹5000 was received from the bank. Every monthly an amount of ₹450 was paid back for an year. What was the interest amount paid back?
Answer» A loan of ₹5000 was received from the bank. Every monthly an amount of ₹450 was paid back for an year. What was the interest amount paid back?

Discussion

35.	Question 9 (i) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: ΔAPD≅ΔCQB
Answer» Question 9 (i) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: $Δ A P D ≅ Δ C Q B$

Discussion

36.	Draw the quadrilateral ABCD with AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm. Compute its area by drawing a triangle of equal area.
Answer» Draw the quadrilateral ABCD with AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm. Compute its area by drawing a triangle of equal area.

Discussion

37.	Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.
Answer» Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.

Discussion

38.	Who among P, Q, R, S, T and U is the tallest, considering that all have different heights? I. Q is taller than P but shorter than T. II. Only two of them are shorter than R. III. S is taller than only U.
Answer» Who among P, Q, R, S, T and U is the tallest, considering that all have different heights? I. Q is taller than P but shorter than T. II. Only two of them are shorter than R. III. S is taller than only U.

38.

Who among P, Q, R, S, T and U is the tallest, considering that all have different heights? I. Q is taller than P but shorter than T. II. Only two of them are shorter than R. III. S is taller than only U.

Answer»

Who among P, Q, R, S, T and U is the tallest, considering that all have different heights?

I. Q is taller than P but shorter than T.

II. Only two of them are shorter than R.

III. S is taller than only U.

Discussion

39.	What is the constant of proportionality in the equation for proportional change y=kx ?
Answer» What is the constant of proportionality in the equation for proportional change $y = \frac{k}{x}$ ?

Discussion

40.	A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Answer» A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Discussion

41.	3+√7 is irrational number!
Answer» 3+√7 is irrational number!

Discussion

42.	The volume of a cube is 512 cm3 .Its total surface area is (a) 256 cm2(b) 384 cm2(c) 512 cm2(d) 64 cm2
Answer» The volume of a cube is $512 c m^{3}$ .Its total surface area is $(a) 256 c m^{2}$ $(b) 384 c m^{2}$ $(c) 512 c m^{2}$ $(d) 64 c m^{2}$

42.

The volume of a cube is 512 cm3 .Its total surface area is (a) 256 cm2(b) 384 cm2(c) 512 cm2(d) 64 cm2

Answer»

The volume of a cube is $512 c m^{3}$ .Its total surface area is

$(a) 256 c m^{2}$

$(b) 384 c m^{2}$

$(c) 512 c m^{2}$

$(d) 64 c m^{2}$

Discussion

43.	If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then AV is
Answer» If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then $\frac{A}{V}$ is

Discussion

44.	The slant height of a cone is 25 cm. If the circumference of the base of the cone is 44 cm, then the volume of the cone is
Answer» The slant height of a cone is 25 cm. If the circumference of the base of the cone is 44 cm, then the volume of the cone is

Discussion

45.	In ∆ABC, side BC is produced to D. If ∠ABC = 50° and ∠ACD = 110° then ∠A = ?(a) 160°(b) 60°(c) 80°(d) 30°
Answer» In ∆ABC, side BC is produced to D. If ∠ABC = 50° and ∠ACD = 110° then ∠A = ? (a) 160° (b) 60° (c) 80° (d) 30°

Discussion

46.	Question 3(i) For any integer a, what is (−1)×a equal to?
Answer» Question 3(i) For any integer a, what is $(- 1) \times a$ equal to?

Discussion

47.	Question 13Vijay had some bananas and he divided them into two lots A and B. He sold the first lot at the rate of Rs. 2 for 3 bananas and the second lot at the rate of Rs. 1 per banana and got a total of Rs. 400. If he had sold the first lot at the rate of Rs. 1 per banana and the second lot at the rate of Rs. 4 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.
Answer» Question 13 Vijay had some bananas and he divided them into two lots A and B. He sold the first lot at the rate of Rs. 2 for 3 bananas and the second lot at the rate of Rs. 1 per banana and got a total of Rs. 400. If he had sold the first lot at the rate of Rs. 1 per banana and the second lot at the rate of Rs. 4 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.

Discussion

48.	Find the principal which will give compound interest of Rs 408 in 2 years at 4% pa., compounded annually.
Answer» Find the principal which will give compound interest of Rs 408 in 2 years at 4% pa., compounded annually.

Discussion

49.	The bisectors of any two adjacent angles of a parallelogram intersect at(a) 30°(b) 45°(c) 60°(d) 90°
Answer» The bisectors of any two adjacent angles of a parallelogram intersect at (a) 30° (b) 45° (c) 60° (d) 90°

Discussion

50.	Which of these is a solution of 2x + 3y = 11?
Answer» Which of these is a solution of 2x + 3y = 11?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

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.

