32581 + Interview Questions in Mathematics Page 254 InterviewSolution

12651.	Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm :(i) gt=t2-3, ft=2t4+3t3-2t2-9t-12(ii) gx=x3-3x+1, fx=x5-4x3+x2+3x+1(iii) gx=2x2-x+3, fx=6x5-x4+4x3-5x2-x-15
Answer» Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm : (i) $g (t) = t^{2} - 3, f (t) = 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$ (ii) $g (x) = x^{3} - 3 x + 1, f (x) = x^{5} - 4 x^{3} + x^{2} + 3 x + 1$ (iii) $g (x) = 2 x^{2} - x + 3, f (x) = 6 x^{5} - x^{4} + 4 x^{3} - 5 x^{2} - x - 15$

Discussion

12652.	A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is(a) 2 cm(b) 3 cm(c) 4 cm(d) 6 cm
Answer» A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is (a) 2 cm (b) 3 cm (c) 4 cm (d) 6 cm

Discussion

12653.	The cost of polishing a closed container, which is of the shape of the frustum of a cone, is Rs 440 at the rate of Re 1 per 100 cm2. The respective radii of the upper and the lower bases of the frustum are 1 m and 40 cm. What is the height of the container? (Use π = 22/7)
Answer» The cost of polishing a closed container, which is of the shape of the frustum of a cone, is Rs 440 at the rate of Re 1 per 100 cm². The respective radii of the upper and the lower bases of the frustum are 1 m and 40 cm. What is the height of the container? (Use π = ²²/₇)

12653.

The cost of polishing a closed container, which is of the shape of the frustum of a cone, is Rs 440 at the rate of Re 1 per 100 cm2. The respective radii of the upper and the lower bases of the frustum are 1 m and 40 cm. What is the height of the container? (Use π = 22/7)

Answer»

The cost of polishing a closed container, which is of the shape of the frustum of a cone, is Rs 440 at the rate of Re 1 per 100 cm². The respective radii of the upper and the lower bases of the frustum are 1 m and 40 cm.

What is the height of the container? (Use π = ²²/₇)

Discussion

12654.	If AB=12cm, BC=16cm and AB is perpendicular to BC, then find the radius of circle passing through the points A, B and C. (Explain with the help of a diagram followed by explaination)
Answer» If AB=12cm, BC=16cm and AB is perpendicular to BC, then find the radius of circle passing through the points A, B and C. (Explain with the help of a diagram followed by explaination)

Discussion

12655.	The numbers of the book bought at a book fair by 200 students from a school are given in the following table. No. of books01234No. of students3564681815 Calculate the standard deviation.
Answer» The numbers of the book bought at a book fair by 200 students from a school are given in the following table. $\begin{matrix} N o . o f b o o k s & 0 & 1 & 2 & 3 & 4 N o . o f s t u d e n t s & 35 & 64 & 68 & 18 & 15 \end{matrix}$ Calculate the standard deviation.

12655.

The numbers of the book bought at a book fair by 200 students from a school are given in the following table. No. of books01234No. of students3564681815 Calculate the standard deviation.

Answer»

The numbers of the book bought at a book fair by 200 students from a school are given in the following table.

$\begin{matrix} N o . o f b o o k s & 0 & 1 & 2 & 3 & 4 N o . o f s t u d e n t s & 35 & 64 & 68 & 18 & 15 \end{matrix}$

Calculate the standard deviation.

Discussion

12656.	If the sum and the difference of two expressions P and Q is 2x^2 - 8x + 6 and 2x - 2 respectively, then find the HCF of P and Q.
Answer» If the sum and the difference of two expressions P and Q is 2x^2 - 8x + 6 and 2x - 2 respectively, then find the HCF of P and Q.

Discussion

12657.	Question 2 (iii)Verify that each of the following is an AP and then write its next three terms.√3, 2√3, 3√3,⋯
Answer» Question 2 (iii) Verify that each of the following is an AP and then write its next three terms. $\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}, \dots$

Discussion

12658.	Question 2A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Answer» Question 2 A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Discussion

12659.	Value of theta if sintheta+sin2theta+sin3theta=sinalphaAnd costheta+cos2theta+cos3theta=cosalpha
Answer» Value of theta if sintheta+sin2theta+sin3theta=sinalpha And costheta+cos2theta+cos3theta=cosalpha

Discussion

12660.	Which of the following graphs represent the solution of the inequation written below: 2x−5≤5x+4<11,xϵR
Answer» Which of the following graphs represent the solution of the inequation written below: $2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

12660.

