32581 + Interview Questions in Mathematics

1.	Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.
Answer» Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.

Discussion

2.	The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions 2 m ×1.25 m ×1 m, then find the number of boxes.
Answer» The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions $2$ m $\times 1.25$ m $\times 1$ m, then find the number of boxes.

Discussion

3.	Franklin saves ₹25 every month. Plot a graph for his savings in 9 consecutive months. Also, find the equation of the line that represents the situation.
Answer» Franklin saves ₹25 every month. Plot a graph for his savings in 9 consecutive months. Also, find the equation of the line that represents the situation.

Discussion

4.	if α and β are zeores of polynomial p(y)= x2+x-2, find the value of: {1\α} -{1\β}
Answer» if α and β are zeores of polynomial p(y)= x²+x-2, find the value of: {1\α} -{1\β}

Discussion

5.	Show that:(i) tan10∘tan15∘tan75∘tan80∘=1(ii) sin42∘sec48∘+cos42∘ cosec 48∘=2
Answer» Show that: $(i) tan 10^{\circ} tan 15^{\circ} tan 75^{\circ} tan 80^{\circ} = 1$ $(i i) sin 42^{\circ} sec 48^{\circ} + cos 42^{\circ}$ cosec $48^{\circ} = 2$

Discussion

6.	A six face dice is marked with the numbers 1, 2, 3, 4, 5 and 6. What is the probability of getting a number which is not even?
Answer» A six face dice is marked with the numbers 1, 2, 3, 4, 5 and 6. What is the probability of getting a number which is not even?

Discussion

7.	The line graph shows the percentage of students passing in 10th and 12 board exams from 5 different schools. Study the graph carefully to answer questions. Q. If the ratio of students who passed in 10th from school B and the students who failed in 12th from school D was 16:3, then total students who wrote 12th from school D were what percent more or less than those students who wrote 10th from school B
Answer» The line graph shows the percentage of students passing in 10th and 12 board exams from 5 different schools. Study the graph carefully to answer questions. Q. If the ratio of students who passed in 10th from school B and the students who failed in 12th from school D was 16:3, then total students who wrote 12th from school D were what percent more or less than those students who wrote 10th from school B

Discussion

8.	If a and b are relatively prime numbers, then what is their HCF?
Answer» If a and b are relatively prime numbers, then what is their HCF?

Discussion

9.	Match the following events with corresponding probability on tossing two coins simultaneously.
Answer» Match the following events with corresponding probability on tossing two coins simultaneously.

Discussion

10.	If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.
Answer» If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

Discussion

11.	If a hexagon ABCDEF circumscribe a circle. Prove thatAB+CD+EF = BC+DE+FA
Answer» If a hexagon ABCDEF circumscribe a circle. Prove that AB+CD+EF = BC+DE+FA

Discussion

12.	A letter is chosen at random from the words of ‘Byju’s Learning App’. Find the probability that the selected letter is a vowel.
Answer» A letter is chosen at random from the words of ‘Byju’s Learning App’. Find the probability that the selected letter is a vowel.

Discussion

13.	If the circumference and the area of a circle are numerically equal, then diameter of the circle is(a) π2(b) 2π(c) 2(d) 4
Answer» If the circumference and the area of a circle are numerically equal, then diameter of the circle is (a) $\frac{π}{2}$ (b) 2 $π$ (c) 2 (d) 4

Discussion

14.	If \operatorname{secθ-\operatorname{cosθ=5, then \operatorname{sec^2θ+\operatorname{cos^2θ is equal to
Answer» If \operatorname{secθ-\operatorname{cosθ=5, then \operatorname{sec^2θ+\operatorname{cos^2θ is equal to

Discussion

15.	Let →a=^i−3^j+2^k. Then a vector which is parallel to →a and double in magnitude is:
Answer» Let $\to a =^i - 3^j + 2^k$ . Then a vector which is parallel to $\to a$ and double in magnitude is:

Discussion

16.	tan 90∘
Answer» tan $90^{\circ}$

Discussion

17.	If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, find the possible values of k.
Answer» If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, find the possible values of k.

Discussion

18.	find two consecutive odd natural numbers the sum of whose square is 394
Answer» find two consecutive odd natural numbers the sum of whose square is 394

Discussion

19.	What some should Ashok invest in RS 25 shares selling at RS 36 to obtain and income of RS 720 if the dividend declared by the company is 12% also find: 1. The number of shares bought by Ashok 2. The percentage return on his income
Answer» What some should Ashok invest in RS 25 shares selling at RS 36 to obtain and income of RS 720 if the dividend declared by the company is 12% also find: 1. The number of shares bought by Ashok 2. The percentage return on his income

Discussion

20.	Can inches be used in Pythagoras theorem?
Answer» Can inches be used in Pythagoras theorem?

Discussion

21.	Find the sum of first 24 terms of an AP whose nth term is given by an=3+2n.
Answer» Find the sum of first $24$ terms of an AP whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$ .