In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar(ΔABC) = ar(ΔABD)

Alex played a shooting game. Shown below the marks of gun shots. Area of the shot Points Exterior of the circle 2 Interior of the circle 5 Boundary of the circle 10 Find the total points scored by Alex.

In the given figure, ∠PQR=∠PRQ, then prove that ∠PQS=∠PRT.

The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-3, 0) then the distance of point B from the origin is ___ units.

WHAT IS AN ALLELE

Following are the ages of 360 patients getting medical treatment in a hospital on a day: Age (in years): 10-20 20-30 30-40 40-50 50-60 60-70 No.of Patients: 90 50 60 80 50 30 Construct a cumulative frequency distribution.

The amount of time allotted for various subjects is given. If the teacher wants to distribute the time equally, the time should be of the total time.

The image of the point (3, –5) in the x-axis has the coordinates __________.

When are three or more points are said to be collinear?

Write the value of argz+argz¯.

Factorise: 10(3x+1x)2−(3x+1x)−3

Consider the equation x(y + 1) = x + 3 . Check whether x is directly or inversely proportional to y. [3 MARKS]

If the sides of a triangle is 5cm,7cm and 7cm.Find the perimeter of the triangle.

In the following figure, △ABC≅△ACD if ___.

If the ratio of the number of diagonals to number of interior angles in a polygon is 7, then the number of sides of the polygon is:

Question 19The value of 4√(81)−2 isA) 19B) 13C) 9D) 181

What is the value of (a+b)(a–b)?

In ΔABC, if ∠C&gt;∠B, then(a) BC&gt;AC (b) AB&gt;AC (c) AB&lt;AC (d) BC&lt;AC

The line l is tangent to the circle S at the point A; B and C are points on 'i' on opposite sides of A and the other tangents from B, C to S intersect at a point P. If B,C vary along 'i' in such a way that the product of AB.AC is constant, find the locus of P.

Q 9/15 Express in terms of four significant figues"6.608543"

Let set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {1, 3, 5, 7, 9}. Prove that (A ∩ B)’ = A’ ∪ B.’

A set S has 7 elements. How many subsets having at most 5 elements does it have?

Let ABC be a triangle in which AB = AC . Let I be its incentre . Suppose that BC =AB+AI . Find angle BAC

In the figure given below, find the measure of the angles denoted by x,y,z,p,q and r.

The value of 2 tan 30∘1 −tan2 30∘ is _______.

If p(x) = 2x3 + ax2 − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?

Question 10 Write True or False and justify your answer : In the figure, if AOB is a diameter and ∠ADC=120∘, then ∠CAB=30∘.

Let →a=2→i+^j+^k, →b=^i+2^j−^k and a unit vector →c be coplanar. If →c is perpendicular to →a, then →c is equal to

In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___ ∘.

In the adjoining figure, if BE^ AC, ∠EBC = 40o and ∠DAC = 30o, find and .

A loan of ₹5000 was received from the bank. Every monthly an amount of ₹450 was paid back for an year. What was the interest amount paid back?

Question 9 (i) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: ΔAPD≅ΔCQB

Draw the quadrilateral ABCD with AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm. Compute its area by drawing a triangle of equal area.

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.

Who among P, Q, R, S, T and U is the tallest, considering that all have different heights? I. Q is taller than P but shorter than T. II. Only two of them are shorter than R. III. S is taller than only U.

What is the constant of proportionality in the equation for proportional change y=kx ?

A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

3+√7 is irrational number!

The volume of a cube is 512 cm3 .Its total surface area is (a) 256 cm2(b) 384 cm2(c) 512 cm2(d) 64 cm2

If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then AV is

The slant height of a cone is 25 cm. If the circumference of the base of the cone is 44 cm, then the volume of the cone is

In ∆ABC, side BC is produced to D. If ∠ABC = 50° and ∠ACD = 110° then ∠A = ?(a) 160°(b) 60°(c) 80°(d) 30°

Question 3(i) For any integer a, what is (−1)×a equal to?

Find the principal which will give compound interest of Rs 408 in 2 years at 4% pa., compounded annually.

The bisectors of any two adjacent angles of a parallelogram intersect at(a) 30°(b) 45°(c) 60°(d) 90°

Which of these is a solution of 2x + 3y = 11?

In ΔABC, if ∠C>∠B, then(a) BC>AC (b) AB>AC (c) AB<AC (d) BC<AC