24740 + Interview Questions in Mathematics

1.	Assertion: The points (-3,5) and (5,-3) are at different positions in the coordinate plane. Reason: The position of (x,y) in the Cartesian plane is different from the position of (y, x). Which of the following is correct?
Answer» Assertion: The points (-3,5) and (5,-3) are at different positions in the coordinate plane. Reason: The position of (x,y) in the Cartesian plane is different from the position of (y, x). Which of the following is correct?

1.

Assertion: The points (-3,5) and (5,-3) are at different positions in the coordinate plane. Reason: The position of (x,y) in the Cartesian plane is different from the position of (y, x). Which of the following is correct?

Answer»

Assertion: The points (-3,5) and (5,-3) are at different positions in the coordinate plane.

Reason: The position of (x,y) in the Cartesian plane is different from the position of (y, x).

Which of the following is correct?

2.	Construct a triangle ABC in which BC=7 cm, ∠B=75∘ and AB+AC=13 cm
Answer» Construct a triangle ABC in which $B C = 7 c m, ∠ B = 75^{\circ} a n d A B + A C = 13 c m$

Discussion

3.	Derive the formula or the relationship between mean, mode,and median of a set of numbers, i.e., Mode=(3×median)-(2×mean) In an asymmetrical set of numbers
Answer» Derive the formula or the relationship between mean, mode,and median of a set of numbers, i.e., Mode=(3×median)-(2×mean) In an asymmetrical set of numbers

Discussion

4.	Question 109Solve the followingA carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charge is Rs. 200 per hour. For how many hours did the carpenter work?
Answer» Question 109 Solve the following A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charge is Rs. 200 per hour. For how many hours did the carpenter work?

4.

Question 109Solve the followingA carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charge is Rs. 200 per hour. For how many hours did the carpenter work?

Answer»

Question 109

Solve the following

A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charge is Rs. 200 per hour. For how many hours did the carpenter work?

Discussion

5.	Question 37Without actually calculating the cubes, find the value of(i) (12)3+(13)3−(56)3(ii) (0.2)3−(0.3)3+(0.1)3
Answer» Question 37 Without actually calculating the cubes, find the value of (i) ${(\frac{1}{2})}^{3} + {(\frac{1}{3})}^{3} - {(\frac{5}{6})}^{3}$ (ii) $(0.2)^{3} - (0.3)^{3} + (0.1)^{3}$

Discussion

6.	f:R→R is defined as f(x)=x4−6x2+12. The range of f(x) is
Answer» $f : R \to R$ is defined as $f (x) = x^{4} - 6 x^{2} + 12$ . The range of f(x) is

Discussion

7.	Let the vectors a, b, c and d be such that (a×b)×(c×d)=0. Let P1 and P2 be planes determined by pair of vectors a, b and c, d respectively. Then the angle between P1 and P2 is
Answer» Let the vectors a, b, c and d be such that $(a \times b) \times (c \times d) = 0$ . Let $P_{1}$ and $P_{2}$ be planes determined by pair of vectors a, b and c, d respectively. Then the angle between $P_{1}$ and $P_{2}$ is

Discussion

8.	The distance of a point (2, 3) from the y - axis is.
Answer» The distance of a point (2, 3) from the y - axis is.

Discussion

9.	In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.
Answer» In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.

Discussion

10.	Evaluate the following product using the specific formula (y−34)(y−43)
Answer» Evaluate the following product using the specific formula $(y - \frac{3}{4}) (y - \frac{4}{3})$

Discussion

11.	In the given figure, T is a point on QR such that QT : TR = 1 : 3 and U is a point on PR such that PU : UR = 1 : 3, then the value of UT equals
Answer» In the given figure, T is a point on QR such that QT : TR = 1 : 3 and U is a point on PR such that PU : UR = 1 : 3, then the value of UT equals

Discussion

12.	A samsung tablet is to be sent as a gift to a person. The shopkeeper has to wrap the tablet which is in a box of dimensions 20 cm × 10 cm × 5 cm. How much paper would be required to wrap it? (assuming negligible thickness)
Answer» A samsung tablet is to be sent as a gift to a person. The shopkeeper has to wrap the tablet which is in a box of dimensions 20 cm $\times$ 10 cm $\times$ 5 cm. How much paper would be required to wrap it? (assuming negligible thickness)

Discussion

13.	sigma k=1 to 2004 ,[1/1+tan^4(k pi/4010)] value
Answer» sigma k=1 to 2004 ,[1/1+tan^4(k pi/4010)] value

Discussion

14.	Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?
Answer» Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?

