24740 + Interview Questions in Mathematics

1.	If lengths of tangents drawn from the vertices of triangles whose vertices are (0,0),(5,0) and (0,12) to it's incircle are a,b,c(a<b<c) units. Then (a+b)×c is
Answer» If lengths of tangents drawn from the vertices of triangles whose vertices are $(0, 0), (5, 0)$ and $(0, 12)$ to it's incircle are $a, b, c (a < b < c)$ units. Then $(a + b) \times c$ is

Discussion

2.	Two numbers are such that two times of one is same as 3 times of the other. Write a linear equation in two variables to represent.
Answer» Two numbers are such that two times of one is same as 3 times of the other. Write a linear equation in two variables to represent.

Discussion

3.	If two angles and the included side of a triangle are equal to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.
Answer» If two angles and the included side of a triangle are equal to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

Discussion

4.	There are 10 cards numbered from 1 to 10. A card is drawn randomly. The probability of gettingan even numbered card is(a) 110 (b) 15 (c) 12 (d) 25
Answer» There are 10 cards numbered from 1 to 10. A card is drawn randomly. The probability of getting an even numbered card is (a) $\frac{1}{10}$ (b) $\frac{1}{5}$ (c) $\frac{1}{2}$ (d) $\frac{2}{5}$

Discussion

5.	Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90∘. Then the circumcentre of this triangle lies on the third side.
Answer» Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90 $^{\circ}$ . Then the circumcentre of this triangle lies on the third side.

5.

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90∘. Then the circumcentre of this triangle lies on the third side.

Answer»

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90 $^{\circ}$ . Then the circumcentre of this triangle lies on the third side.

Discussion

6.	14. Calculate the distance between the points P(2,2) and Q(5,4) correct to three significant figures.
Answer» 14. Calculate the distance between the points P(2,2) and Q(5,4) correct to three significant figures.

Discussion

7.	A rod of uniform thickness is placed along x-axis with one end at origin.If length of rod is L and its linear mass density is proportional to x,then find dis†an ce of its mass from origin
Answer» A rod of uniform thickness is placed along x-axis with one end at origin.If length of rod is L and its linear mass density is proportional to x,then find dis†an ce of its mass from origin

Discussion

8.	In Fig. 69, if AB \|\| CD, then the values of x and y are(a) x = 106, y = 307(b) x = 307, y = 106(C) x =107, y = 306(d) x = 105, y = 308
Answer» In Fig. 69, if AB \|\| CD, then the values of x and y are (a) x = 106, y = 307 (b) x = 307, y = 106 (C) x =107, y = 306 (d) x = 105, y = 308

Discussion

9.	Let x be a rational number and y be an irrational number. Is x + y necessarily an irrational number? Give a example in support of your answer.
Answer» Let x be a rational number and y be an irrational number. Is x + y necessarily an irrational number? Give a example in support of your answer.

Discussion

10.	Two natural numbers differ by 3 and their product is 504. Find the numbers.
Answer» Two natural numbers differ by 3 and their product is 504. Find the numbers.

Discussion

11.	State the criteria for proving the congruency of two triangles.
Answer» State the criteria for proving the congruency of two triangles.

Discussion

12.	5(25)n+1-25(5)2n --------------------------------------- 5*(5)2n+3-(25)n+1
Answer» 5(25)ⁿ⁺¹-25(5)²ⁿ ^{---------------------------------------} 5*(5)²ⁿ⁺³-(25)ⁿ⁺¹

12.

5(25)n+1-25(5)2n --------------------------------------- 5*(5)2n+3-(25)n+1

Answer»

5*(25)ⁿ⁺¹-25*(5)²ⁿ

^{---------------------------------------}

5*(5)²ⁿ⁺³-(25)ⁿ⁺¹

Discussion

13.	State whether each of the following sets is finite or infinite : (i) The set of lines which are parallel to the x-axis. (ii) The set of letters in the English alphabet. (iii) The set of numbers which are multiples of 5. (iv) The set of animals living on the earth. (v) The set of circles passing through the origin (0, 0).
Answer» State whether each of the following sets is finite or infinite : (i) The set of lines which are parallel to the x-axis. (ii) The set of letters in the English alphabet. (iii) The set of numbers which are multiples of 5. (iv) The set of animals living on the earth. (v) The set of circles passing through the origin (0, 0).

13.

State whether each of the following sets is finite or infinite : (i) The set of lines which are parallel to the x-axis. (ii) The set of letters in the English alphabet. (iii) The set of numbers which are multiples of 5. (iv) The set of animals living on the earth. (v) The set of circles passing through the origin (0, 0).

