24740 + Interview Questions in Mathematics Page 152 InterviewSolution

7551.	What is the graph of the equation X=Y .
Answer» What is the graph of the equation X=Y .

Discussion

7552.	The degree of the algebraic expression \lbrack(x2 – 3x)2 ÷ 3x2\rbrack is = ?
Answer» The degree of the algebraic expression \lbrack(x2 – 3x)2 ÷ 3x2\rbrack is = ?

Discussion

7553.	1. A unit square has its corner corner chopped off to from a regular polygon with eight sides. What is the area of this polygon?
Answer» 1. A unit square has its corner corner chopped off to from a regular polygon with eight sides. What is the area of this polygon?

Discussion

7554.	Question 15 If the angles of a triangle are x , y and 40∘, and the difference between the two angles x and y is 30∘, then , find the value of x and y.
Answer» Question 15 If the angles of a triangle are $x$ , $y$ and $40^{\circ}$ , and the difference between the two angles $x$ and $y$ is $30^{\circ}$ , then , find the value of $x$ and $y$ .

Discussion

7555.	Solve the equations by substitution method:6x=7y+7 7y−x=8
Answer» Solve the equations by substitution method: $6 x = 7 y + 7$ $7 y - x = 8$

7555.

Solve the equations by substitution method:6x=7y+7 7y−x=8

Answer»

Solve the equations by substitution method:

$6 x = 7 y + 7$

$7 y - x = 8$

Discussion

7556.	In the equation ax+by+c=0, if y= (cx+d)b and a = d, then what is the value of 'x' ?
Answer» In the equation $a x + b y + c = 0$ , if y= $\frac{(c x + d)}{b}$ and a = d, then what is the value of ' $x$ ' ?

Discussion

7557.	If the hcf of two numbers a and b is 1 then a and b always = (1)even natural numbers (2)odd natural numbers (3) co prime numbers (4) even number andodd number respctivel
Answer» If the hcf of two numbers a and b is 1 then a and b always = (1)even natural numbers (2)odd natural numbers (3) co prime numbers (4) even number andodd number respctivel

Discussion

7558.	x+2 is a factor of f(x)=2x3−ax2−bx+20. When f(x) is divided by (x−1), the remainder is 12. The value of a and b is:
Answer» $x + 2 is a factor of f (x) = 2 x^{3} - a x^{2} - b x + 20. When f (x) is divided by (x - 1), the remainder is 12. The value of a and b is:$

Discussion

7559.

The investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below: Sectors Investment (in ten crores of rupees) Central Government Securities State Government Securities Securities guaranteed by the Government Private Sectors Socially oriented sectors (Plans) Socially oriented sectors (Non-Plan) 45 11 23 18 46 11 Represent the above data with the help of bar graph.

Answer» The investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below:

Sectors	Investment (in ten crores of rupees)
Central Government Securities State Government Securities Securities guaranteed by the Government Private Sectors Socially oriented sectors (Plans) Socially oriented sectors (Non-Plan)	45 11 23 18 46 11

Represent the above data with the help of bar graph.

Discussion

7560.	Which of the following is an irrational number?
Answer» Which of the following is an irrational number?

Discussion

7561.	If A (a2,2a) ,B (1/a2,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1
Answer» If A (a²,2a) ,B (1/a²,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1

Discussion

7562.	In a ΔABC, the sides BC=5,CA=4,AB=3. If A(0,0) and the internal bisector of angle A meets BC in D(127,127), then incentre of △ABC is
Answer» In a $Δ A B C,$ the sides $B C = 5, C A = 4, A B = 3 .$ If $A (0, 0)$ and the internal bisector of angle $A$ meets $B C$ in $D (\frac{12}{7}, \frac{12}{7})$ , then incentre of $△ A B C$ is

Discussion

7563.	A hemispherical bowl fits exactly on the open surface of a right cone with height 5 cm and radius 3.5 cm. The volume of the solid formed is [Take π=227]
Answer» A hemispherical bowl fits exactly on the open surface of a right cone with height $5 c m$ and radius $3.5 c m$ . The volume of the solid formed is [Take $π = \frac{22}{7}$ ]

7563.

