32581 + Interview Questions in Mathematics Page 62 InterviewSolution

3051.	In the given figure, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use π=227 and 5=2.236). [CBSE 2015]
Answer» In the given figure, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use $π = \frac{22}{7} and \sqrt{5} = 2.236$ ). [CBSE 2015]

Discussion

3052.	first term of ap is a and the sum of first p terms is zero show that the sum of its next q terms is _a(p+q)q/p-1
Answer» first term of ap is a and the sum of first p terms is zero show that the sum of its next q terms is _a(p+q)q/p-1

Discussion

3053.	A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
Answer» A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.

Discussion

3054.	26. In a triangle ABC, AB = AC.show that the altitude AD is median also.
Answer» 26. In a triangle ABC, AB = AC.show that the altitude AD is median also.

Discussion

3055.	Question 2980 bulbs are selected at random from a lot and their life time ( in hours) is recorded in the form of a frequency table given below:Lifetime (in hours)3005007009001100Frequency1012232510One bulb is selected at random from the lot. The probability that its life is 1150 h, is:A) 180B) 716C) 0D) 1
Answer» Question 29 80 bulbs are selected at random from a lot and their life time ( in hours) is recorded in the form of a frequency table given below: $\begin{matrix} Lifetime (in hours) & 300 & 500 & 700 & 900 & 1100 Frequency & 10 & 12 & 23 & 25 & 10 \end{matrix}$ One bulb is selected at random from the lot. The probability that its life is 1150 h, is: A) $\frac{1}{80}$ B) $\frac{7}{16}$ C) 0 D) 1

Discussion

3056.	Tick the correct answer in the following:Area of a sector of angle p (in degrees) of a circle with radius R is
Answer» Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is

Discussion

3057.	The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP. [CBSE 2013]
Answer» The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP. [CBSE 2013]

Discussion

3058.	The lengths of three consecutive sides of a quadrilateral circumscrbing a circle are 4cm, 5cm, and 7 cm respectively. Determine the length of the fourth side.
Answer» The lengths of three consecutive sides of a quadrilateral circumscrbing a circle are 4cm, 5cm, and 7 cm respectively. Determine the length of the fourth side.

Discussion

3059.	In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —
Answer» In $△$ ABC, AB = 3 and, AC = 4 cm and AD is the bisector of $∠$ A. Then, BD : DC is —

3059.

In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —

Answer»

In $△$ ABC, AB = 3 and, AC = 4 cm and AD is the bisector of $∠$ A. Then, BD : DC is —

Discussion

3060.	Question 7 Only one of the four options is correct. Write the correct one. On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is a) 12 b) 24 c) 27 d) 36
Answer» Question 7 Only one of the four options is correct. Write the correct one. On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is a) 12 b) 24 c) 27 d) 36

3060.

Question 7 Only one of the four options is correct. Write the correct one. On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is a) 12 b) 24 c) 27 d) 36

Answer»

Question 7

Only one of the four options is correct. Write the correct one.

On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is

a) 12

b) 24

c) 27

d) 36

Discussion

3061.	Fill in the blank using greater or less to make the statement true. 8 -13 -15 is __ than -15 -39 + 6
Answer» Fill in the blank using greater or less to make the statement true. 8 -13 -15 is __ than -15 -39 + 6

3061.

Fill in the blank using greater or less to make the statement true. 8 -13 -15 is __ than -15 -39 + 6

Answer»

Fill in the blank using greater or less to make the statement true.

8 -13 -15 is __ than -15 -39 + 6

Discussion

3062.	In triangle ABC, right angled at B, if ∠A is made larger and larger till it becomes 90∘, what can you say about AC and AB if BC = 1 unit?
Answer» In triangle ABC, right angled at B, if $∠$ A is made larger and larger till it becomes $90^{\circ}$ , what can you say about AC and AB if BC = 1 unit?

Discussion

3063.	The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms. [CBSE 2013C]
Answer» The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms. [CBSE 2013C]

Discussion

3064.	Distance of a point P(x,y) from x-axis is
Answer» Distance of a point P(x,y) from x-axis is

Discussion

3065.	Find the value of k for which each of the following quadratic equation has equal roots. (k-4)x2 +2(k-4)x +4=0.
Answer» Find the value of k for which each of the following quadratic equation has equal roots. (k-4)x² +2(k-4)x +4=0.

3065.

Find the value of k for which each of the following quadratic equation has equal roots. (k-4)x2 +2(k-4)x +4=0.

Answer»

Find the value of k for which each of the following quadratic equation has equal roots.