Which of the following graphs represent the solution of the inequation written below: 2x−5≤5x+4<11,xϵR

Answer»

Which of the following graphs represent the solution of the inequation written below:

$2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

Discussion

12661.	Question 3 (i) The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC. The median from A meets BC at D. find the coordinates of the point D.
Answer» Question 3 (i) The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. The median from A meets BC at D. find the coordinates of the point D.

Discussion

12662.	In Fig. 1, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is(a) 4(b) 1(c) 2(d) 3
Answer» In Fig. 1, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is (a) 4 (b) 1 (c) 2 (d) 3

Discussion

12663.	With the vertices of △ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]
Answer» With the vertices of $△ A B C$ as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

12663.

With the vertices of △ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

Answer»

With the vertices of $△ A B C$ as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

Discussion

12664.	If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.
Answer» If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.

Discussion

12665.	If tan A = cot B, prove that A+B=90∘.
Answer» If tan A = cot B, prove that $A + B = 90^{\circ}$ .

Discussion

12666.	Question 1 The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.
Answer» Question 1 The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

Discussion

12667.	If p and q are the roots of the equation x2−2x−1=0, find the quadratic equation in x whose roots are (p+q)2 and (p−q)2 :
Answer» If p and q are the roots of the equation $x^{2} - 2 x - 1 = 0$ , find the quadratic equation in x whose roots are $(p + q)^{2}$ and $(p - q)^{2}$ :

Discussion

12668.	Verify that 3, -2, 1 are the zeroes of the cubic polynomial p(x)=x3−2x2−5x+6
Answer» Verify that 3, -2, 1 are the zeroes of the cubic polynomial $p (x) = x^{3} - 2 x^{2} - 5 x + 6$

Discussion

12669.	If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are two parallel tangents to a circle, then the length of its diameter is _____________.
Answer» If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are two parallel tangents to a circle, then the length of its diameter is _____________.

Discussion

12670.	Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the line joining the points of trisection of the line AB.
Answer» Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the line joining the points of trisection of the line AB.

Discussion

12671.	The angle of elevation of the top of a tree from a point A on the ground is 60∘ . On walking 20 m away from its base, to a point B, the angle of elevation changes to 30∘. Find the height of the tree.
Answer» The angle of elevation of the top of a tree from a point A on the ground is $60^{\circ}$ . On walking 20 m away from its base, to a point B, the angle of elevation changes to $30^{\circ}$ . Find the height of the tree.

Discussion

12672.	Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.
Answer» Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)^th of the corresponding sides of ΔXYZ. Write the steps of construction.

Discussion

12673.	A whole number is added to 49 and the same number is subtracted from 49. The sum of the resulting numbers is
Answer» A whole number is added to $49$ and the same number is subtracted from $49$ . The sum of the resulting numbers is

Discussion

12674.	Question 6Is the following statement true? Why?''Two quadrilaterals are similar if their corresponding angles are equal”.
Answer» Question 6 Is the following statement true? Why? ''Two quadrilaterals are similar if their corresponding angles are equal”.

Discussion

12675.	Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:3x2 – x – 4
Answer» Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: 3x²– x – 4

Discussion

12676.	The perimeter of the quadrant of a circle is 25 cm. Find its area. [CBSE 2012]
Answer» The perimeter of the quadrant of a circle is 25 cm. Find its area. [CBSE 2012]

Discussion

12677.	A shopkeeper buys a number of books for ₹40. If he had bought 2 more books for the same amount, then each book would have cost him ₹1 less. The number of books he bought is
Answer» A shopkeeper buys a number of books for $₹ 40$ . If he had bought $2$ more books for the same amount, then each book would have cost him $₹ 1$ less. The number of books he bought is

Discussion

12678.	The volumes of two spheres are in the ratio 27 : 64. What is the ratio of their radii?
Answer» The volumes of two spheres are in the ratio 27 : 64. What is the ratio of their radii?

Discussion

12679.

