32581 + Interview Questions in Mathematics Page 194 InterviewSolution

9651.	Q. The total surface area of a cone is 628 sq cm and its slant height is 10 cm. Find the radius of the cone. [ pie=3.14]
Answer» Q. The total surface area of a cone is 628 sq cm and its slant height is 10 cm. Find the radius of the cone. [ pie=3.14]

Discussion

9652.	A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h(1+tan α cot β)m.
Answer» A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be $α$ and $β$ , respectively. Prove that the height of the other house is $h (1 + t a n α c o t β) m$ .

Discussion

9653.	A={x:xbelongs to Z,x is solution of x⁴-16=0}then A=
Answer» A={x:xbelongs to Z,x is solution of x⁴-16=0}then A=

Discussion

9654.	If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.
Answer» If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.

9654.

If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.

Answer»

If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.

Discussion

9655.	Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:1)3x^2-12)1-2x-3x^2
Answer» Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients: 1)3x^2-1 2)1-2x-3x^2

Discussion

9656.	Find a quadratic polynomial having zeroes equal to 7 and -3 ?
Answer» Find a quadratic polynomial having zeroes equal to 7 and -3 ?

Discussion

9657.	Solve the following quadratic equations by factorization:1x-1x-2=3, x≠0, 2
Answer» Solve the following quadratic equations by factorization: $\frac{1}{x} - \frac{1}{x - 2} = 3, x \neq 0, 2$

Discussion

9658.	The average number of students in a government school in Bangalore is 4800 and the average number in private schools is 6400. If there are 6 private schools and 4 government schools in an area, what is the average number of students per school in that area?
Answer» The average number of students in a government school in Bangalore is 4800 and the average number in private schools is 6400. If there are 6 private schools and 4 government schools in an area, what is the average number of students per school in that area?

Discussion

9659.	In each of the following experiments specify appropriate sample space.(i) A boy has a 1 rupee coin, a 2 rupee coin and a 5 rupee coin in this pocket. He takes out two coins out of his pocket, one after the other.(ii) A person is noting down the number of accidents along a busy highway during a year.
Answer» In each of the following experiments specify appropriate sample space. $(i)$ A boy has a $1$ rupee coin, a $2$ rupee coin and a $5$ rupee coin in this pocket. He takes out two coins out of his pocket, one after the other. $(i i)$ A person is noting down the number of accidents along a busy highway during a year.

Discussion

9660.	{ Q }3/10 The number of consecutive zeros in }2^3×3^4×}{5^4×7 is:
Answer» { Q }3/10 The number of consecutive zeros in }2^3×3^4×}{5^4×7 is:

Discussion

9661.	What is Sum of angle ?
Answer» What is Sum of angle ?

Discussion

9662.	Find the mean of the following data, using step-deviation method: Class5−1515−2525−3535−4545−5555−6565−75Frequency61016152487
Answer» Find the mean of the following data, using step-deviation method: $\begin{matrix} Class & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 Frequency & 6 & 10 & 16 & 15 & 24 & 8 & 7 \end{matrix}$

Discussion

9663.	The sum of the digits of a two digit number is 9 . If 27 is added to it , the digits of the number get reversed . th number is (a) 25 (b) 72 (c) 63 (d) 36
Answer» The sum of the digits of a two digit number is 9 . If 27 is added to it , the digits of the number get reversed . th number is (a) 25 (b) 72 (c) 63 (d) 36

Discussion

9664.	ntIntegrate the following with respect to xn nt(1+sec x)n
Answer» ntIntegrate the following with respect to xn nt(1+sec x)n

Discussion

9665.	A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m per second. In how much time will the tank be filled?
Answer» A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m per second. In how much time will the tank be filled?

Discussion

9666.	What is the slope of the line joining the points (x1,y1) and (x2,y2)?
Answer» What is the slope of the line joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ ?

Discussion

9667.	Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.) Draw the graph of the same.
Answer» Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.) Draw the graph of the same.

Discussion

9668.	If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, then a possible values of k is .
Answer» If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, then a possible values of k is .