A hemispherical bowl fits exactly on the open surface of a right cone with height 5 cm and radius 3.5 cm. The volume of the solid formed is [Take π=227]

Answer»

A hemispherical bowl fits exactly on the open surface of a right cone with height $5 c m$ and radius $3.5 c m$ . The volume of the solid formed is

[Take $π = \frac{22}{7}$ ]

Discussion

7564.	The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?
Answer» The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?

Discussion

7565.	The base of a prism is a rectangle with sides 3 cm and 4 cm respectively. The height of the prism is 10 cm. It is split vertically along a diagonal of the base into two triangular prisms. What is the total surface area of each of these triangular prisms?
Answer» The base of a prism is a rectangle with sides 3 cm and 4 cm respectively. The height of the prism is 10 cm. It is split vertically along a diagonal of the base into two triangular prisms. What is the total surface area of each of these triangular prisms?

Discussion

7566.	If one zero of the polynomial 3x2 -7px+10p be 5, find p and other zero.
Answer» If one zero of the polynomial 3x2 -7px+10p be 5, find p and other zero.

Discussion

7567.	Question 5 (ii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income(in ₹)Vehicles per family012Above 2Less than 7000101602507000−10000030527210000−13000153529113000−160002469592516000 or more15798288 Suppose a family is chosen, find the probability that the family chosen is (ii) earning ₹16000 or more per month and owning exactly 1vehicle.
Answer» Question 5 (ii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: $\begin{matrix} Monthly income(in ₹) & Vehicles per family 0 & 1 & 2 & Above 2 Less than 7000 & 10 & 160 & 25 & 0 7000 - 10000 & 0 & 305 & 27 & 2 10000 - 13000 & 1 & 535 & 29 & 1 13000 - 16000 & 2 & 469 & 59 & 25 16000 or more & 1 & 579 & 82 & 88 \end{matrix}$ Suppose a family is chosen, find the probability that the family chosen is (ii) earning ₹16000 or more per month and owning exactly 1vehicle.

Discussion

7568.	Prove that the perimeter of the triangle is greater than the sum of its all medians
Answer» Prove that the perimeter of the triangle is greater than the sum of its all medians

Discussion

7569.	The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10m and height h. Then the height of the cuboidal tank (in metres) is ___
Answer» The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10m and height h. Then the height of the cuboidal tank (in metres) is ___

Discussion

7570.	Question 4 (d)Fill in the blank with a suitable word.Unwanted sound is called _______.
Answer» Question 4 (d) Fill in the blank with a suitable word. Unwanted sound is called _______.

Discussion

7571.	If the height and radius of a cone of volume V are doubled, then the volume of the cone, is(a) 3 V(b) 4 V(c) 6 V(d) 8 V
Answer» If the height and radius of a cone of volume V are doubled, then the volume of the cone, is (a) 3 V (b) 4 V (c) 6 V (d) 8 V

Discussion

7572.	determine the missing digit :2 , 6, ? 61, 121
Answer» determine the missing digit : 2 , 6, ? 61, 121

Discussion

7573.	Class mark of a particular class is 9.5 and the class size is 6, then the class interval is
Answer» Class mark of a particular class is 9.5 and the class size is 6, then the class interval is

Discussion

7574.	What is the probability that two friends have different birthdays in a normal year?
Answer» What is the probability that two friends have different birthdays in a normal year?

Discussion

7575.	In ΔABC,∠A=45∘, ∠B=60∘, and ∠C=75∘. Find the angles formed by joining the mid-points of the sides of the given triangle.
Answer» In $Δ A B C, ∠ A = 45^{\circ}, ∠ B = 60^{\circ}$ , and $∠ C = 75^{\circ}$ . Find the angles formed by joining the mid-points of the sides of the given triangle.