Discussion

22.	Which of the following stateements is not true ? (a) If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P. (b) If a point P lies on the circle, then one and only tangent can eb drawn to the circle at P. (c) If a point P lies outside the circle, then only two tangents can be drawn to the circle from P (d) A circle can have more than two parallel tangents, parallel to a given line.
Answer» Which of the following stateements is not true ? (a) If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P. (b) If a point P lies on the circle, then one and only tangent can eb drawn to the circle at P. (c) If a point P lies outside the circle, then only two tangents can be drawn to the circle from P (d) A circle can have more than two parallel tangents, parallel to a given line.

22.

Which of the following stateements is not true ? (a) If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P. (b) If a point P lies on the circle, then one and only tangent can eb drawn to the circle at P. (c) If a point P lies outside the circle, then only two tangents can be drawn to the circle from P (d) A circle can have more than two parallel tangents, parallel to a given line.

Answer»

Which of the following stateements is not true ?

(a) If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P.

(b) If a point P lies on the circle, then one and only tangent can eb drawn to the circle at P.

(c) If a point P lies outside the circle, then only two tangents can be drawn to the circle from P

(d) A circle can have more than two parallel tangents, parallel to a given line.

Discussion

23.	Which of the following represents the correct truth table for the electrical network shown in figure given below?
Answer» Which of the following represents the correct truth table for the electrical network shown in figure given below?

Discussion

24.	The sum and product of the zeros of a quadratic polynomial are -12 and −3 respectively. What is the quadratic polynomial.
Answer» The sum and product of the zeros of a quadratic polynomial are $- \frac{1}{2}$ and −3 respectively. What is the quadratic polynomial.

Discussion

25.	To draw a pair of tangents to a circle, which are inclined to each other at angle of 450 , we have to draw the tangents at the end points of those two radii, the angle between which is [CBSE 2011](a) 1050(b) 1350(c) 1400(d) 1450
Answer» To draw a pair of tangents to a circle, which are inclined to each other at angle of 45⁰ , we have to draw the tangents at the end points of those two radii, the angle between which is [CBSE 2011] (a) 105⁰ (b) 135⁰ (c) 140⁰ (d) 145⁰

Discussion

26.	Solve each of the following quadratic equations: x2−(1+√2)x+√2=0
Answer» Solve each of the following quadratic equations: $x^{2} - (1 + \sqrt{2}) x + \sqrt{2} = 0$

Discussion

27.	31. Find the distance between the points A(7,13) and B(10,9)
Answer» 31. Find the distance between the points A(7,13) and B(10,9)

Discussion

28.

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk. Age (years) Less than 5 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 No. of patients 38 32 50 36 24 20

Answer» Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

Age (years)	Less than 5	5 - 9	10 - 14	15 - 19	20 - 24	25 - 29
No. of patients	38	32	50	36	24	20

Discussion

29.	Image formed by plane mirror is
Answer» Image formed by plane mirror is

Discussion

30.	Question 91 In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.
Answer» Question 91 In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

30.

Question 91 In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

Answer»

Question 91

In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

Discussion

31.	In the given figure, ∠DAB = ∠ABC = 90∘. Also if α + φ = 90∘ and α = 2φ. The the ratio of H and h is ___
Answer» In the given figure, $∠ D A B$ = $∠ A B C$ = $90^{\circ}$ . Also if $α$ + $φ$ = $90^{\circ}$ and α = 2 $φ$ . The the ratio of H and h is ___

31.

In the given figure, ∠DAB = ∠ABC = 90∘. Also if α + φ = 90∘ and α = 2φ. The the ratio of H and h is ___

Answer»

In the given figure, $∠ D A B$ = $∠ A B C$ = $90^{\circ}$ . Also if $α$ + $φ$ = $90^{\circ}$ and α = 2 $φ$ . The the ratio of H and h is ___

Discussion

32.	Prove that 3 + 1 3 - cot 30° = tan360° - 2sin 60° .
Answer» Prove that $(\sqrt{3} + 1) (3 - c o t 30^{°}) = \tan^{3} 60^{°} - 2 \sin 60^{°}$ .