Discussion

15.	Find the third side of a triangle whose two sides are (3m2−5m) and (4m2+12) and perimeter is (8m2−9m+4).
Answer» Find the third side of a triangle whose two sides are $(3 m^{2} - 5 m$ ) and $(4 m^{2} + 12$ ) and perimeter is $(8 m^{2} - 9 m + 4$ ).

Discussion

16.	Question 1How will you describe the position of a table lamp on your study table to another person?
Answer» Question 1 How will you describe the position of a table lamp on your study table to another person?

Discussion

17.	If three sides of a triangle are equal to the corresponding three sides of another triangle, named in sequence, then the two triangles are said to be __ triangles.
Answer» If three sides of a triangle are equal to the corresponding three sides of another triangle, named in sequence, then the two triangles are said to be __ triangles.

Discussion

18.	In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then the possible values of x are
Answer» In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then the possible values of x are

Discussion

19.	516−314 =_____
Answer» $5 \frac{1}{6} - 3 \frac{1}{4}$ =_____

Discussion

20.	Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m. Find the distance between their tops.
Answer» Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m. Find the distance between their tops.

Discussion

21.	A round ballon of radius r subtends an α at the eye of the observer while the an elevation of its centre β. The height of centre of the balloon is
Answer» A round ballon of radius r subtends an $α$ at the eye of the observer while the an elevation of its centre $β$ . The height of centre of the balloon is

Discussion

22.	In which quadrant are the following points ?(i) whose both co-ordinates are positive. (ii) whose both co-ordinates are negative.(iii) whose x co-ordinate is positive, and the y co-ordinate is negative.(iv) whose x co-ordinate is negative and y co-ordinate is positive.
Answer» In which quadrant are the following points ? (i) whose both co-ordinates are positive. (ii) whose both co-ordinates are negative. (iii) whose x co-ordinate is positive, and the y co-ordinate is negative. (iv) whose x co-ordinate is negative and y co-ordinate is positive.

Discussion

23.	The circumference of a circular field is 528 cm. Then its radius is __________.
Answer» The circumference of a circular field is 528 cm. Then its radius is __________.

Discussion

24.	if the remainder which the number 9^100 gives when divided by 8 is R, find 19R
Answer» if the remainder which the number 9^100 gives when divided by 8 is R, find 19R

Discussion

25.	If centroid of the triangle formed by the points (α2,2α)(3α,1−α) and (1,3) is (13,13), then centroid of the triangle formed by the points (2α−1,α3)(1−3α,2α2+3) and (0,−3α) is
Answer» If centroid of the triangle formed by the points $(α^{2}, 2 α) (3 α, 1 - α)$ and $(1, 3)$ is $(\frac{1}{3}, \frac{1}{3})$ , then centroid of the triangle formed by the points $(2 α - 1, α^{3}) (1 - 3 α, 2 α^{2} + 3)$ and $(0, - 3 α)$ is

Discussion

26.	Question 3 Plot the point P(1, 0), Q(4, 0) and S(1,3). Find the coordinates of the point R such that PQRS is a square.
Answer» Question 3 Plot the point P(1, 0), Q(4, 0) and S(1,3). Find the coordinates of the point R such that PQRS is a square.

Discussion

27.	The steps to draw a triangle with the base BC, a base angle ∠B and the difference of other two sides is given below.1. Draw the base BC and at point B make an angle say XBC equal to the given angle.2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').3. Join DC and draw the perpendicular bisector, say PQ of DC.The next step will be:
Answer» The steps to draw a triangle with the base BC, a base angle $∠$ B and the difference of other two sides is given below. 1. Draw the base BC and at point B make an angle say XBC equal to the given angle. 2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX'). 3. Join DC and draw the perpendicular bisector, say PQ of DC. The next step will be:

Discussion

28.	Two coins are tossed 1000 times and the outcomes are recorded as belowNumber of heads210Frequency200550250Based on this information, the probability for atmost one head is:
Answer» Two coins are tossed 1000 times and the outcomes are recorded as below $\begin{matrix} Number of heads & 2 & 1 & 0 Frequency & 200 & 550 & 250 \end{matrix}$ Based on this information, the probability for atmost one head is:

Discussion

29.	37.Three vectors P,Q and R are shown in the figure. Let S be any point on the vector R . The distance between the points P and S is b\|R\|. The general relation among vectors P,Q and S is
Answer» 37.Three vectors P,Q and R are shown in the figure. Let S be any point on the vector R . The distance between the points P and S is b\|R\|. The general relation among vectors P,Q and S is

Discussion

30.	If we start at (0, 0) on a rectangular coordinate system and move 3 units left and 6 units up, where do we end up?
Answer» If we start at (0, 0) on a rectangular coordinate system and move 3 units left and 6 units up, where do we end up?

Discussion

31.	{ The base of an isosceles triangle is equal to }4 units and the }}{ base angle is equal to }45^° . A straight line cuts the extension }}{ of the base at a point }M at the angle }θ and bisects the lateral }}{ side of the triangle which is nearest to }M.} 19. The area of quadrilateral which the straight line cuts off } from the given triangle is
Answer» { The base of an isosceles triangle is equal to }4 units and the }}{ base angle is equal to }45^° . A straight line cuts the extension }}{ of the base at a point }M at the angle }θ and bisects the lateral }}{ side of the triangle which is nearest to }M.} 19. The area of quadrilateral which the straight line cuts off } from the given triangle is

Discussion

32.	Rectangle ABCD and Parallelogram PQRS are between the same parallels.If AB=QR and area parallelogram PQRS=30cm2, then area Rectangle ABCD= ___cm2
Answer» Rectangle ABCD and Parallelogram PQRS are between the same parallels.If AB=QR and area parallelogram $P Q R S = 30 c m^{2}$ , then area Rectangle ABCD= ___ $c m^{2}$

Discussion

33.	Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.
Answer» Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.

Discussion

34.	In the above diagram identify the points which are equidistant from point V.
Answer» In the above diagram identify the points which are equidistant from point V.

Discussion

35.	Question 20If x + 2a is a factor of x5–4a2x3+2x+2a+3, then find the value of a.
Answer» Question 20 If x + 2a is a factor of $x^{5} - 4 a^{2} x^{3} + 2 x + 2 a + 3$ , then find the value of a.

Discussion

36.	2. The vertices of square are z1 z2 z3 and z4 taken anti clockwise order then z3=?
Answer» 2. The vertices of square are z1 z2 z3 and z4 taken anti clockwise order then z3=?

Discussion

37.	Question 3 (iii)On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent.32x+53y=7;9x−10y=14
Answer» Question 3 (iii) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent. $\frac{3}{2} x + \frac{5}{3} y = 7; 9 x - 10 y = 14$

Discussion

38.	Points (1, –1), (2, –2), (–3, –4), (4, –5)(a) all lie in the II quadrant(b) all lie in the III quadrant(c) all lie in the IV quadrant(d) do not lie in the same quadrant
Answer» Points (1, –1), (2, –2), (–3, –4), (4, –5) (a) all lie in the II quadrant (b) all lie in the III quadrant (c) all lie in the IV quadrant (d) do not lie in the same quadrant

Discussion

39.	What is the angle formed between north and south direction?
Answer» What is the angle formed between north and south direction?

Discussion

40.	Find the median of the following data: 12,17,3,14,5,8,7,15
Answer» Find the median of the following data: 12,17,3,14,5,8,7,15

40.

Find the median of the following data: 12,17,3,14,5,8,7,15

Answer»

Find the median of the following data:

12,17,3,14,5,8,7,15

Discussion

41.	In figure AD = DC and AB = BC(i) Is ΔABD ≅ ΔCBD?(ii) State the three parts of matching pairs you have used to answer (i).
Answer» In figure AD = DC and AB = BC (i) Is ΔABD ≅ ΔCBD? (ii) State the three parts of matching pairs you have used to answer (i).

41.

In figure AD = DC and AB = BC(i) Is ΔABD ≅ ΔCBD?(ii) State the three parts of matching pairs you have used to answer (i).

Answer»

In figure AD = DC and AB = BC

(i) Is ΔABD ≅ ΔCBD?

(ii) State the three parts of matching pairs you have used to answer (i).