Discussion

7576.

The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below: Refinery: Barauni Koyali Mathura Mumbai Florida Production of oil (in lakh tonnes) 30 70 40 45 25 Construct a bar graph to represent the above data so that the bars are drawn horizontally.

Answer» The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:

Refinery:	Barauni	Koyali	Mathura	Mumbai	Florida
Production of oil (in lakh tonnes)	30	70	40	45	25

Construct a bar graph to represent the above data so that the bars are drawn horizontally.

Discussion

7577.	Find the area of a triangle whose sides are 9 cm,12 cm, and 15 cm.
Answer» Find the area of a triangle whose sides are $9 c m, 12 c m$ , and $15 c m .$

Discussion

7578.	Question 1Show that the points A(1, 2), B(-1, -16) and C(0, -7) lie on the graph of the linear equation:y = 9x - 7.
Answer» Question 1 Show that the points A(1, 2), B(-1, -16) and C(0, -7) lie on the graph of the linear equation: y = 9x - 7.

Discussion

7579.	S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true?
Answer» S1: AM = $\frac{A P}{2}$ , BN= $\frac{B P}{2}$ S2: OO' = AM + BN Which of the above statements are true?

7579.

S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true?

Answer»

S1: AM = $\frac{A P}{2}$ , BN= $\frac{B P}{2}$

S2: OO' = AM + BN

Which of the above statements are true?

Discussion

7580.	If PQ ∥ BC and PR ∥CD in the given figure, then prove that ARAD= AQAB.
Answer» If PQ $∥$ BC and PR $∥$ CD in the given figure, then prove that $\frac{A R}{A D}$ = $\frac{A Q}{A B}$ .

7580.

If PQ ∥ BC and PR ∥CD in the given figure, then prove that ARAD= AQAB.

Answer»

If PQ $∥$ BC and PR $∥$ CD in the given figure, then prove that $\frac{A R}{A D}$ = $\frac{A Q}{A B}$ .

Discussion

7581.	What are the coordinates of the foot of the perpendicular drawn from the point (3, 5) to the line, 2x + 3y + 7 = 0?
Answer» What are the coordinates of the foot of the perpendicular drawn from the point (3, 5) to the line, 2x + 3y + 7 = 0?

Discussion

7582.	Question 2 (b) How many diagonals does each of the following have? (b) A regular hexagon
Answer» Question 2 (b) How many diagonals does each of the following have? (b) A regular hexagon

Discussion

7583.	The measures of some angles are given below. Write the measures of their complementary angles.(i) 40∘(ii) 63∘(iii)45∘(iv) 55∘(v) 20∘(vi) 90∘(vii)x∘
Answer» The measures of some angles are given below. Write the measures of their complementary angles. (i) $40^{\circ}$ (ii) $63^{\circ}$ (iii) $45^{\circ}$ (iv) $55^{\circ}$ (v) $20^{\circ}$ (vi) $90^{\circ}$ (vii) $x^{\circ}$

Discussion

7584.	O is a point that lies in the interior of triangle ABC. Is 2(OA+OB+OC)>Perimeter of triangle ABC?
Answer» O is a point that lies in the interior of triangle ABC. Is 2(OA+OB+OC)>Perimeter of triangle ABC?

Discussion

7585.	Five cards - the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. (a) What is the probability that the drawn card is the queen? (b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen [4 MARKS]
Answer» Five cards - the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. (a) What is the probability that the drawn card is the queen? (b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen [4 MARKS]

Discussion

7586.	What is the value of (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ) when tanθ=43.
Answer» What is the value of $\frac{(1 + sin θ) (1 - sin θ)}{(1 + cos θ) (1 - cos θ)}$ when $tan θ = \frac{4}{3}$ .