Discussion

9669.	Lcm of 18 and 24 is
Answer» Lcm of 18 and 24 is

Discussion

9670.	Question 3 (i) In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that (i)AB2=BC×BD
Answer» Question 3 (i) In the given figure, ABD is a triangle right angled at A and $A C ⊥ B D$ . Show that $(i) A B^{2} = B C \times B D$

Discussion

9671.	Which of the following expressions is a polynomial in one variable?
Answer» Which of the following expressions is a polynomial in one variable?

Discussion

9672.	A and B together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Form the quadratic equation to find how many marbles they had to start with, if A had x marbles
Answer» A and B together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Form the quadratic equation to find how many marbles they had to start with, if A had x marbles

Discussion

9673.	Which of the given objects has the largest radius?
Answer» Which of the given objects has the largest radius?

Discussion

9674.	If a, b are the roots of the equation x2+x+1=0, then a2+b2=
Answer» If a, b are the roots of the equation $x^{2} + x + 1 = 0,$ $t h e n a^{2} + b^{2} =$

Discussion

9675.	Find the area of a rectangle, if the length of the rectangle is x and the breadth is twice the length the area of the rectangle?
Answer» Find the area of a rectangle, if the length of the rectangle is x and the breadth is twice the length the area of the rectangle?

Discussion

9676.	How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?
Answer» How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?

Discussion

9677.	Find the nature of roots of a quadratic equation, if its discriminant is equal to 4.
Answer» Find the nature of roots of a quadratic equation, if its discriminant is equal to 4.

Discussion

9678.	If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is(a) π:2(b) π:3(c) π:4(d) π:6
Answer» If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is (a) $π : 2$ (b) $π : 3$ (c) $π : 4$ (d) $π : 6$

Discussion

9679.	In an AP, where the first term is 7 and the common difference is 4, ___ th term of the AP will be five times the first term. (Enter a number)
Answer» In an AP, where the first term is 7 and the common difference is 4, ___ $^{t h}$ term of the AP will be five times the first term. (Enter a number)

Discussion

9680.	(i) In the given figure, 3 × CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4 cm. Find CD. (iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.
Answer» (i) In the given figure, 3 $\times$ CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 $\times$ PA = 3 $\times$ AB = 30 cm and PC = 4 cm. Find CD. (iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

9680.

(i) In the given figure, 3 × CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4 cm. Find CD. (iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

Answer»

(i) In the given figure, 3 $\times$ CP = PD = 9 cm and AP = 4.5 cm. Find BP.

(ii) In the given figure, 5 $\times$ PA = 3 $\times$ AB = 30 cm and PC = 4 cm. Find CD.

(iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

Discussion

9681.	Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.
Answer» Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

Discussion

9682.	Very-Short-Answer QuestionsFind the solution of the quadratic equation 33x2+10x+3=0. [CBSE 2009]
Answer» Very-Short-Answer Questions Find the solution of the quadratic equation $3 \sqrt{3} x^{2} + 10 x + \sqrt{3} = 0$ . [CBSE 2009]

Discussion

9683.	If one of the zeroes of the cubic polynomial x³+ax²+bx+c is -1, then product of the other two zeroes is 1. b-a+12. b-a-13.a-b+14. a-b-1
Answer» If one of the zeroes of the cubic polynomial x³+ax²+bx+c is -1, then product of the other two zeroes is 1. b-a+1 2. b-a-1 3.a-b+1 4. a-b-1

Discussion

9684.	How many spherical bullets can be made out of a solid cube of lead whose edge measure 44cm,each bullet being 4cm in diameter . Use pie =22 by 7
Answer» How many spherical bullets can be made out of a solid cube of lead whose edge measure 44cm,each bullet being 4cm in diameter . Use pie =22 by 7

Discussion

9685.	A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a solid cone of base diameters 8 cm . the hieght of the cone will b
Answer» A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a solid cone of base diameters 8 cm . the hieght of the cone will b

Discussion

9686.	Question 1 The following table shows the ages of the patients admitted in a hospital during a year: Age(in years)5−1515−2525−3535−4545−5555−65Number of patients6112123145 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Answer» Question 1 The following table shows the ages of the patients admitted in a hospital during a year: $\begin{matrix} Age(in years) & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 Number of patients & 6 & 11 & 21 & 23 & 14 & 5 \end{matrix}$ Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

9686.