Kalpana and Kanika were partners in a firm sharing profits in the ratio of 3 : 2. On 1st April, 2019, they admitted Karuna as a new partner for 1/5th share in the profits of the firm. The Balance Sheet of Kalpana and Kanika as on 1st April, 2019 was as follows: BALANCE SHEET OF KALPANA AND KANIKA as on 1st April, 2019 Liabilities ₹ Assets ₹ Capital A/cs: Land and Building 2,10,000 Kalpana 4,80,000 Plant 2,70,000 Kanika 2,10,000 6,90,000 Stock 2,10,000 General Reserve 60,000 Debtors 1,32,000 Workmen's Compensation Fund 1,00,000 Less: Provision 12,000 1,20,000 Creditors 90,000 Cash 26,000 1,30,000 9,40,000 9,40,000 It was agreed that:(a) the value of Land and Building will be appreciated by 20%.(b) the value of plant be increased by ₹ 60,000.(c) Karuna will bring ₹ 80,000 for her share of goodwill premium.(d) the liabilities of Workmen's Compensation Fund were determined at ₹ 60,000.(e) Karuna will bring in cash as capital to the extent of 1/5th share of the total capital of the new firm.Prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet of the new firm.

Answer» Kalpana and Kanika were partners in a firm sharing profits in the ratio of 3 : 2. On 1st April, 2019, they admitted Karuna as a new partner for 1/5th share in the profits of the firm. The Balance Sheet of Kalpana and Kanika as on 1st April, 2019 was as follows:


BALANCE SHEET OF KALPANA AND KANIKA as on 1st April, 2019
Liabilities		₹	Assets		₹
Capital A/cs:			Land and Building		2,10,000
Kalpana	4,80,000		Plant		2,70,000
Kanika	2,10,000	6,90,000	Stock		2,10,000
General Reserve		60,000	Debtors	1,32,000
Workmen's Compensation Fund		1,00,000	Less: Provision	12,000	1,20,000
Creditors		90,000	Cash		26,000
					1,30,000

		9,40,000			9,40,000

It was agreed that:

(a) the value of Land and Building will be appreciated by 20%.

(b) the value of plant be increased by ₹ 60,000.

(c) Karuna will bring ₹ 80,000 for her share of goodwill premium.

(d) the liabilities of Workmen's Compensation Fund were determined at ₹ 60,000.

(e) Karuna will bring in cash as capital to the extent of 1/5th share of the total capital of the new firm.

Prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet of the new firm.

Discussion

12680.	Minimum value of 4 sin^2 theta + 9cosec^2 theta is 13
Answer» Minimum value of 4 sin^2 theta + 9cosec^2 theta is 13

Discussion

12681.	Construct a ∆ABC, with BC = 7 cm, ∠B = 60º and AB = 6 cm. Construct another triangle whose sides are 34 times the corresponding sides of ∆ABC. [CBSE 2008, '09, '15]
Answer» Construct a ∆ABC, with BC = 7 cm, $∠$ B = 60º and AB = 6 cm. Construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of ∆ABC. [CBSE 2008, '09, '15]

Discussion

12682.	Which of the following is the frequency distribution table for the following distributions? Marks (more than)Cumulative Frequency0100108720653055404250366031702180189071000
Answer» Which of the following is the frequency distribution table for the following distributions? $\begin{matrix} M a r k s (m o r e t h a n) & C u m u l a t i v e F r e q u e n c y 0 & 100 10 & 87 20 & 65 30 & 55 40 & 42 50 & 36 60 & 31 70 & 21 80 & 18 90 & 7 100 & 0 \end{matrix}$

12682.

Which of the following is the frequency distribution table for the following distributions? Marks (more than)Cumulative Frequency0100108720653055404250366031702180189071000

Answer»

Which of the following is the frequency distribution table for the following distributions?

$\begin{matrix} M a r k s (m o r e t h a n) & C u m u l a t i v e F r e q u e n c y 0 & 100 10 & 87 20 & 65 30 & 55 40 & 42 50 & 36 60 & 31 70 & 21 80 & 18 90 & 7 100 & 0 \end{matrix}$

Discussion

12683.	If the sum of the first p terms of an A.P is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
Answer» If the sum of the first p terms of an A.P is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Discussion

12684.	Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Answer» Seats for Mathematics, Physics and Biology in a school are in the ratio $5 : 7 : 8.$ There is a proposal to increase these seats by $40 %,$ $50 %$ and $75 %$ respectively. What will be the ratio of increased seats?

Discussion

12685.	In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true ?
Answer» In the given figure, D and E are mid points of sides AB and AC of $△$ ABC. Which of the following is true ?

12685.

In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true ?

Answer»

In the given figure, D and E are mid points of sides AB and AC of $△$ ABC. Which of the following is true ?