Discussion

7587.	Sec theta(1-sin theta)(sec theta+ tan theta)=1
Answer» Sec theta(1-sin theta)(sec theta+ tan theta)=1

Discussion

7588.	How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum calculated at simple interest?
Answer» How much time will it take for an amount of $R s . 450$ to yield $R s . 81$ as interest at $4.5 %$ per annum calculated at simple interest?

Discussion

7589.	Which congruency criterion could be used only to check for congruency of two right-angled triangles?
Answer» Which congruency criterion could be used only to check for congruency of two right-angled triangles?

Discussion

7590.	If I sell 45 of 10 apples, how many are left?
Answer» If I sell $\frac{4}{5}$ of 10 apples, how many are left?

Discussion

7591.	10. Draw the graph of }y=\vert x\vert-3
Answer» 10. Draw the graph of }y=\vert x\vert-3

Discussion

7592.	Question 9The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is(A) 56 cm(B) 42 cm(C) 28 cm(D) 16 cm
Answer» Question 9 The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is (A) 56 cm (B) 42 cm (C) 28 cm (D) 16 cm

Discussion

7593.	If A=[α011] and B=[1031], Then the value of α for which A2=B is
Answer» If $A = [\begin{matrix} α & 0 1 & 1 \end{matrix}]$ and $B = [\begin{matrix} 1 & 0 3 & 1 \end{matrix}],$ Then the value of $α$ for which $A^{2} = B$ is

Discussion

7594.	The number of consecutive zeros in 23 ×34 ×54 ×7, is(a) 3(b) 2(c) 4(d) 5
Answer» The number of consecutive zeros in $2^{3} \times 3^{4} \times 5^{4} \times 7$ , is (a) 3 (b) 2 (c) 4 (d) 5

Discussion

7595.	If A is an idempotent matrix and (2I+A)4=aI+bA,(I is unit matrix),a,b∈R. Then (a+b)=
Answer» If $A$ is an idempotent matrix and $(2 I + A)^{4} = a I + b A, (I is unit matrix), a, b \in R .$ Then $(a + b) =$

Discussion

7596.	Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it.What is the probability of:(i) getting a number 6.(ii) getting a number greater than 6.(iii) getting a 1-digit number.
Answer» Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it.What is the probability of: (i) getting a number 6. (ii) getting a number greater than 6. (iii) getting a 1-digit number.

Discussion

7597.	Question 4In the given graph the letter that indicates the point (0,3) is (a) P(b) Q(c) R(d) S
Answer» Question 4 In the given graph the letter that indicates the point (0,3) is (a) P (b) Q (c) R (d) S

Discussion

7598.	ABC is the right angled triangle with ∠ABC = 90∘, the centre of the circle passing through ABC lies on _______.
Answer» ABC is the right angled triangle with $∠$ ABC = $90^{\circ}$ , the centre of the circle passing through ABC lies on _______.

Discussion

7599.	Which of the following is not a solution of the linear equation x + 2y = 6?
Answer» Which of the following is not a solution of the linear equation x + 2y = 6?

Discussion

7600.	The locus of z satisfying arg z=π3 is ____________.
Answer» The locus of z satisfying $\arg (z) = \frac{π}{3}$ is ____________.

Discussion

Explore topic-wise InterviewSolutions in .

What is the graph of the equation X=Y .

The degree of the algebraic expression \lbrack(x2 – 3x)2 ÷ 3x2\rbrack is = ?

1. A unit square has its corner corner chopped off to from a regular polygon with eight sides. What is the area of this polygon?

Question 15 If the angles of a triangle are x , y and 40∘, and the difference between the two angles x and y is 30∘, then , find the value of x and y.

Solve the equations by substitution method:6x=7y+7 7y−x=8

In the equation ax+by+c=0, if y= (cx+d)b and a = d, then what is the value of 'x' ?