Question 1 The following table shows the ages of the patients admitted in a hospital during a year: Age(in years)5−1515−2525−3535−4545−5555−65Number of patients6112123145 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer»

Question 1
The following table shows the ages of the patients admitted in a hospital during a year:

$\begin{matrix} Age(in years) & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 Number of patients & 6 & 11 & 21 & 23 & 14 & 5 \end{matrix}$

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Discussion

9687.	Solve 9x2= 36
Answer» Solve 9x²= 36

Discussion

9688.	Prove the following trigonometric identitiescosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
Answer» Prove the following trigonometric identities cosec⁶θ = cot⁶θ + 3 cot²θ cosec²θ + 1

Discussion

9689.	State SAS similarity criterion.
Answer» State SAS similarity criterion.

Discussion

9690.	The height of a cone is 10 cm. The cone is divided into two parts usign a plane parallel to its base at the middle of its height. Find the ration of the volumes of two parts.
Answer» The height of a cone is 10 cm. The cone is divided into two parts usign a plane parallel to its base at the middle of its height. Find the ration of the volumes of two parts.

Discussion

9691.	The H.C.F. and L.C.M. of two expression are (x − 3) and (x3 − 5x2 − 2x + 24) respectively. If one of the expression is (x2 − 7x + 12) find the other.
Answer» The H.C.F. and L.C.M. of two expression are (x − 3) and (x³ − 5x² − 2x + 24) respectively. If one of the expression is (x² − 7x + 12) find the other.

Discussion

9692.	A thief, after commiting a theft runs at a uniform speed of 50 m/minute . After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute everey suceeding minute. After how many minutes, the policeman will catch the thief.?
Answer» A thief, after commiting a theft runs at a uniform speed of 50 m/minute . After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute everey suceeding minute. After how many minutes, the policeman will catch the thief.?

Discussion

9693.	A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 liters of a 40% acid solution? [ 4 MARKS]
Answer» A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 liters of a 40% acid solution? [ 4 MARKS]

Discussion

9694.	The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is(a) 179321(b) 178321(c) 175321(d) 176321
Answer» The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is (a) $\frac{179}{321}$ (b) $\frac{178}{321}$ (c) $\frac{175}{321}$ (d) $\frac{176}{321}$

Discussion

9695.	If PT is a tangent to a circle with centre O and PQ is a chord of the circle such that ∠QPT = 70∘ then find the measure of ∠POQ
Answer» If PT is a tangent to a circle with centre O and PQ is a chord of the circle such that ∠QPT = 70^∘ then find the measure of ∠POQ

Discussion

9696.	The line joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP/AB = 2/5. Find the coordinates of P.
Answer» The line joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP/AB = 2/5. Find the coordinates of P.

Discussion

9697.	Mukund possesses Rs 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.
Answer» Mukund possesses Rs 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.

Discussion

9698.	33. Let C1 and C2 be two concentric circles such that the radius of C2 is double that of C1. From a point on C2, tangent PA and PB are drwan to C1. Prove that the centroid of triangle PAB lies on C1.
Answer» 33. Let C1 and C2 be two concentric circles such that the radius of C2 is double that of C1. From a point on C2, tangent PA and PB are drwan to C1. Prove that the centroid of triangle PAB lies on C1.

Discussion

9699.	What is a journal? Give a specimen of a journal showing at least five entries.
Answer» What is a journal? Give a specimen of a journal showing at least five entries.

Discussion

9700.	It is proposed to build a single circular park whose area is equal to the sum of the areas of two circular parks of diameters 24 m and 10 m in a locality. The radius of the new park will be
Answer» It is proposed to build a single circular park whose area is equal to the sum of the areas of two circular parks of diameters $24 m$ and $10 m$ in a locality. The radius of the new park will be

Discussion

Explore topic-wise InterviewSolutions in .

Q. The total surface area of a cone is 628 sq cm and its slant height is 10 cm. Find the radius of the cone. [ pie=3.14]

A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h(1+tan α cot β)m.