Answer»

State whether each of the following sets is finite or infinite :

(i) The set of lines which are parallel to the x-axis.

(ii) The set of letters in the English alphabet.

(iii) The set of numbers which are multiples of 5.

(iv) The set of animals living on the earth.

(v) The set of circles passing through the origin (0, 0).

Discussion

14.	Simplify ab2c3×a4b5c−6a−7b−8c9×a10b11c−12×a13b−14c15
Answer» Simplify $\frac{a b^{2} c^{3} \times a^{4} b^{5} c^{- 6}}{a^{- 7} b^{- 8} c^{9} \times a^{10} b^{11} c^{- 12} \times a^{13} b^{- 14} c^{15}}$

Discussion

15.	M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.
Answer» M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

15.

M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

Answer»

M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

Discussion

16.	If the point (4,-2) lies on the graph of 2x=any+3,find the value of a
Answer» If the point (4,-2) lies on the graph of 2x=any+3,find the value of a

Discussion

17.	In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
Answer» In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

Discussion

18.	Simplify : 5 3√250+7 3√16−14 3√54
Answer» Simplify : $5 \sqrt[3]{250} + 7 \sqrt[3]{16} - 14 \sqrt[3]{54}$

Discussion

19.	The factors of (8a3 + b3 -6ab + 1) are?
Answer» The factors of (8a³ + b³-6ab + 1) are?

Discussion

20.	Which among these is the approximate value of π?
Answer» Which among these is the approximate value of π?

Discussion

21.	For all values of A, B and C, prove that:- cosA + cosB + cosC + cos (A+B+C)= 4cos (A + B/2). cos (B+C/2). cos (C+ A/2)
Answer» For all values of A, B and C, prove that:- cosA + cosB + cosC + cos (A+B+C)= 4cos (A + B/2). cos (B+C/2). cos (C+ A/2)

Discussion

22.	If vectors \overrightarrow A =(\overset∧ i+2\overset∧ j+3\overset∧ k)m and \overrightarrow{B }=(-\overset∧ i-\overset∧ j-\overset∧ k)m represents two sides of a triangle then the third side can have a side equal to? 1) 3m 2) 8m 3) 6m 4) Both 1 and
Answer» If vectors \overrightarrow A =(\overset∧ i+2\overset∧ j+3\overset∧ k)m and \overrightarrow{B }=(-\overset∧ i-\overset∧ j-\overset∧ k)m represents two sides of a triangle then the third side can have a side equal to? 1) 3m 2) 8m 3) 6m 4) Both 1 and

Discussion

23.	Using identities, evaluate: 1.02×9.8
Answer» Using identities, evaluate: $1.02 \times 9.8$

Discussion

24.	72. cotA/2-TanA/2 is equal to 1)2tanA. 2)2 cosA 3)2secA. 4)2 cot A
Answer» 72. cotA/2-TanA/2 is equal to 1)2tanA. 2)2 cosA 3)2secA. 4)2 cot A

Discussion

25.	For a polynomial, x2 - 3x +2, which of the following is a factor ?
Answer» For a polynomial, x² - 3x +2, which of the following is a factor ?

Discussion

26.	In ∆ABC, bisectors of ∠A and ∠B intersect at point O. If ∠C = 70° . Find measure of ∠AOB.
Answer» In $∆$ ABC, bisectors of $∠$ A and $∠$ B intersect at point O. If $∠$ C = 70^° . Find measure of $∠$ AOB.

Discussion

27.	Factorise: (y+1/y)² - 5(y+1/y) + 4
Answer» Factorise: (y+1/y)² - 5(y+1/y) + 4

Discussion

28.	In a family with two sons, a father has a field in the form of a right-angled triangle with sides including right angle are 18m and 40m. He wants to give independent charge to his sons, so he divided the field in the ratio 2 : 1 : 1, the bigger part he kept for himself and divided remaining equally among the sons, find the total area distributed to the sons.
Answer» In a family with two sons, a father has a field in the form of a right-angled triangle with sides including right angle are 18m and 40m. He wants to give independent charge to his sons, so he divided the field in the ratio 2 : 1 : 1, the bigger part he kept for himself and divided remaining equally among the sons, find the total area distributed to the sons.