If the hcf of two numbers a and b is 1 then a and b always = (1)even natural numbers (2)odd natural numbers (3) co prime numbers (4) even number andodd number respctivel

x+2 is a factor of f(x)=2x3−ax2−bx+20. When f(x) is divided by (x−1), the remainder is 12. The value of a and b is:

Which of the following is an irrational number?

If A (a​​​​​​2,2a) ,B​​​​​​ (1/a​​​​​​2,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1

In a ΔABC, the sides BC=5,CA=4,AB=3. If A(0,0) and the internal bisector of angle A meets BC in D(127,127), then incentre of △ABC is

A hemispherical bowl fits exactly on the open surface of a right cone with height 5 cm and radius 3.5 cm. The volume of the solid formed is [Take π=227]

The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?

The base of a prism is a rectangle with sides 3 cm and 4 cm respectively. The height of the prism is 10 cm. It is split vertically along a diagonal of the base into two triangular prisms. What is the total surface area of each of these triangular prisms?

If one zero of the polynomial 3x2 -7px+10p be 5, find p and other zero.

Prove that the perimeter of the triangle is greater than the sum of its all medians

The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10m and height h. Then the height of the cuboidal tank (in metres) is ___

Question 4 (d)Fill in the blank with a suitable word.Unwanted sound is called _______.

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is(a) 3 V(b) 4 V(c) 6 V(d) 8 V

determine the missing digit :2 , 6, ? 61, 121

Class mark of a particular class is 9.5 and the class size is 6, then the class interval is

What is the probability that two friends have different birthdays in a normal year?

In ΔABC,∠A=45∘, ∠B=60∘, and ∠C=75∘. Find the angles formed by joining the mid-points of the sides of the given triangle.

The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below: Refinery: Barauni Koyali Mathura Mumbai Florida Production of oil (in lakh tonnes) 30 70 40 45 25 Construct a bar graph to represent the above data so that the bars are drawn horizontally.

Find the area of a triangle whose sides are 9 cm,12 cm, and 15 cm.

Question 1Show that the points A(1, 2), B(-1, -16) and C(0, -7) lie on the graph of the linear equation:y = 9x - 7.

S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true?

If PQ ∥ BC and PR ∥CD in the given figure, then prove that ARAD= AQAB.

What are the coordinates of the foot of the perpendicular drawn from the point (3, 5) to the line, 2x + 3y + 7 = 0?

Question 2 (b) How many diagonals does each of the following have? (b) A regular hexagon

The measures of some angles are given below. Write the measures of their complementary angles.(i) 40∘(ii) 63∘(iii)45∘(iv) 55∘(v) 20∘(vi) 90∘(vii)x∘

O is a point that lies in the interior of triangle ABC. Is 2(OA+OB+OC)>Perimeter of triangle ABC?

What is the value of (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ) when tanθ=43.

Sec theta(1-sin theta)(sec theta+ tan theta)=1

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum calculated at simple interest?

Which congruency criterion could be used only to check for congruency of two right-angled triangles?

If I sell 45 of 10 apples, how many are left?

10. Draw the graph of }y=\vert x\vert-3

Question 9The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is(A) 56 cm(B) 42 cm(C) 28 cm(D) 16 cm

If A=[α011] and B=[1031], Then the value of α for which A2=B is

The number of consecutive zeros in 23 ×34 ×54 ×7, is(a) 3(b) 2(c) 4(d) 5

If A is an idempotent matrix and (2I+A)4=aI+bA,(I is unit matrix),a,b∈R. Then (a+b)=

Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it.What is the probability of:(i) getting a number 6.(ii) getting a number greater than 6.(iii) getting a 1-digit number.

Question 4In the given graph the letter that indicates the point (0,3) is (a) P(b) Q(c) R(d) S

ABC is the right angled triangle with ∠ABC = 90∘, the centre of the circle passing through ABC lies on _______.

Which of the following is not a solution of the linear equation x + 2y = 6?

The locus of z satisfying arg z=π3 is ____________.

If A (a2,2a) ,B (1/a2,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1