(k-4)x² +2(k-4)x +4=0.

Discussion

3066.	The cardinality of two disjoint sets A and B is in the ratio 2:1. If the cardinality of the union of these sets is 45, find the cardinality of the two sets.
Answer» The cardinality of two disjoint sets A and B is in the ratio 2:1. If the cardinality of the union of these sets is 45, find the cardinality of the two sets.

Discussion

3067.	Find the mode of the following data. xifi10101415187219259
Answer» Find the mode of the following data. $\begin{matrix} x_{i} & f_{i} 10 & 10 14 & 15 18 & 7 21 & 9 25 & 9 \end{matrix}$

Discussion

3068.	If a, b and c are in A.P, then which of the following seies does not form an A.P.?
Answer» If a, b and c are in A.P, then which of the following seies does not form an A.P.?

Discussion

3069.	P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that ΔBPQ is an isosceles triangle.
Answer» P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that ΔBPQ is an isosceles triangle.

Discussion

3070.	Question 9 (i) Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the (i) radius r' of the new sphere.
Answer» Question 9 (i) Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the (i) radius r' of the new sphere.

Discussion

3071.	Draw a direct common tangent to two congruent circles of radii 3 cm and whose centres are 9 cm apart.
Answer» Draw a direct common tangent to two congruent circles of radii 3 cm and whose centres are 9 cm apart.

Discussion

3072.	State the converse of Thale's theorem.
Answer» State the converse of Thale's theorem.

Discussion

3073.	The 4th term from the end of the AP: –11, –8, –5, ..., 49 is(a) 37(b) 40(c) 43(d) 58
Answer» The 4^th term from the end of the AP: –11, –8, –5, ..., 49 is (a) 37 (b) 40 (c) 43 (d) 58

Discussion

3074.	How are pyramids and cones alike?
Answer» How are pyramids and cones alike?

Discussion

3075.	The system of pair of equations 4x−3y+12=0 and 2x+3y−15=0 has
Answer» The system of pair of equations $4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$ has

Discussion

3076.	A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 L of the 9% solution, how many litres of 3% solution will have to be added? Or Solve the following system of linear inequalities graphically. 3x+2y≥24, 3x+y≤15, x≥4
Answer» A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 L of the 9% solution, how many litres of 3% solution will have to be added? Or Solve the following system of linear inequalities graphically. $3 x + 2 y \geq 24, 3 x + y \leq 15, x \geq 4$

3076.

A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 L of the 9% solution, how many litres of 3% solution will have to be added? Or Solve the following system of linear inequalities graphically. 3x+2y≥24, 3x+y≤15, x≥4

Answer»

A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 L of the 9% solution, how many litres of 3% solution will have to be added?

Or

Solve the following system of linear inequalities graphically.

$3 x + 2 y \geq 24, 3 x + y \leq 15, x \geq 4$

Discussion

3077.	The coordinates of the mid-points of sides AB, BC and CA of △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.
Answer» The coordinates of the mid-points of sides AB, BC and CA of △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.

Discussion

3078.	If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR=120∘, prove that 2PQ = PO.
Answer» If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that $∠ Q P R = 120^{\circ}$ , prove that 2PQ = PO.

Discussion

3079.	Sum of the areas of two squares is 640m2. If the difference of their perimeters is 64m, find the sides of two squares.
Answer» Sum of the areas of two squares is $640 m^{2} .$ If the difference of their perimeters is 64m, find the sides of two squares.

Discussion

3080.	In a two digit number the digit in the unit place is twice of the digit in the 10th if the digits are reversed the new number is 27 more then the given number find the number
Answer» In a two digit number the digit in the unit place is twice of the digit in the 10th if the digits are reversed the new number is 27 more then the given number find the number

Discussion

3081.	Divide 56 into 4 parts which are in AP such that the ratio of products of extremes to the products of means is 5:6.
Answer» Divide $56$ into $4$ parts which are in AP such that the ratio of products of extremes to the products of means is $5 : 6.$

Discussion

3082.	A rectangular playground has two semi circles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m & 21 m, find the area of the playground.
Answer» A rectangular playground has two semi circles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m & 21 m, find the area of the playground.