Discussion

42.	Factorise8a3+27b3+36a2b+54ab2
Answer» Factorise $8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$

Discussion

43.	If x + 2 and x − 1 are the factors of x3 + 10x2 + mx + n, then the values of m and n are respectively(a) 5 and −3(b) 17 and −8(c) 7 and −18(d) 23 and −19
Answer» If x + 2 and x − 1 are the factors of x³ + 10x² + mx + n, then the values of m and n are respectively (a) 5 and −3 (b) 17 and −8 (c) 7 and −18 (d) 23 and −19

Discussion

44.	The average mark of 18 students was calculated to be 65. However,it was later found out that the marks of one students had been wrongly entered as 24 instead of 34 and another 88 instead of 78. Find the correct average?
Answer» The average mark of 18 students was calculated to be 65. However,it was later found out that the marks of one students had been wrongly entered as 24 instead of 34 and another 88 instead of 78. Find the correct average?

Discussion

45.	In the figure, lines AB and CD intersect at O.If ∠AOC+∠BOE=70∘ and ∠BOD=40∘, find ∠BOE and reflex ∠COE . [4 MARKS]
Answer» In the figure, lines AB and CD intersect at O.If $∠ A O C + ∠ B O E = 70^{\circ}$ and $∠ B O D = 40^{\circ}$ , find $∠ B O E$ and reflex $∠ C O E$ . [4 MARKS]

45.

In the figure, lines AB and CD intersect at O.If ∠AOC+∠BOE=70∘ and ∠BOD=40∘, find ∠BOE and reflex ∠COE . [4 MARKS]

Answer»

In the figure, lines AB and CD intersect at O.If $∠ A O C + ∠ B O E = 70^{\circ}$ and $∠ B O D = 40^{\circ}$ , find $∠ B O E$ and reflex $∠ C O E$ . [4 MARKS]

Discussion

46.	When p(x)=x3+ax2+2x+a is divided by (x+a), the remainder is: (a) 0 (b) a (c) -a (d) 2a
Answer» When $p (x) = x^{3} + a x^{2} + 2 x + a$ is divided by (x+a), the remainder is: (a) 0 (b) a (c) -a (d) 2a

Discussion

47.	Question 2Solve 2x + 3y = 11 and 2x - 4y = - 24 and hence find the value of 'm' for which y = mx + 3.
Answer» Question 2 Solve 2x + 3y = 11 and 2x - 4y = - 24 and hence find the value of 'm' for which y = mx + 3.

Discussion

48.	If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Answer» If sec² θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

Discussion

49.	In the following figure, a transversal cuts two parallel lines l and m at points G and H respectively and the angles thus formed are marked. If ∠1 is an acute angle, then, which of the following statements is false?
Answer» In the following figure, a transversal cuts two parallel lines l and m at points $G$ and $H$ respectively and the angles thus formed are marked. If $∠ 1$ is an acute angle, then, which of the following statements is false?

Discussion

50.	Question 3 Plot the points (x,y) given by the following table. x24−3−230y4205−30
Answer» Question 3 Plot the points (x,y) given by the following table. $\begin{matrix} x & 2 & 4 & - 3 & - 2 & 3 & 0 y & 4 & 2 & 0 & 5 & - 3 & 0 \end{matrix}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Assertion: The points (-3,5) and (5,-3) are at different positions in the coordinate plane. Reason: The position of (x,y) in the Cartesian plane is different from the position of (y, x). Which of the following is correct?

Construct a triangle ABC in which BC=7 cm, ∠B=75∘ and AB+AC=13 cm

Derive the formula or the relationship between mean, mode,and median of a set of numbers, i.e., Mode=(3×median)-(2×mean) In an asymmetrical set of numbers

Question 109Solve the followingA carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charge is Rs. 200 per hour. For how many hours did the carpenter work?

Question 37Without actually calculating the cubes, find the value of(i) (12)3+(13)3−(56)3(ii) (0.2)3−(0.3)3+(0.1)3

f:R→R is defined as f(x)=x4−6x2+12. The range of f(x) is

Let the vectors a, b, c and d be such that (a×b)×(c×d)=0. Let P1 and P2 be planes determined by pair of vectors a, b and c, d respectively. Then the angle between P1 and P2 is

The distance of a point (2, 3) from the y - axis is.

In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.

