32581 + Interview Questions in Mathematics

1.	Assertion(A)Reason(R)In the given fifure, a quad.ABCD isIn two concentric circles, the chorddrawn to circumscribe a given circle,of the larger circle, which touchesas shown. the smaller circle, is bisected at theThen,AB+BC=AD+DC. point of contact. The correct answer is (a)/(b)/(c)/(d).
Answer» $\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I n t h e g i v e n f i f u r e, a q u a d . A B C D i s & I n t w o c o n c e n t r i c c i r c l e s, t h e c h o r d d r a w n t o c i r c u m s c r i b e a g i v e n c i r c l e, & o f t h e l a r g e r c i r c l e, w h i c h t o u c h e s a s s h o w n . & t h e s m a l l e r c i r c l e, i s b i s e c t e d a t t h e T h e n, A B + B C = A D + D C . & p o i n t o f c o n t a c t . \end{matrix}$ The correct answer is (a)/(b)/(c)/(d).

1.

Assertion(A)Reason(R)In the given fifure, a quad.ABCD isIn two concentric circles, the chorddrawn to circumscribe a given circle,of the larger circle, which touchesas shown. the smaller circle, is bisected at theThen,AB+BC=AD+DC. point of contact. The correct answer is (a)/(b)/(c)/(d).

Answer»

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I n t h e g i v e n f i f u r e, a q u a d . A B C D i s & I n t w o c o n c e n t r i c c i r c l e s, t h e c h o r d d r a w n t o c i r c u m s c r i b e a g i v e n c i r c l e, & o f t h e l a r g e r c i r c l e, w h i c h t o u c h e s a s s h o w n . & t h e s m a l l e r c i r c l e, i s b i s e c t e d a t t h e T h e n, A B + B C = A D + D C . & p o i n t o f c o n t a c t . \end{matrix}$

The correct answer is (a)/(b)/(c)/(d).

3.	If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then
Answer» If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

4.	There is a boat with speed 17 km/hr. The stream has a speed of x km/hr. What are the upstream and downstream speeds respectively?
Answer» There is a boat with speed 17 km/hr. The stream has a speed of x km/hr. What are the upstream and downstream speeds respectively?

5.	Question 48 PQRS is a trapezium in which PQ∥SR and ∠P=130∘,∠Q=110∘. Then, ∠R is equal to a) 70∘ b) 50∘ c) 65∘ d) 55∘
Answer» Question 48 PQRS is a trapezium in which $P Q ∥ S R$ and $∠ P = 130^{\circ}, ∠ Q = 110^{\circ}$ . Then, $∠ R$ is equal to a) $70^{\circ}$ b) $50^{\circ}$ c) $65^{\circ}$ d) $55^{\circ}$

6.	An iron spherical ball of radius 21 cm is melted and it is re-cast into small hemispheres radius 7 cm each. The number of hemispheres formed will be
Answer» An iron spherical ball of radius 21 cm is melted and it is re-cast into small hemispheres radius 7 cm each. The number of hemispheres formed will be

7.	If a line segment is drawn between the points (-2,4) and (6,4) then find the coordinates of the point on the same segment which is 4 units from (-2,4).
Answer» If a line segment is drawn between the points (-2,4) and (6,4) then find the coordinates of the point on the same segment which is 4 units from (-2,4).

8.	If A=[42−11] and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =
Answer» If $A = [\begin{matrix} 4 & 2 - 1 & 1 \end{matrix}]$ and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

10.	A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.
Answer» A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.

11.	How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
Answer» How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

12.	There are 12 candies which Ram and Hari shared among themselves. If Ram gets x candies, the no. of candies that Hari gets is:
Answer» There are 12 candies which Ram and Hari shared among themselves. If Ram gets x candies, the no. of candies that Hari gets is:

13.	In figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.
Answer» In figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

15.	In fig. OPQR is a rhombus, three of whose vertices lie on the circle with centre O. If the area of the rhombus is 50∗ underoot3 cm sq., find the radius of the circle. Also, find the area of the sector ROPMR
Answer» In fig. OPQR is a rhombus, three of whose vertices lie on the circle with centre O. If the area of the rhombus is $50 *$ underoot3 cm sq., find the radius of the circle. Also, find the area of the sector ROPMR

16.	2 dices are thrown together.What is the probability of 1.) Product of two number is 12 2.) Sum of two number is 7
Answer» 2 dices are thrown together.What is the probability of 1.) Product of two number is 12 2.) Sum of two number is 7

21.	Question 28 If each side of a rhombus is doubled, how much will its area increase? (a) 1.5 times (b) 2 times (c) 3 times (d) 4 times
Answer» Question 28 If each side of a rhombus is doubled, how much will its area increase? (a) 1.5 times (b) 2 times (c) 3 times (d) 4 times

22.	Question 7 A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Answer» Question 7 A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per $m^{2}$ . (Note that the base of the tent will not be covered with canvas.)