Discussion

33.	If ax2 + bx + c = 0 has equal roots, then c =(a) -b2a(b) b2a(c) -b24a(d) b24a
Answer» If ax² + bx + c = 0 has equal roots, then c = (a) $\frac{- b}{2 a}$ (b) $\frac{b}{2 a}$ (c) $\frac{- b^{2}}{4 a}$ (d) $\frac{b^{2}}{4 a}$

Discussion

34.	Complete the factor trees of 36.
Answer» Complete the factor trees of 36.

Discussion

35.	If PQ = RS and ∠ORS=48∘ in the given figure, what are the values of ∠OPQ and ∠SOR?
Answer» If PQ = RS and $∠ O R S = 48^{\circ}$ in the given figure, what are the values of $∠ O P Q$ and $∠ S O R$ ?

Discussion

36.	Which of the following polynomials can be divided by a polynomial of degree 4?
Answer» Which of the following polynomials can be divided by a polynomial of degree 4?

Discussion

37.	Use graph paper for this question. Take 1 cm = 1 unit on both axes.(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).(ii) Construct the locus of points equidistant from A and B.(iii) Construct the locus of points equidistant from AB and AC.(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC.Then the length(approximately) of PA in cm is
Answer» Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(1, 1), B(5, 3) and C(2, 7). (ii) Construct the locus of points equidistant from A and B. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length(approximately) of PA in cm is

37.

Use graph paper for this question. Take 1 cm = 1 unit on both axes.(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).(ii) Construct the locus of points equidistant from A and B.(iii) Construct the locus of points equidistant from AB and AC.(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC.Then the length(approximately) of PA in cm is

Answer»

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC.

Then the length(approximately) of PA in cm is

Discussion

38.	What is the average water level of River – A in all the four months together?
Answer» What is the average water level of River – A in all the four months together?

Discussion

39.	A mixture of 70 litres of wine and water contains 10% of water. What quantity of water must be added to make the water content 12.5% of the resulting mixture?
Answer» A mixture of 70 litres of wine and water contains $10 %$ of water. What quantity of water must be added to make the water content $12.5 %$ of the resulting mixture?

Discussion

40.	25. Radial nodes present in 3s and 3p orbitals are respectively
Answer» 25. Radial nodes present in 3s and 3p orbitals are respectively

Discussion

41.	In a school of 100 children, 50 play cricket and 60 play football. Find the probability that a student selected at random plays both the sports if each of the student plays at least one sport.
Answer» In a school of 100 children, 50 play cricket and 60 play football. Find the probability that a student selected at random plays both the sports if each of the student plays at least one sport.

Discussion

42.	If cosθ=23, then write the value of secθ-1secθ+1.
Answer» $If \cos θ = \frac{2}{3}, then write the value of \frac{(\sec θ - 1)}{(\sec θ + 1)} .$

Discussion

43.	Question 1 (iii) Fill in the blanks:(iii) The longest chord of a circle is the __________ of the circle.
Answer» Question 1 (iii) Fill in the blanks: (iii) The longest chord of a circle is the __________ of the circle.

Discussion

44.	If (x-2,4)and (3,y+1)are two equal pairs of RR find the values of x and y
Answer» If (x-2,4)and (3,y+1)are two equal pairs of RR find the values of x and y

Discussion

45.	A rational number is its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form pq ? Give reasons.
Answer» A rational number is its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form $\frac{p}{q}$ ? Give reasons.

Discussion

46.	If A=[1−223], then the value of A3−4A2+10A=
Answer» If $A = [\begin{matrix} 1 & - 2 2 & 3 \end{matrix}],$ then the value of $A^{3} - 4 A^{2} + 10 A =$

Discussion

47.	If x2+px+q=0 and x2+qx+p=0 have a common root, then which of the following is correct about p and q.
Answer» If $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0$ have a common root, then which of the following is correct about p and q.

Discussion

48.	The decimal expansion of the rational number 4324×53 will terminate after how many places of decimals?
Answer» The decimal expansion of the rational number $\frac{43}{2^{4} \times 5^{3}}$ will terminate after how many places of decimals?

Discussion

49.	Question 1Write whether the following statements are true or false? Justify your answer.(i) Point (3,0) lies in the first quadrant.(ii) Points (1, - 1) and (-1, 1) lie in the same quadrant.(iii) The coordinates of a point whose ordinate is −12 and abscissa is 1 are (−12,1).(iv) A point lies on Y-axis at a distance of 2 units from the X-axis, its coordinates are (2,0).(v) (-1,7) is a point in the second quadrant.
Answer» Question 1 Write whether the following statements are true or false? Justify your answer. (i) Point (3,0) lies in the first quadrant. (ii) Points (1, - 1) and (-1, 1) lie in the same quadrant. (iii) The coordinates of a point whose ordinate is $- \frac{1}{2}$ and abscissa is 1 are $(- \frac{1}{2}, 1)$ . (iv) A point lies on Y-axis at a distance of 2 units from the X-axis, its coordinates are (2,0). (v) (-1,7) is a point in the second quadrant.

