24740 + Interview Questions in Mathematics

1.	Two trees A and B are on the same side of a river. From a point C in the river, the distance of trees A and B are 250 m and 300 m respectively. If ∠C=45∘, find the distance between the trees (Use √2 = 144.)
Answer» Two trees A and B are on the same side of a river. From a point C in the river, the distance of trees A and B are 250 m and 300 m respectively. If $∠ C = 45^{\circ},$ find the distance between the trees (Use $\sqrt{2}$ = 144.)

Discussion

2.	The part of the number line between the points denoted by the numbers 13 and 12 is divided into four equal parts as shown below. Find the numbers denoted by A,B, and C.
Answer» The part of the number line between the points denoted by the numbers $\frac{1}{3}$ and $\frac{1}{2}$ is divided into four equal parts as shown below. Find the numbers denoted by A,B, and C.

Discussion

3.	The number 0.318564318564318564….. is:
Answer» The number 0.318564318564318564….. is:

Discussion

4.	ABCD is a square, AC and BD intersect at O. State the measure of ∠AOB.
Answer» ABCD is a square, AC and BD intersect at O. State the measure of $∠ A O B .$

4.

ABCD is a square, AC and BD intersect at O. State the measure of ∠AOB.

Answer»

ABCD is a square, AC and BD intersect at O. State the measure of $∠ A O B .$

Discussion

5.	Which one of the following is the smallest even whole number ?(a) 0 (b) 1 (c) 2 (d) None of these
Answer» Which one of the following is the smallest even whole number ? (a) 0 (b) 1 (c) 2 (d) None of these

Discussion

6.	Question 11 (iv)In ΔABC and ΔDEF ,AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.
Answer» Question 11 (iv) In $Δ A B C a n d Δ D E F$ ,AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.

Discussion

7.	The data below shows the number of times of all outcomes of a dice. Find the frequency of getting a number greater than 2 but less than or equal to 5. Number on dice123456Frequency101264810
Answer» The data below shows the number of times of all outcomes of a dice. Find the frequency of getting a number greater than 2 but less than or equal to 5. $\begin{matrix} Number on dice & 1 & 2 & 3 & 4 & 5 & 6 Frequency & 10 & 12 & 6 & 4 & 8 & 10 \end{matrix}$

Discussion

8.	Find the measure of an angle, if six times it's complement is 12 degree less than twice it's supplement.
Answer» Find the measure of an angle, if six times it's complement is 12 degree less than twice it's supplement.

Discussion

9.	If an angle of a parellelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
Answer» If an angle of a parellelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

Discussion

10.	The percentage of marks obtained by students of a class in mathematics are : 64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1. Find their mean.
Answer» The percentage of marks obtained by students of a class in mathematics are : 64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1. Find their mean.

Discussion

11.	The value of ddx{x2√9+x2+92log(x+√9+x2)} is equal to:
Answer» The value of $\frac{d}{d x} {\frac{x}{2} \sqrt{9 + x^{2}} + \frac{9}{2} log (x + \sqrt{9 + x^{2}})}$ is equal to:

Discussion

12.	Factorise the expression x3−6x2+11x−6.
Answer» Factorise the expression $x^{3} - 6 x^{2} + 11 x - 6$ .

Discussion

13.	Let A={1,2,3,....,10} and f:A→A be defined as f(k)={k+1if k is oddkif k is even. Then the number of possible functions g:A→A such that gof=f is:
Answer» Let $A = {1, 2, 3, . . . ., 10}$ and $f : A \to A$ be defined as $f (k) = {\begin{matrix} k + 1 & if k is odd k & if k is even \end{matrix} .$ Then the number of possible functions $g : A \to A$ such that $g o f = f$ is:

Discussion

14.	11.2+12.3+13.4+....+....1n(n+1) equals [AMU 1995; RPET 1996; UPSEAT 1999, 2001]
Answer» $\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + . . . . + . . . . \frac{1}{n (n + 1)}$ equals [AMU 1995; RPET 1996; UPSEAT 1999, 2001]

Discussion

15.	In the given figure, AD \|\| BC, AC and BD intersect at H. E is a point on BD such that DE < HE. F and G are points such that AEDF and ACGD are parallelograms. If ar(ABEF)=80 cm2, then ar(ACGD) equals
Answer» In the given figure, AD \|\| BC, AC and BD intersect at H. E is a point on BD such that DE < HE. F and G are points such that AEDF and ACGD are parallelograms. If $a r (A B E F) = 80 c m^{2},$ then ar(ACGD) equals