Discussion

12686.	63. Two straight lines rotate about two fixed points (-a, 0)and (a, 0) in antic clockwise direction. If they start fromtheir position of coincidence such that one rotates at arate double of the other, then locus of curve is
Answer» 63. Two straight lines rotate about two fixed points (-a, 0)and (a, 0) in antic clockwise direction. If they start fromtheir position of coincidence such that one rotates at arate double of the other, then locus of curve is

Discussion

12687.	1. Let A be a non-empty set such that AB=AC. show that B=C
Answer» 1. Let A be a non-empty set such that AB=AC. show that B=C

Discussion

12688.	Find the volume of the figure.
Answer» Find the volume of the figure.

12688.

Find the volume of the figure.

Answer»

Find the volume of the figure.

Discussion

12689.	The next term of the A.P. 7, 28, 63, ....(a) 70(b) 84(c) 97(d) 112
Answer» The next term of the A.P. $\sqrt{7}, \sqrt{28}, \sqrt{63}, . . . .$ (a) $\sqrt{70}$ (b) $\sqrt{84}$ (c) $\sqrt{97}$ (d) $\sqrt{112}$

Discussion

12690.	The HCF of two numbers is 4 and their LCM is 400. How many pairs of values can the numbers assume?
Answer» The HCF of two numbers is 4 and their LCM is 400. How many pairs of values can the numbers assume?

Discussion

12691.	A cylindrical pipe has inner diameter of 7 cm and water flows through it at the rate of 192.5 litres per minute. Find the rate of flow in kilometres per hour.
Answer» A cylindrical pipe has inner diameter of 7 cm and water flows through it at the rate of 192.5 litres per minute. Find the rate of flow in kilometres per hour.

Discussion

12692.	16. If Q be the foot of perpendicular from P(2,4,3) on the line joining the points a(1,2,4) and b(3,4,5) ,then coordinates of Q?
Answer» 16. If Q be the foot of perpendicular from P(2,4,3) on the line joining the points a(1,2,4) and b(3,4,5) ,then coordinates of Q?

Discussion

12693.	The system kx-y=2 and 6x-2y=3 has a unique solution only when(a) k = 0 (b) k≠0 (c) k = 3 (d) k≠3
Answer» The system $k x - y = 2 and 6 x - 2 y = 3$ has a unique solution only when (a) k = 0 (b) $k \neq 0$ (c) k = 3 (d) $k \neq 3$

Discussion

12694.	In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PBthen the length of each tangent. [CBSE 2013](a) 3 cm(b) 4 cm(c) 5 cm(d) 6 cm
Answer» In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB then the length of each tangent. [CBSE 2013] (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Discussion

12695.	In the figure given below, find x if AB \|\| CD.
Answer» In the figure given below, find $x$ if AB \|\| CD.

12695.

In the figure given below, find x if AB || CD.

Answer»

In the figure given below, find $x$ if AB || CD.

Discussion

12696.	a sailor goes 8km downstream in 40 min and returns in 1 hr.determine the speed of sailor in still water and the spwed of the current
Answer» a sailor goes 8km downstream in 40 min and returns in 1 hr.determine the speed of sailor in still water and the spwed of the current

Discussion

12697.	In a mathematical statement , if one quantity is not equal to another then it is called as ___
Answer» In a mathematical statement , if one quantity is not equal to another then it is called as ___

Discussion

12698.	Find the mean age from the following frequency distribution: Age (in years)25−2930−3435−3940−4445−4950−5455−59Number of persons4142216653
Answer» Find the mean age from the following frequency distribution: $\begin{matrix} Age (in years) & 25 - 29 & 30 - 34 & 35 - 39 & 40 - 44 & 45 - 49 & 50 - 54 & 55 - 59 Number of persons & 4 & 14 & 22 & 16 & 6 & 5 & 3 \end{matrix}$

Discussion

12699.	Find the square of 32.
Answer» Find the square of 32.

Discussion

12700.	There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?
Answer» There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

Discussion

Explore topic-wise InterviewSolutions in .

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm :(i) gt=t2-3, ft=2t4+3t3-2t2-9t-12(ii) gx=x3-3x+1, fx=x5-4x3+x2+3x+1(iii) gx=2x2-x+3, fx=6x5-x4+4x3-5x2-x-15

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is(a) 2 cm(b) 3 cm(c) 4 cm(d) 6 cm

The cost of polishing a closed container, which is of the shape of the frustum of a cone, is Rs 440 at the rate of Re 1 per 100 cm2. The respective radii of the upper and the lower bases of the frustum are 1 m and 40 cm. What is the height of the container? (Use π = 22/7)

If AB=12cm, BC=16cm and AB is perpendicular to BC, then find the radius of circle passing through the points A, B and C. (Explain with the help of a diagram followed by explaination)

The numbers of the book bought at a book fair by 200 students from a school are given in the following table. No. of books01234No. of students3564681815 Calculate the standard deviation.