Discussion

29.	Question 17 (i) (i) A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
Answer» Question 17 (i) (i) A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

Discussion

30.	3. ABCD and PQRC are rectangles and Q is the mid point of AC. Show that P is the mid point of DC and R is the mid point of BC .also find ratio of at(ABCD)and at( PQRC)
Answer» 3. ABCD and PQRC are rectangles and Q is the mid point of AC. Show that P is the mid point of DC and R is the mid point of BC .also find ratio of at(ABCD)and at( PQRC)

Discussion

31.	Define triangle.
Answer» Define triangle.

Discussion

32.	Mark the correct alternative in each of the following: If − 3x+17<-13, then(a) x∈(10, ∞)(b) x∈[10, ∞)(c) x∈(-∞, 10](d) x∈[-10, 10)
Answer» Mark the correct alternative in each of the following: If − 3x $+$ 17 $< -$ 13, then (a) x $\in$ (10, $\infty$ ) (b) x $\in$ [10, $\infty$ ) (c) x $\in$ ( $- \infty$ , 10] (d) x $\in$ [ $-$ 10, 10)

Discussion

33.	The sum of an angle and half of its complementary angle is 75°. The measure of the angle is(a) 40°(b) 50°(c) 60°(d) 80°
Answer» The sum of an angle and half of its complementary angle is 75°. The measure of the angle is (a) 40° (b) 50° (c) 60° (d) 80°

Discussion

34.	Identify the figure in which all the points could be collinear.
Answer» Identify the figure in which all the points could be collinear.

Discussion

35.	In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.
Answer» In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

35.

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

Answer»

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

Discussion

36.	How many possibilities of even numbers are there when a single die is thrown?
Answer» How many possibilities of even numbers are there when a single die is thrown?

Discussion

37.	How to prove pythagoras theorem?
Answer» How to prove pythagoras theorem?

Discussion

38.	Factorise: x2+7x−98
Answer» Factorise: $x^{2} + 7 x - 98$

Discussion

39.	If x = 1/3-√5, find the value of (√x+1/√x) is
Answer» If x = 1/3-√5, find the value of (√x+1/√x) is

Discussion

40.	What is mean?
Answer» What is mean?

Discussion

41.	Find five rational numbers between 0 and 1.
Answer» Find five rational numbers between 0 and 1.

Discussion

42.	Name the quadrant in which both abscissa and ordinate of a point are negative.
Answer» Name the quadrant in which both abscissa and ordinate of a point are negative.

Discussion

43.	One tenth of 100 is ____.
Answer» One tenth of 100 is ____.

Discussion

44.	Question 7A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?
Answer» Question 7 A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Discussion

45.	Question 3 ΔABC, if AB =AC and ∠B=50∘ then ∠C is equal to (A) 40∘ (B) 50∘ (C) 80∘ (D) 130∘
Answer» Question 3 $Δ A B C$ , if AB =AC and $∠ B = 50^{\circ}$ then $∠ C$ is equal to (A) $40^{\circ}$ (B) $50^{\circ}$ (C) $80^{\circ}$ (D) $130^{\circ}$

Discussion

46.	If G is the centroid of △ ABC then prove that AB^2+BC^2+AC^2=3(GA^2+GB^2+GC^2)
Answer» If G is the centroid of △ ABC then prove that AB^2+BC^2+AC^2=3(GA^2+GB^2+GC^2)

Discussion

47.	In the given figure, if AB∥CD, CD∥EF and y:z=3:7, find x.
Answer» In the given figure, if $A B ∥ C D, C D ∥ E F$ and $y : z = 3 : 7$ , find $x$ .

47.

In the given figure, if AB∥CD, CD∥EF and y:z=3:7, find x.

Answer»

In the given figure, if $A B ∥ C D, C D ∥ E F$ and $y : z = 3 : 7$ , find $x$ .

Discussion

48.	Question 22If x + 1 is a factor of ax3+x2–2x+4a–9, then find the value of a.
Answer» Question 22 If x + 1 is a factor of $a x^{3} + x^{2} - 2 x + 4 a - 9$ , then find the value of a.

Discussion

49.	Factorize 3x²-5x+6
Answer» Factorize 3x²-5x+6

Discussion

50.	Given x + y = 2, then expressing x2-2y-4 in terms of y gives
Answer» Given x + y = 2, then expressing x²-2y-4 in terms of y gives

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If lengths of tangents drawn from the vertices of triangles whose vertices are (0,0),(5,0) and (0,12) to it's incircle are a,b,c(a&lt;b&lt;c) units. Then (a+b)×c is

Two numbers are such that two times of one is same as 3 times of the other. Write a linear equation in two variables to represent.