14.	A circle of diameter 6cm was drawn. From a point outside the circle, the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is ___.
Answer» A circle of diameter 6cm was drawn. From a point outside the circle, the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is ___.

20.	Shruti can row downstream 30 km in 3 hours, and upstream 10 km in 5 hours. Find her speed of rowing in still water and the speed of the current
Answer» Shruti can row downstream 30 km in 3 hours, and upstream 10 km in 5 hours. Find her speed of rowing in still water and the speed of the current

23.	Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.
Answer» Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.

24.	What is the factorization of x2−5x+6?
Answer» What is the factorization of $x^{2} - 5 x + 6$ ?

26.	Find a solution of the equation cot x + tan x = 2 sec x.
Answer» Find a solution of the equation cot x + tan x = 2 sec x.

28.	Find the sum and the product of the roots of the following equations 3x2 + 6x + 9 = 0
Answer» Find the sum and the product of the roots of the following equations 3 $x^{2}$ + 6x + 9 = 0

29.	Which of the following can you say about the roots of x2–2x–3=0?
Answer» Which of the following can you say about the roots of $x^{2} - 2 x - 3 = 0$ ?

32.	In a △ABC right angled at B , the length AC is 37 cm and AB = 12 cm. Find the length of BC
Answer» In a $△ A B C$ right angled at B , the length AC is 37 cm and AB = 12 cm. Find the length of BC

33.	Question 5 The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.
Answer» Question 5 The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

34.	The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers.
Answer» The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers.

Explore topic-wise InterviewSolutions in Current Affairs.

Assertion(A)Reason(R)In the given fifure, a quad.ABCD isIn two concentric circles, the chorddrawn to circumscribe a given circle,of the larger circle, which touchesas shown. the smaller circle, is bisected at theThen,AB+BC=AD+DC. point of contact. The correct answer is (a)/(b)/(c)/(d).

(i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5. (ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8 Measure the two parts.

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

There is a boat with speed 17 km/hr. The stream has a speed of x km/hr. What are the upstream and downstream speeds respectively?

Question 48 PQRS is a trapezium in which PQ∥SR and ∠P=130∘,∠Q=110∘. Then, ∠R is equal to a) 70∘ b) 50∘ c) 65∘ d) 55∘

An iron spherical ball of radius 21 cm is melted and it is re-cast into small hemispheres radius 7 cm each. The number of hemispheres formed will be

If a line segment is drawn between the points (-2,4) and (6,4) then find the coordinates of the point on the same segment which is 4 units from (-2,4).

If A=[42−11] and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

Find the value of k for which the following system of equations has a unique solution: (5-8) 4x - 5y = k 2x - 3y = 12

A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

There are 12 candies which Ram and Hari shared among themselves. If Ram gets x candies, the no. of candies that Hari gets is:

In figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

A circle of diameter 6cm was drawn. From a point outside the circle, the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is ___.

In fig. OPQR is a rhombus, three of whose vertices lie on the circle with centre O. If the area of the rhombus is 50∗ underoot3 cm sq., find the radius of the circle. Also, find the area of the sector ROPMR

2 dices are thrown together.What is the probability of 1.) Product of two number is 12 2.) Sum of two number is 7

Make a frequency polygon from the given data. Weight (kg)Number Of Students35.5−40.5540.5−45.5245.5−50.51250.5−55.5255.5−60.545 [4 MARKS]

Question 85 When 0.02964 is divided by 0.004, what will be the quotient?

Question 62 Write the number in the box , such that 37× = 1598.

Shruti can row downstream 30 km in 3 hours, and upstream 10 km in 5 hours. Find her speed of rowing in still water and the speed of the current

Question 28 If each side of a rhombus is doubled, how much will its area increase? (a) 1.5 times (b) 2 times (c) 3 times (d) 4 times

Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.

What is the factorization of x2−5x+6?

Prove that: 1. √sec2A+cosec2A = tanA + cotA 2. sin2A(1+cot2A)+cos2A(1+tan2A) = 2

Find a solution of the equation cot x + tan x = 2 sec x.

Question 16(b) The present age of the father is 42 years and that of his son is 14 years. Find the ratio of: Age of the father to the age of the son, when the son was 12 years old.

Find the sum and the product of the roots of the following equations 3x2 + 6x + 9 = 0

Which of the following can you say about the roots of x2–2x–3=0?