A={x:xbelongs to Z,x is solution of x⁴-16=0}then A=

If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:1)3x^2-12)1-2x-3x^2

Find a quadratic polynomial having zeroes equal to 7 and -3 ?

Solve the following quadratic equations by factorization:1x-1x-2=3, x≠0, 2

The average number of students in a government school in Bangalore is 4800 and the average number in private schools is 6400. If there are 6 private schools and 4 government schools in an area, what is the average number of students per school in that area?

{ Q }3/10 The number of consecutive zeros in }2^3×3^4×}{5^4×7 is:

What is Sum of angle ?

Find the mean of the following data, using step-deviation method: Class5−1515−2525−3535−4545−5555−6565−75Frequency61016152487

The sum of the digits of a two digit number is 9 . If 27 is added to it , the digits of the number get reversed . th number is (a) 25 (b) 72 (c) 63 (d) 36

ntIntegrate the following with respect to xn nt(1+sec x)n

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m per second. In how much time will the tank be filled?

What is the slope of the line joining the points (x1,y1) and (x2,y2)?

Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.) Draw the graph of the same.

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

Lcm of 18 and 24 is

Question 3 (i) In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that (i)AB2=BC×BD

Which of the following expressions is a polynomial in one variable?

A and B together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Form the quadratic equation to find how many marbles they had to start with, if A had x marbles

Which of the given objects has the largest radius?

If a, b are the roots of the equation x2+x+1=0, then a2+b2=

Find the area of a rectangle, if the length of the rectangle is x and the breadth is twice the length the area of the rectangle?

How many coins 1.75 cm in diameter &amp; 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?

Find the nature of roots of a quadratic equation, if its discriminant is equal to 4.

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is(a) π:2(b) π:3(c) π:4(d) π:6

In an AP, where the first term is 7 and the common difference is 4, ___ th term of the AP will be five times the first term. (Enter a number)

(i) In the given figure, 3 × CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 × PA = 3 × AB = 30 cm and PC = 4 cm. Find CD. (iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

Very-Short-Answer QuestionsFind the solution of the quadratic equation 33x2+10x+3=0. [CBSE 2009]

If one of the zeroes of the cubic polynomial x³+ax²+bx+c is -1, then product of the other two zeroes is 1. b-a+12. b-a-13.a-b+14. a-b-1

How many spherical bullets can be made out of a solid cube of lead whose edge measure 44cm,each bullet being 4cm in diameter . Use pie =22 by 7

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a solid cone of base diameters 8 cm . the hieght of the cone will b

Question 1 The following table shows the ages of the patients admitted in a hospital during a year: Age(in years)5−1515−2525−3535−4545−5555−65Number of patients6112123145 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Solve 9x2= 36

Prove the following trigonometric identitiescosec6θ = cot6θ + 3 cot2θ cosec2θ + 1

State SAS similarity criterion.

The height of a cone is 10 cm. The cone is divided into two parts usign a plane parallel to its base at the middle of its height. Find the ration of the volumes of two parts.

The H.C.F. and L.C.M. of two expression are (x − 3) and (x3 − 5x2 − 2x + 24) respectively. If one of the expression is (x2 − 7x + 12) find the other.

A thief, after commiting a theft runs at a uniform speed of 50 m/minute . After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute everey suceeding minute. After how many minutes, the policeman will catch the thief.?

A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 liters of a 40% acid solution? [ 4 MARKS]

The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is(a) 179321(b) 178321(c) 175321(d) 176321

If PT is a tangent to a circle with centre O and PQ is a chord of the circle such that ∠QPT = 70∘ then find the measure of ∠POQ

The line joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP/AB = 2/5. Find the coordinates of P.

Mukund possesses Rs 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.

33. Let C1 and C2 be two concentric circles such that the radius of C2 is double that of C1. From a point on C2, tangent PA and PB are drwan to C1. Prove that the centroid of triangle PAB lies on C1.

What is a journal? Give a specimen of a journal showing at least five entries.

It is proposed to build a single circular park whose area is equal to the sum of the areas of two circular parks of diameters 24 m and 10 m in a locality. The radius of the new park will be

How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?