If two angles and the included side of a triangle are equal to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

There are 10 cards numbered from 1 to 10. A card is drawn randomly. The probability of gettingan even numbered card is(a) 110 (b) 15 (c) 12 (d) 25

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90∘. Then the circumcentre of this triangle lies on the third side.

14. Calculate the distance between the points P(2,2) and Q(5,4) correct to three significant figures.

A rod of uniform thickness is placed along x-axis with one end at origin.If length of rod is L and its linear mass density is proportional to x,then find dis†an ce of its mass from origin

In Fig. 69, if AB || CD, then the values of x and y are(a) x = 106, y = 307(b) x = 307, y = 106(C) x =107, y = 306(d) x = 105, y = 308

Let x be a rational number and y be an irrational number. Is x + y necessarily an irrational number? Give a example in support of your answer.

Two natural numbers differ by 3 and their product is 504. Find the numbers.

State the criteria for proving the congruency of two triangles.

5*(25)n+1-25*(5)2n --------------------------------------- 5*(5)​​​​2n+3-(25)n+1 ​​​​​​​​​ ​​​​​​​​​

Simplify ab2c3×a4b5c−6a−7b−8c9×a10b11c−12×a13b−14c15

M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

If the point (4,-2) lies on the graph of 2x=any+3,find the value of a

In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

Simplify : 5 3√250+7 3√16−14 3√54

The factors of (8a3 + b​​​​​​3 -6ab + 1) are?

Which among these is the approximate value of π?

For all values of A, B and C, prove that:- cosA + cosB + cosC + cos (A+B+C)= 4cos (A + B/2). cos (B+C/2). cos (C+ A/2)

If vectors \overrightarrow A =(\overset∧ i+2\overset∧ j+3\overset∧ k)m and \overrightarrow{B }=(-\overset∧ i-\overset∧ j-\overset∧ k)m represents two sides of a triangle then the third side can have a side equal to? 1) 3m 2) 8m 3) 6m 4) Both 1 and

Using identities, evaluate: 1.02×9.8

72. cotA/2-TanA/2 is equal to 1)2tanA. 2)2 cosA 3)2secA. 4)2 cot A

For a polynomial, x2 - 3x +2, which of the following is a factor ?

In ∆ABC, bisectors of ∠A and ∠B intersect at point O. If ∠C = 70° . Find measure of ∠AOB.

Factorise: (y+1/y)² - 5(y+1/y) + 4

Question 17 (i) (i) A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

3. ABCD and PQRC are rectangles and Q is the mid point of AC. Show that P is the mid point of DC and R is the mid point of BC .also find ratio of at(ABCD)and at( PQRC)

Define triangle.

Mark the correct alternative in each of the following: If − 3x+17&lt;-13, then(a) x∈(10, ∞)(b) x∈[10, ∞)(c) x∈(-∞, 10](d) x∈[-10, 10)

The sum of an angle and half of its complementary angle is 75°. The measure of the angle is(a) 40°(b) 50°(c) 60°(d) 80°

Identify the figure in which all the points could be collinear.

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

How many possibilities of even numbers are there when a single die is thrown?

How to prove pythagoras theorem?

Factorise: x2+7x−98

If x = 1/3-√5, find the value of (√x+1/√x) is

What is mean?

Find five rational numbers between 0 and 1.

Name the quadrant in which both abscissa and ordinate of a point are negative.

One tenth of 100 is ____.

Question 7A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Question 3 ΔABC, if AB =AC and ∠B=50∘ then ∠C is equal to (A) 40∘ (B) 50∘ (C) 80∘ (D) 130∘

If G is the centroid of △ ABC then prove that AB^2+BC^2+AC^2=3(GA^2+GB^2+GC^2)

In the given figure, if AB∥CD, CD∥EF and y:z=3:7, find x.

Question 22If x + 1 is a factor of ax3+x2–2x+4a–9, then find the value of a.

Factorize 3x²-5x+6

Given x + y = 2, then expressing x2-2y-4 in terms of y gives

If lengths of tangents drawn from the vertices of triangles whose vertices are (0,0),(5,0) and (0,12) to it's incircle are a,b,c(a<b<c) units. Then (a+b)×c is

5(25)n+1-25(5)2n --------------------------------------- 5*(5)2n+3-(25)n+1

The factors of (8a3 + b3 -6ab + 1) are?

Mark the correct alternative in each of the following: If − 3x+17<-13, then(a) x∈(10, ∞)(b) x∈[10, ∞)(c) x∈(-∞, 10](d) x∈[-10, 10)