Discussion

3083.	Question 3A plumbline ( Sahul) is the combination of ( see figure)(A) a cone and a cylinder(B) a hemisphere and a cone(C) frustum of a cone and a cylinder(D) sphere and cylinder
Answer» Question 3 A plumbline ( Sahul) is the combination of ( see figure) (A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder

Discussion

3084.	If x∈(0,1), then the expression 12cos−1(1−x1+x) simplifies to:
Answer» If $x \in (0, 1)$ , then the expression $\frac{1}{2} {cos}^{- 1} (\frac{1 - x}{1 + x})$ simplifies to:

Discussion

3085.	Thimpu arranges cubes of volume 1 cu. cm into a 7 x 7 layer as shown below. How many such layers should be stacked one above other to form a cube of volume 343 cu. cm ?
Answer» Thimpu arranges cubes of volume 1 cu. cm into a 7 x 7 layer as shown below. How many such layers should be stacked one above other to form a cube of volume 343 cu. cm ?

Discussion

3086.	Solve the following quadratic equations by factorization:4x-3=52x+3, x≠0, -32
Answer» Solve the following quadratic equations by factorization: $\frac{4}{x} - 3 = \frac{5}{2 x + 3}, x \neq 0, - \frac{3}{2}$

Discussion

3087.	The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is
Answer» The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is

Discussion

3088.	If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are real, then k =(a) -32(b) 32(c) 23(d) -23
Answer» If the sum and product of the roots of the equation kx² + 6x + 4k = 0 are real, then k = (a) $- \frac{3}{2}$ (b) $\frac{3}{2}$ (c) $\frac{2}{3}$ (d) $- \frac{2}{3}$

Discussion

3089.	In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C=200, find ∠AOD
Answer» In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If $∠ C = 20^{0}$ , find $∠ A O D$

3089.

In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C=200, find ∠AOD

Answer»

In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If $∠ C = 20^{0}$ , find $∠ A O D$

Discussion

3090.	A field is in the form of a circle. A fence is to be erected around the field. The cost fencing would be Rs. 2640 at the rate of Rs. 12 per metre. The, the field is to be thoroughly ploughed at the cost of Re. 0.50 per m2. What is the amount required to plough the field? [Take π = 22/7].
Answer» A field is in the form of a circle. A fence is to be erected around the field. The cost fencing would be Rs. 2640 at the rate of Rs. 12 per metre. The, the field is to be thoroughly ploughed at the cost of Re. 0.50 per m2. What is the amount required to plough the field? [Take π = 22/7].

Discussion

3091.	In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).
Answer» In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

Discussion

3092.	If the roots of the equation b-cx2+c-ax+a-b=0 are equal, then prove that 2b = a + c.
Answer» If the roots of the equation $(b - c) x^{2} + (c - a) x + (a - b) = 0$ are equal, then prove that 2b = a + c.

Discussion

3093.	ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC
Answer» ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC

Discussion

3094.	If 29x+37y=103 and 37x+29y=95 then (a) x=1,y=2 (b) x=2,y=1 (c) x=3,y=2 (d) x=2,y=3
Answer» If $29 x + 37 y = 103 a n d 37 x + 29 y = 95$ then (a) x=1,y=2 (b) x=2,y=1 (c) x=3,y=2 (d) x=2,y=3

3094.

If 29x+37y=103 and 37x+29y=95 then (a) x=1,y=2 (b) x=2,y=1 (c) x=3,y=2 (d) x=2,y=3

Answer»

If $29 x + 37 y = 103 a n d 37 x + 29 y = 95$ then

(a) x=1,y=2 (b) x=2,y=1 (c) x=3,y=2 (d) x=2,y=3

Discussion

3095.	What will be the remainder when 4x4−3x3+2x2−x is divided by x+1?
Answer» What will be the remainder when $4 x^{4} - 3 x^{3} + 2 x^{2} - x$ is divided by $x + 1$ ?

Discussion

3096.	Volume of a cylinder is 343π and if the radius isequal to the height, then what is the height(in cm) of the cylinder?7
Answer» $Volume of a cylinder is 343 π and if the radius is$ $equal to the height, then what is the height$ $(in cm) of the cylinder?$ 7

Discussion

3097.	Find the value of cos 38o cosec 52otan 18o tan 35o tan 60o tan 72o tan 55o
Answer» Find the value of $\frac{c o s 38^{o} c o s e c 52^{o}}{t a n 18^{o} t a n 35^{o} t a n 60^{o} t a n 72^{o} t a n 55^{o}}$

Discussion

3098.	If A=200020002 such that A5 = λA, then λ = ___________.
Answer» If $A = [\begin{matrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{matrix}]$ such that A⁵ = λA, then λ = ___________.

Discussion

3099.	If the set A has 3 elements and the set B={3,4,5}, then find the number of elements in (A×B).
Answer» If the set $A$ has $3$ elements and the set $B = {3, 4, 5}$ , then find the number of elements in $(A \times B)$ .