Discussion

16.	Factorise 25x2−16y2
Answer» Factorise $25 x^{2} - 16 y^{2}$

Discussion

17.	The abscissa and ordinate of the origin are(a) (0, 0)(b) (1, 0)(c) (0, 1)(d) (1, 1)
Answer» The abscissa and ordinate of the origin are (a) (0, 0) (b) (1, 0) (c) (0, 1) (d) (1, 1)

Discussion

18.	The polynomials 2x3+x2-ax+2 and 2x3-3x2-3x+a when divided by (x – 2) leave the same remainder. Find the value of a.
Answer» The polynomials $(2 x^{3} + x^{2} - a x + 2) and (2 x^{3} - 3 x^{2} - 3 x + a)$ when divided by (x – 2) leave the same remainder. Find the value of a.

Discussion

19.	Question 7A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. [Assume π=227]
Answer» Question 7 A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. $[A s s u m e π = \frac{22}{7}]$

Discussion

20.	In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced prove that ∠MOC = ∠ABC.
Answer» In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced prove that ∠MOC = ∠ABC.

Discussion

21.	Question 82 (iii)Subtract2ab2c2+4a2b2c−5a2bc2 from−10a2b2c+4ab2c2+2a2bc2
Answer» Question 82 (iii) Subtract $2 a b^{2} c^{2} + 4 a^{2} b^{2} c - 5 a^{2} b c^{2} f r o m - 10 a^{2} b^{2} c + 4 a b^{2} c^{2} + 2 a^{2} b c^{2}$

21.

Question 82 (iii)Subtract2ab2c2+4a2b2c−5a2bc2 from−10a2b2c+4ab2c2+2a2bc2

Answer»

Question 82 (iii)

Subtract

$2 a b^{2} c^{2} + 4 a^{2} b^{2} c - 5 a^{2} b c^{2} f r o m - 10 a^{2} b^{2} c + 4 a b^{2} c^{2} + 2 a^{2} b c^{2}$

Discussion

22.	Find the value of A:1250 = A100
Answer» Find the value of A: $\frac{12}{50} =$ $\frac{A}{100}$

Discussion

23.	Is log N to the base a always unique? explain
Answer» Is log N to the base a always unique? explain

Discussion

24.	Question 3Write True or False and justify your answer:The area of the isosceles triangle is 54√11cm2 if the perimeter is 11cm and the base is 5cm.
Answer» Question 3 Write True or False and justify your answer: The area of the isosceles triangle is $\frac{5}{4} \sqrt{11} c m^{2}$ if the perimeter is 11cm and the base is 5cm.

Discussion

25.	Euclid stated that 'all right angles are equal to each other',in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof
Answer» Euclid stated that 'all right angles are equal to each other',in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

25.

Euclid stated that 'all right angles are equal to each other',in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

Answer»

Euclid stated that 'all right angles are equal to each other',in the form of

(a) a definition

(b) an axiom

(c) a postulate

(d) a proof

Discussion

26.	Factorise:(a) a2+14a+48(b) m2–10m–56
Answer» Factorise: $(a) a^{2} + 14 a + 48$ $(b) m^{2} - 10 m - 56$

Discussion

27.	Which of the following methods or concepts is not used in either method for triangle construction 1?
Answer» Which of the following methods or concepts is not used in either method for triangle construction 1?

Discussion

28.	ABCD is a trapezium with AB \|\| DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).[Hint: Join CX.]
Answer» ABCD is a trapezium with AB \|\| DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). [Hint: Join CX.]

28.

ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).[Hint: Join CX.]

Answer»

ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).

[Hint: Join CX.]

Discussion

29.	If A = {prime numbers between 19 and 23}, then A is
Answer» If A = {prime numbers between 19 and 23}, then A is

Discussion

30.	If each observation of the data is increased by 8, then their mean(a) remains the same(b) is decreased by 8(c) is increased by 5(d) becomes 8 times the original mean
Answer» If each observation of the data is increased by 8, then their mean (a) remains the same (b) is decreased by 8 (c) is increased by 5 (d) becomes 8 times the original mean

Discussion

31.	Give an example of two irrational numbers whose(i) difference is an irrational number.(ii) difference is a rational number.(iii) sum is an irrational number.(iv) sum is a rational number.(v) product is an irrational number.(vi) product is a rational number.(vii) quotient is an irrational number.(viii) quotient is a rational number.
Answer» Give an example of two irrational numbers whose (i) difference is an irrational number. (ii) difference is a rational number. (iii) sum is an irrational number. (iv) sum is a rational number. (v) product is an irrational number. (vi) product is a rational number. (vii) quotient is an irrational number. (viii) quotient is a rational number.