Discussion

50.	The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs (iv) a face card (v) a queen of diamond.
Answer» The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs (iv) a face card (v) a queen of diamond.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.

The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions 2 m ×1.25 m ×1 m, then find the number of boxes.

Franklin saves ₹25 every month. Plot a graph for his savings in 9 consecutive months. Also, find the equation of the line that represents the situation.

if α and β are zeores of polynomial p(y)= x2+x-2, find the value of: {1\α} -{1\β}

Show that:(i) tan10∘tan15∘tan75∘tan80∘=1(ii) sin42∘sec48∘+cos42∘ cosec 48∘=2

A six face dice is marked with the numbers 1, 2, 3, 4, 5 and 6. What is the probability of getting a number which is not even?

If a and b are relatively prime numbers, then what is their HCF?

Match the following events with corresponding probability on tossing two coins simultaneously.

If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

If a hexagon ABCDEF circumscribe a circle. Prove thatAB+CD+EF = BC+DE+FA

A letter is chosen at random from the words of ‘Byju’s Learning App’. Find the probability that the selected letter is a vowel.

If the circumference and the area of a circle are numerically equal, then diameter of the circle is(a) π2(b) 2π(c) 2(d) 4

If \operatorname{secθ-\operatorname{cosθ=5, then \operatorname{sec^2θ+\operatorname{cos^2θ is equal to

Let →a=^i−3^j+2^k. Then a vector which is parallel to →a and double in magnitude is:

tan 90∘

If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, find the possible values of k.

find two consecutive odd natural numbers the sum of whose square is 394

What some should Ashok invest in RS 25 shares selling at RS 36 to obtain and income of RS 720 if the dividend declared by the company is 12% also find: 1. The number of shares bought by Ashok 2. The percentage return on his income

Can inches be used in Pythagoras theorem?

Find the sum of first 24 terms of an AP whose nth term is given by an=3+2n.

Which of the following represents the correct truth table for the electrical network shown in figure given below?

The sum and product of the zeros of a quadratic polynomial are -12 and −3 respectively. What is the quadratic polynomial.

To draw a pair of tangents to a circle, which are inclined to each other at angle of 450 , we have to draw the tangents at the end points of those two radii, the angle between which is [CBSE 2011](a) 1050(b) 1350(c) 1400(d) 1450

Solve each of the following quadratic equations: x2−(1+√2)x+√2=0

31. Find the distance between the points A(7,13) and B(10,9)

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk. Age (years) Less than 5 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 No. of patients 38 32 50 36 24 20

Image formed by plane mirror is

Question 91 In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

In the given figure, ∠DAB = ∠ABC = 90∘. Also if α + φ = 90∘ and α = 2φ. The the ratio of H and h is ___

Prove that 3 + 1 3 - cot 30° = tan360° - 2sin 60° .

If ax2 + bx + c = 0 has equal roots, then c =(a) -b2a(b) b2a(c) -b24a(d) b24a

Complete the factor trees of 36.

If PQ = RS and ∠ORS=48∘ in the given figure, what are the values of ∠OPQ and ∠SOR?

Which of the following polynomials can be divided by a polynomial of degree 4?

What is the average water level of River – A in all the four months together?

A mixture of 70 litres of wine and water contains 10% of water. What quantity of water must be added to make the water content 12.5% of the resulting mixture?

25. Radial nodes present in 3s and 3p orbitals are respectively

In a school of 100 children, 50 play cricket and 60 play football. Find the probability that a student selected at random plays both the sports if each of the student plays at least one sport.

If cosθ=23, then write the value of secθ-1secθ+1.

Question 1 (iii) Fill in the blanks:(iii) The longest chord of a circle is the __________ of the circle.

If (x-2,4)and (3,y+1)are two equal pairs of RR find the values of x and y

A rational number is its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form pq ? Give reasons.

If A=[1−223], then the value of A3−4A2+10A=

If ​​​​​​x2+px+q=0 and x2+qx+p=0 have a common root, then which of the following is correct about p and q.

The decimal expansion of the rational number 4324×53 will terminate after how many places of decimals?

The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs (iv) a face card (v) a queen of diamond.

If x2+px+q=0 and x2+qx+p=0 have a common root, then which of the following is correct about p and q.