Discussion

3100.	Divide x3−125 by x2+5x+25 and find the quotient.
Answer» Divide $x^{3} - 125$ by $x^{2} + 5 x + 25$ and find the quotient.

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use π=227 and 5=2.236). [CBSE 2015]

first term of ap is a and the sum of first p terms is zero show that the sum of its next q terms is _a(p+q)q/p-1

A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.

26. In a triangle ABC, AB = AC.show that the altitude AD is median also.

Tick the correct answer in the following:Area of a sector of angle p (in degrees) of a circle with radius R is

The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP. [CBSE 2013]

The lengths of three consecutive sides of a quadrilateral circumscrbing a circle are 4cm, 5cm, and 7 cm respectively. Determine the length of the fourth side.

In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —

Question 7 Only one of the four options is correct. Write the correct one. On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is a) 12 b) 24 c) 27 d) 36

Fill in the blank using greater or less to make the statement true. 8 -13 -15 is __ than -15 -39 + 6

In triangle ABC, right angled at B, if ∠A is made larger and larger till it becomes 90∘, what can you say about AC and AB if BC = 1 unit?

The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms. [CBSE 2013C]

Distance of a point P(x,y) from x-axis is

Find the value of k for which each of the following quadratic equation has equal roots. (k-4)x​​​​​​2 +2(k-4)x +4=0.

The cardinality of two disjoint sets A and B is in the ratio 2:1. If the cardinality of the union of these sets is 45, find the cardinality of the two sets.

Find the mode of the following data. xifi10101415187219259

If a, b and c are in A.P, then which of the following seies does not form an A.P.?

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that ΔBPQ is an isosceles triangle.

Question 9 (i) Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the (i) radius r' of the new sphere.

Draw a direct common tangent to two congruent circles of radii 3 cm and whose centres are 9 cm apart.

State the converse of Thale's theorem.

The 4th term from the end of the AP: –11, –8, –5, ..., 49 is(a) 37(b) 40(c) 43(d) 58

How are pyramids and cones alike?

The system of pair of equations 4x−3y+12=0 and 2x+3y−15=0 has

The coordinates of the mid-points of sides AB, BC and CA of △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.

If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR=120∘, prove that 2PQ = PO.

Sum of the areas of two squares is 640m2. If the difference of their perimeters is 64m, find the sides of two squares.

In a two digit number the digit in the unit place is twice of the digit in the 10th if the digits are reversed the new number is 27 more then the given number find the number

Divide 56 into 4 parts which are in AP such that the ratio of products of extremes to the products of means is 5:6.

A rectangular playground has two semi circles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m &amp; 21 m, find the area of the playground.

Question 3A plumbline ( Sahul) is the combination of ( see figure)(A) a cone and a cylinder(B) a hemisphere and a cone(C) frustum of a cone and a cylinder(D) sphere and cylinder

If x∈(0,1), then the expression 12cos−1(1−x1+x) simplifies to:

Thimpu arranges cubes of volume 1 cu. cm into a 7 x 7 layer as shown below. How many such layers should be stacked one above other to form a cube of volume 343 cu. cm ?

Solve the following quadratic equations by factorization:4x-3=52x+3, x≠0, -32

The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is

If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are real, then k =(a) -32(b) 32(c) 23(d) -23

In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C=200, find ∠AOD

A field is in the form of a circle. A fence is to be erected around the field. The cost fencing would be Rs. 2640 at the rate of Rs. 12 per metre. The, the field is to be thoroughly ploughed at the cost of Re. 0.50 per m2. What is the amount required to plough the field? [Take π = 22/7].

In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

If the roots of the equation b-cx2+c-ax+a-b=0 are equal, then prove that 2b = a + c.

ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC

If 29x+37y=103 and 37x+29y=95 then (a) x=1,y=2 (b) x=2,y=1 (c) x=3,y=2 (d) x=2,y=3

What will be the remainder when 4x4−3x3+2x2−x is divided by x+1?

Volume of a cylinder is 343π and if the radius isequal to the height, then what is the height(in cm) of the cylinder?7

Find the value of cos 38o cosec 52otan 18o tan 35o tan 60o tan 72o tan 55o

If A=200020002 such that A5 = λA, then λ = ___________.

If the set A has 3 elements and the set B={3,4,5}, then find the number of elements in (A×B).

Divide x3−125 by x2+5x+25 and find the quotient.

Find the value of k for which each of the following quadratic equation has equal roots. (k-4)x2 +2(k-4)x +4=0.

A rectangular playground has two semi circles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m & 21 m, find the area of the playground.