Evaluate the following product using the specific formula (y−34)(y−43)

In the given figure, T is a point on QR such that QT : TR = 1 : 3 and U is a point on PR such that PU : UR = 1 : 3, then the value of UT equals

A samsung tablet is to be sent as a gift to a person. The shopkeeper has to wrap the tablet which is in a box of dimensions 20 cm × 10 cm × 5 cm. How much paper would be required to wrap it? (assuming negligible thickness)

sigma k=1 to 2004 ,[1/1+tan^4(k pi/4010)] value

Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?

Find the third side of a triangle whose two sides are (3m2−5m) and (4m2+12) and perimeter is (8m2−9m+4).

Question 1How will you describe the position of a table lamp on your study table to another person?

If three sides of a triangle are equal to the corresponding three sides of another triangle, named in sequence, then the two triangles are said to be __ triangles.

In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then the possible values of x are

516−314 =_____

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m. Find the distance between their tops.

A round ballon of radius r subtends an α at the eye of the observer while the an elevation of its centre β. The height of centre of the balloon is

In which quadrant are the following points ?(i) whose both co-ordinates are positive. (ii) whose both co-ordinates are negative.(iii) whose x co-ordinate is positive, and the y co-ordinate is negative.(iv) whose x co-ordinate is negative and y co-ordinate is positive.

The circumference of a circular field is 528 cm. Then its radius is __________.

if the remainder which the number 9^100 gives when divided by 8 is R, find 19R

If centroid of the triangle formed by the points (α2,2α)(3α,1−α) and (1,3) is (13,13), then centroid of the triangle formed by the points (2α−1,α3)(1−3α,2α2+3) and (0,−3α) is

Question 3 Plot the point P(1, 0), Q(4, 0) and S(1,3). Find the coordinates of the point R such that PQRS is a square.

Two coins are tossed 1000 times and the outcomes are recorded as belowNumber of heads210Frequency200550250Based on this information, the probability for atmost one head is:

37.Three vectors P,Q and R are shown in the figure. Let S be any point on the vector R . The distance between the points P and S is b|R|. The general relation among vectors P,Q and S is

If we start at (0, 0) on a rectangular coordinate system and move 3 units left and 6 units up, where do we end up?

Rectangle ABCD and Parallelogram PQRS are between the same parallels.If AB=QR and area parallelogram PQRS=30cm2, then area Rectangle ABCD= ___cm2

Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.

In the above diagram identify the points which are equidistant from point V.

Question 20If x + 2a is a factor of x5–4a2x3+2x+2a+3, then find the value of a.

2. The vertices of square are z1 z2 z3 and z4 taken anti clockwise order then z3=?

Question 3 (iii)On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent.32x+53y=7;9x−10y=14

Points (1, –1), (2, –2), (–3, –4), (4, –5)(a) all lie in the II quadrant(b) all lie in the III quadrant(c) all lie in the IV quadrant(d) do not lie in the same quadrant

What is the angle formed between north and south direction?

Find the median of the following data: 12,17,3,14,5,8,7,15

In figure AD = DC and AB = BC(i) Is ΔABD ≅ ΔCBD?(ii) State the three parts of matching pairs you have used to answer (i).

Factorise8a3+27b3+36a2b+54ab2

If x + 2 and x − 1 are the factors of x3 + 10x2 + mx + n, then the values of m and n are respectively(a) 5 and −3(b) 17 and −8(c) 7 and −18(d) 23 and −19

The average mark of 18 students was calculated to be 65. However,it was later found out that the marks of one students had been wrongly entered as 24 instead of 34 and another 88 instead of 78. Find the correct average?

In the figure, lines AB and CD intersect at O.If ∠AOC+∠BOE=70∘ and ∠BOD=40∘, find ∠BOE and reflex ∠COE . [4 MARKS]

When p(x)=x3+ax2+2x+a is divided by (x+a), the remainder is: (a) 0 (b) a (c) -a (d) 2a

Question 2Solve 2x + 3y = 11 and 2x - 4y = - 24 and hence find the value of 'm' for which y = mx + 3.

If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

In the following figure, a transversal cuts two parallel lines l and m at points G and H respectively and the angles thus formed are marked. If ∠1 is an acute angle, then, which of the following statements is false?

Question 3 Plot the points (x,y) given by the following table. x24−3−230y4205−30