Discussion

32.	Rahul was folding the application form of an exam to put it in an envelope. He folded it in such a way that the top margin coincided with the bottom one like in the figure.It is because both the margins are _____.
Answer» Rahul was folding the application form of an exam to put it in an envelope. He folded it in such a way that the top margin coincided with the bottom one like in the figure. It is because both the margins are _____.

32.

Rahul was folding the application form of an exam to put it in an envelope. He folded it in such a way that the top margin coincided with the bottom one like in the figure.It is because both the margins are _____.

Answer»

Rahul was folding the application form of an exam to put it in an envelope. He folded it in such a way that the top margin coincided with the bottom one like in the figure.

It is because both the margins are _____.

Discussion

33.	In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.
Answer» In figure, ABCD is a trapezium with $A B ∥ D C$ . AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.

Discussion

34.	Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.
Answer» Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.

Discussion

35.	19. In triangle ABC, if y = x+1 & y = 2x + 3 are altitude through A & angle bisector of B respectively. If vertex C is ( 3 , 4 ) then equation of median through C is
Answer» 19. In triangle ABC, if y = x+1 & y = 2x + 3 are altitude through A & angle bisector of B respectively. If vertex C is ( 3 , 4 ) then equation of median through C is

Discussion

36.	A feasible region of a system of linear inequalities is said to be ___________ if it can be enclosed within a circle.
Answer» A feasible region of a system of linear inequalities is said to be ___________ if it can be enclosed within a circle.

Discussion

37.	The decimal form of 78 is _.
Answer» The decimal form of $\frac{7}{8}$ is _.

Discussion

38.	the largest number which divides 615 and 963 leaving remainder 6 in each case is
Answer» the largest number which divides 615 and 963 leaving remainder 6 in each case is

Discussion

39.	A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs. 32 per 100 cm2.
Answer» A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs. 32 per 100 $c m^{2}$ .

Discussion

40.	In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?
Answer» In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

Discussion

41.	In a circle, two parallel chords of lengths 16 cm and 24 cm are 20 cm apart. Then the radius of the circle is
Answer» In a circle, two parallel chords of lengths 16 cm and 24 cm are 20 cm apart. Then the radius of the circle is

Discussion

42.	ΔABC and ΔDBC are two isosceles triangles on the same base BC (see figure). Show that ∠ ABD = ∠ ACD.
Answer» ΔABC and ΔDBC are two isosceles triangles on the same base BC (see figure). Show that ∠ ABD = ∠ ACD.

Discussion

43.	Find the quadratic polynomial if the sum of the zeroes and products of zeroes are 1/A and 1/B , respectively.
Answer» Find the quadratic polynomial if the sum of the zeroes and products of zeroes are 1/A and 1/B , respectively.

Discussion

44.	Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.
Answer» Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Discussion

45.	Question 4The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container?
Answer» Question 4 The paint in a certain container is sufficient to paint an area equal to $9.375 m^{2}$ . How many bricks of dimensions $22.5 c m \times 10 c m \times 7.5 c m$ can be painted out of this container?

Discussion

46.	A circular racetrack has inner radius of 25 m and outer radius of 30 m. Find the area of the racetrack.
Answer» A circular racetrack has inner radius of 25 m and outer radius of 30 m. Find the area of the racetrack.

Discussion

47.	If ∫√x4+x−4+2x3dx=ln\|x\|+axb+C, then absolute value of (ba) is (where a,b are fixed contants and C is constant of integration)
Answer» If $\int \frac{\sqrt{x^{4} + x^{- 4} + 2}}{x^{3}} d x = ln \| x \| + \frac{a}{x^{b}} + C$ , then absolute value of $(\frac{b}{a})$ is (where $a, b$ are fixed contants and $C$ is constant of integration)

Discussion

48.	Which of the following shows the visualization of the addition of 5x and 2 ?
Answer» Which of the following shows the visualization of the addition of 5x and 2 ?

Discussion

49.	FInd the solid that can be made by folding the given net.
Answer» FInd the solid that can be made by folding the given net.

49.

FInd the solid that can be made by folding the given net.

Answer»

FInd the solid that can be made by folding the given net.

Discussion

50.	The number 0.318564318564318564 ........ is:(a) a natural number(b) an integer(c) a rational number(d) an irrational number
Answer» The number 0.318564318564318564 ........ is: (a) a natural number (b) an integer (c) a rational number (d) an irrational number

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two trees A and B are on the same side of a river. From a point C in the river, the distance of trees A and B are 250 m and 300 m respectively. If ∠C=45∘, find the distance between the trees (Use √2 = 144.)