Question 10 In the following question, out of the four options, only one is correct. Write the correct answer: The value of(−23)4 is equal to: (a) 1681 (b) 8116 (c) −1681 (d) 81−16

Factorise : 6a2−a−15

In a △ABC right angled at B , the length AC is 37 cm and AB = 12 cm. Find the length of BC

Question 5 The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers.

Given: sin(B+C)=√32 sin(A+C)=sin B and sin A=12. Find sin(A+B−C)

A boy runs to a shopping mall and comes back in 15 minutes. his speed on the way to the mall is 5 metre per second and his speed on the way back is 4 metre per second. find the distance to the mall.

A card is drawn from a pack of 100 cards from 1 to 100. Find the probability of drawing a number which is a perfect square.

In the given figure, ABCD is a rectangle of dimensions 21 cm X 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is (a) 1 : 3 (b) 1 : 8 (c) 1: 9 (d) 1 : 18

If (x+1),3x and (4x+2) are first three terms of an AP then its 5th term is -

If the mode of a series exceeds its mean by 24, then mode exceeds median by___

How many numbers can be formed using the digits 1, 2, 3 without repetition that are divisible by 4?

In Fig. , PQRS is a square of side 4 cm. Find the area of the shaded square.

Find the volume and surface area of a pyramid with a triangular base with each edge 6 cm and a height of 10 cm. [4 MARKS]

Solve the following inequation and represent the solution set on the number line: 2y−3≤y+1≤4y+7,yϵR. [4 MARKS]

Two dice are thrown, what is the probability of getting the sum being 8 or the sum being 10?

Question 6 The equation x = 7, in two variables, can be written as: A) 1.x + 1.y = 7 B) 1.x + 0.y = 7 C) 0.x + 1.y = 7 D) 1.x - 1.y = 7

The distribution of height of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table. Height110115x1120121125Number of students6814f143

35.	Given: sin(B+C)=√32 sin(A+C)=sin B and sin A=12. Find sin(A+B−C)
Answer» Given: $s i n (B + C) = \frac{\sqrt{3}}{2}$ $s i n (A + C) = s i n B$ and $s i n A = \frac{1}{2} .$ Find $s i n (A + B - C)$

36.	A boy runs to a shopping mall and comes back in 15 minutes. his speed on the way to the mall is 5 metre per second and his speed on the way back is 4 metre per second. find the distance to the mall.
Answer» A boy runs to a shopping mall and comes back in 15 minutes. his speed on the way to the mall is 5 metre per second and his speed on the way back is 4 metre per second. find the distance to the mall.

37.	A card is drawn from a pack of 100 cards from 1 to 100. Find the probability of drawing a number which is a perfect square.
Answer» A card is drawn from a pack of 100 cards from 1 to 100. Find the probability of drawing a number which is a perfect square.

38.	In the given figure, ABCD is a rectangle of dimensions 21 cm X 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.
Answer» In the given figure, ABCD is a rectangle of dimensions 21 cm X 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

40.	If (x+1),3x and (4x+2) are first three terms of an AP then its 5th term is -
Answer» If $(x + 1), 3 x a n d (4 x + 2)$ are first three terms of an AP then its $5^{t h}$ term is -

41.	Given below is the distribution of total household expenditure of 200 manual workers in a city. Expenditure (in Rs.) No. of manual workers1000−1500241500−2000402000−2500312500−3000283000−3500323500−4000234000−4500174500−50005 Find the expenditure done by maximum number of manual workers.
Answer» Given below is the distribution of total household expenditure of 200 manual workers in a city. $\begin{matrix} Expenditure (in Rs.) & No. of manual workers 1000 - 1500 & 24 1500 - 2000 & 40 2000 - 2500 & 31 2500 - 3000 & 28 3000 - 3500 & 32 3500 - 4000 & 23 4000 - 4500 & 17 4500 - 5000 & 5 \end{matrix}$ Find the expenditure done by maximum number of manual workers.

42.	If the mode of a series exceeds its mean by 24, then mode exceeds median by___
Answer» If the mode of a series exceeds its mean by 24, then mode exceeds median by___

43.	How many numbers can be formed using the digits 1, 2, 3 without repetition that are divisible by 4?
Answer» How many numbers can be formed using the digits 1, 2, 3 without repetition that are divisible by 4?

45.	Find the volume and surface area of a pyramid with a triangular base with each edge 6 cm and a height of 10 cm. [4 MARKS]
Answer» Find the volume and surface area of a pyramid with a triangular base with each edge 6 cm and a height of 10 cm. [4 MARKS]

46.	Solve the following inequation and represent the solution set on the number line: 2y−3≤y+1≤4y+7,yϵR. [4 MARKS]
Answer» Solve the following inequation and represent the solution set on the number line: $2 y - 3 \leq y + 1 \leq 4 y + 7, y ϵ R .$ [4 MARKS]