If the sum and the difference of two expressions P and Q is 2x^2 - 8x + 6 and 2x - 2 respectively, then find the HCF of P and Q.

Question 2 (iii)Verify that each of the following is an AP and then write its next three terms.√3, 2√3, 3√3,⋯

Question 2A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Value of theta if sintheta+sin2theta+sin3theta=sinalphaAnd costheta+cos2theta+cos3theta=cosalpha

Which of the following graphs represent the solution of the inequation written below: 2x−5≤5x+4&lt;11,xϵR

Question 3 (i) The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC. The median from A meets BC at D. find the coordinates of the point D.

In Fig. 1, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is(a) 4(b) 1(c) 2(d) 3

With the vertices of △ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.

If tan A = cot B, prove that A+B=90∘.

Question 1 The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

If p and q are the roots of the equation x2−2x−1=0, find the quadratic equation in x whose roots are (p+q)2 and (p−q)2 :

Verify that 3, -2, 1 are the zeroes of the cubic polynomial p(x)=x3−2x2−5x+6

If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are two parallel tangents to a circle, then the length of its diameter is _____________.

Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the line joining the points of trisection of the line AB.

The angle of elevation of the top of a tree from a point A on the ground is 60∘ . On walking 20 m away from its base, to a point B, the angle of elevation changes to 30∘. Find the height of the tree.

Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.

A whole number is added to 49 and the same number is subtracted from 49. The sum of the resulting numbers is

Question 6Is the following statement true? Why?''Two quadrilaterals are similar if their corresponding angles are equal”.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:3x2 – x – 4

The perimeter of the quadrant of a circle is 25 cm. Find its area. [CBSE 2012]

A shopkeeper buys a number of books for ₹40. If he had bought 2 more books for the same amount, then each book would have cost him ₹1 less. The number of books he bought is

The volumes of two spheres are in the ratio 27 : 64. What is the ratio of their radii?

Minimum value of 4 sin^2 theta + 9cosec^2 theta is 13

Construct a ∆ABC, with BC = 7 cm, ∠B = 60º and AB = 6 cm. Construct another triangle whose sides are 34 times the corresponding sides of ∆ABC. [CBSE 2008, '09, '15]

Which of the following is the frequency distribution table for the following distributions? Marks (more than)Cumulative Frequency0100108720653055404250366031702180189071000

If the sum of the first p terms of an A.P is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true ?

63. Two straight lines rotate about two fixed points (-a, 0)and (a, 0) in antic clockwise direction. If they start fromtheir position of coincidence such that one rotates at arate double of the other, then locus of curve is

1. Let A be a non-empty set such that A*B=A*C. show that B=C

Find the volume of the figure.

The next term of the A.P. 7, 28, 63, ....(a) 70(b) 84(c) 97(d) 112

The HCF of two numbers is 4 and their LCM is 400. How many pairs of values can the numbers assume?

A cylindrical pipe has inner diameter of 7 cm and water flows through it at the rate of 192.5 litres per minute. Find the rate of flow in kilometres per hour.

16. If Q be the foot of perpendicular from P(2,4,3) on the line joining the points a(1,2,4) and b(3,4,5) ,then coordinates of Q?

The system kx-y=2 and 6x-2y=3 has a unique solution only when(a) k = 0 (b) k≠0 (c) k = 3 (d) k≠3

In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PBthen the length of each tangent. [CBSE 2013](a) 3 cm(b) 4 cm(c) 5 cm(d) 6 cm

In the figure given below, find x if AB || CD.

​a sailor goes 8km downstream in 40 min and returns in 1 hr.determine the speed of sailor in still water and the spwed of the current

In a mathematical statement , if one quantity is not equal to another then it is called as ___

Find the mean age from the following frequency distribution: Age (in years)25−2930−3435−3940−4445−4950−5455−59Number of persons4142216653

Find the square of 32.

There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

Which of the following graphs represent the solution of the inequation written below: 2x−5≤5x+4<11,xϵR

1. Let A be a non-empty set such that AB=AC. show that B=C

a sailor goes 8km downstream in 40 min and returns in 1 hr.determine the speed of sailor in still water and the spwed of the current