The part of the number line between the points denoted by the numbers 13 and 12 is divided into four equal parts as shown below. Find the numbers denoted by A,B, and C.

The number 0.318564318564318564….. is:

ABCD is a square, AC and BD intersect at O. State the measure of ∠AOB.

Which one of the following is the smallest even whole number ?(a) 0 (b) 1 (c) 2 (d) None of these

Question 11 (iv)In ΔABC and ΔDEF ,AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.

The data below shows the number of times of all outcomes of a dice. Find the frequency of getting a number greater than 2 but less than or equal to 5. Number on dice123456Frequency101264810

Find the measure of an angle, if six times it's complement is 12 degree less than twice it's supplement.

If an angle of a parellelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

The percentage of marks obtained by students of a class in mathematics are : 64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1. Find their mean.

The value of ddx{x2√9+x2+92log(x+√9+x2)} is equal to:

Factorise the expression x3−6x2+11x−6.

Let A={1,2,3,....,10} and f:A→A be defined as f(k)={k+1if k is oddkif k is even. Then the number of possible functions g:A→A such that gof=f is:

11.2+12.3+13.4+....+....1n(n+1) equals [AMU 1995; RPET 1996; UPSEAT 1999, 2001]

In the given figure, AD || BC, AC and BD intersect at H. E is a point on BD such that DE &lt; HE. F and G are points such that AEDF and ACGD are parallelograms. If ar(ABEF)=80 cm2, then ar(ACGD) equals

Factorise 25x2−16y2

The abscissa and ordinate of the origin are(a) (0, 0)(b) (1, 0)(c) (0, 1)(d) (1, 1)

The polynomials 2x3+x2-ax+2 and 2x3-3x2-3x+a when divided by (x – 2) leave the same remainder. Find the value of a.

Question 7A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. [Assume π=227]

In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced prove that ∠MOC = ∠ABC.

Question 82 (iii)Subtract2ab2c2+4a2b2c−5a2bc2 from−10a2b2c+4ab2c2+2a2bc2

Find the value of A:1250 = A100

Is log N to the base a always unique? explain

Question 3Write True or False and justify your answer:The area of the isosceles triangle is 54√11cm2 if the perimeter is 11cm and the base is 5cm.

Euclid stated that 'all right angles are equal to each other',in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

Factorise:(a) a2+14a+48(b) m2–10m–56

Which of the following methods or concepts is not used in either method for triangle construction 1?

ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).[Hint: Join CX.]

If A = {prime numbers between 19 and 23}, then A is

If each observation of the data is increased by 8, then their mean(a) remains the same(b) is decreased by 8(c) is increased by 5(d) becomes 8 times the original mean

Rahul was folding the application form of an exam to put it in an envelope. He folded it in such a way that the top margin coincided with the bottom one like in the figure.It is because both the margins are _____.

In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.

Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.

19. In triangle ABC, if y = x+1 & y = 2x + 3 are altitude through A & angle bisector of B respectively. If vertex C is ( 3 , 4 ) then equation of median through C is

A feasible region of a system of linear inequalities is said to be ___________ if it can be enclosed within a circle.

The decimal form of 78 is _.

the largest number which divides 615 and 963 leaving remainder 6 in each case is

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs. 32 per 100 cm2.

In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

In a circle, two parallel chords of lengths 16 cm and 24 cm are 20 cm apart. Then the radius of the circle is

ΔABC and ΔDBC are two isosceles triangles on the same base BC (see figure). Show that ∠ ABD = ∠ ACD.

Find the quadratic polynomial if the sum of the zeroes and products of zeroes are 1/A and 1/B , respectively.

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Question 4The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container?

A circular racetrack has inner radius of 25 m and outer radius of 30 m. Find the area of the racetrack.

If ∫√x4+x−4+2x3dx=ln|x|+axb+C, then absolute value of (ba) is (where a,b are fixed contants and C is constant of integration)

Which of the following shows the visualization of the addition of 5x and 2 ?

FInd the solid that can be made by folding the given net.

The number 0.318564318564318564 ........ is:(a) a natural number(b) an integer(c) a rational number(d) an irrational number

In the given figure, AD || BC, AC and BD intersect at H. E is a point on BD such that DE < HE. F and G are points such that AEDF and ACGD are parallelograms. If ar(ABEF)=80 cm2, then ar(ACGD) equals