32581 + Interview Questions in Mathematics

1.	If 2f(x)=f(xy)+f(x/y) for all positive values of x and y, f(1)=0 and f'(1)=1,find the value of f(e).
Answer» If 2f(x)=f(xy)+f(x/y) for all positive values of x and y, f(1)=0 and f'(1)=1,find the value of f(e).

Discussion

2.	Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :3x − 4y − 1 = 02x-83y+5=0
Answer» Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) : 3x − 4y − 1 = 0 $2 x - \frac{8}{3} y + 5 = 0$

Discussion

3.	Sort the following in increasing order.
Answer» Sort the following in increasing order.

Discussion

4.	Which of the following is not a geometric progression?
Answer» Which of the following is not a geometric progression?

Discussion

5.

Complete the entries in the third column of the table. S. No. Equation Value of variable Equation satisfied Yes/No (a) 10y = 80 y = 10 - (b) 10y = 80 y = 8 - (c) 10y = 80 y = 5 - (d) 4l = 20 l = 20 - (e) 4l = 20 l = 80 - (f) 4l = 20 l = 5 - (g) b + 5 = 9 b =5 - (h) b + 5 = 9 b = 9 - (i) b + 5 = 9 b = 4 - (j) h − 8 = 5 h = 13 - (k) h − 8 = 5 h = 8 - (l) h − 8 = 5 h = 0 - (m) p + 3 = 1 p = 3 - (n) p + 3 = 1 p = 1 - (o) p + 3 = 1 p = 0 - (p) p + 3 = 1 P = − 1 - (q) p + 3 = 1 P = − 2 -

Answer»

Complete the entries in the third column of the table.

S. No.	Equation	Value of variable	Equation satisfied Yes/No
(a)	10y = 80	y = 10	-
(b)	10y = 80	y = 8	-
(c)	10y = 80	y = 5	-
(d)	4l = 20	l = 20	-
(e)	4l = 20	l = 80	-
(f)	4l = 20	l = 5	-
(g)	b + 5 = 9	b =5	-
(h)	b + 5 = 9	b = 9	-
(i)	b + 5 = 9	b = 4	-
(j)	h − 8 = 5	h = 13	-
(k)	h − 8 = 5	h = 8	-
(l)	h − 8 = 5	h = 0	-
(m)	p + 3 = 1	p = 3	-
(n)	p + 3 = 1	p = 1	-
(o)	p + 3 = 1	p = 0	-
(p)	p + 3 = 1	P = − 1	-
(q)	p + 3 = 1	P = − 2	-

Discussion

6.	A purchases an article for ₹ 3,100 and sells it to B for ₹ 4250. B in turn sells it to C for ₹ 5000. If VAT is 10%, find the VAT levied on A and B.
Answer» A purchases an article for ₹ 3,100 and sells it to B for ₹ 4250. B in turn sells it to C for ₹ 5000. If VAT is 10%, find the VAT levied on A and B.

Discussion

7.	Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh2r + h.
Answer» Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is $πh (2 r + h)$ .

Discussion

8.	If the numerical value of total surface area and volume of a hemisphere are equal, then the volume of the smallest cubical box in which it can be placed is.
Answer» If the numerical value of total surface area and volume of a hemisphere are equal, then the volume of the smallest cubical box in which it can be placed is.

Discussion

9.	Divide and write the quotient and the remainder.(5x3–3x2)÷x2
Answer» Divide and write the quotient and the remainder. $(5 x^{3} - 3 x^{2}) \div x^{2}$

Discussion

10.	Construct a triangle ABC with AB+BC+CA=12 cm ∠B=45° and ∠C = 60°
Answer» Construct a triangle ABC with AB+BC+CA=12 cm ∠B=45° and ∠C = 60°

Discussion

11.	The height of the vertical pole is 3 times the length of its shadow on the ground, then angle of elevation of the sun at that time is(a) 30º (b) 60º (b) 45º (b) 75º [CBSE 2014]
Answer» The height of the vertical pole is $\sqrt{3}$ times the length of its shadow on the ground, then angle of elevation of the sun at that time is (a) 30º (b) 60º (b) 45º (b) 75º [CBSE 2014]

Discussion

12.	3. If xcube + axsquare + bx + 6 has x-2 as a factor and leaves a remainder 3 when divided by x-3, then find the value of a and b
Answer» 3. If xcube + axsquare + bx + 6 has x-2 as a factor and leaves a remainder 3 when divided by x-3, then find the value of a and b

Discussion

13.	Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.
Answer» Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.

13.

Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.

Answer»

Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.

Discussion

14.	A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.
Answer» A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.

Discussion

15.	Match the following shapes with their volumes if each small cube is a cube of volume 1 cm3.
Answer» Match the following shapes with their volumes if each small cube is a cube of volume $1 {cm}^{3} .$

Discussion

16.	Tangents drawn at two ends of a diameter of a circle are _____.
Answer» Tangents drawn at two ends of a diameter of a circle are _____.

Discussion

17.	x+y=a+b ax+by=a^2+b^2 find the values of a and b.
Answer» x+y=a+b ax+by=a^2+b^2 find the values of a and b.

Discussion

18.	USE EUCLID'S DIVISION ALGORITHM TO FIND THE H.C.F OF 1190 AND1445 AND EXPRESS THE HCF IN THE FORM OF 1190m+1445n
Answer» USE EUCLID'S DIVISION ALGORITHM TO FIND THE H.C.F OF 1190 AND1445 AND EXPRESS THE HCF IN THE FORM OF 1190m+1445n

Discussion

19.	Two sides of a parallelogram are of length 6 centimetres and 4 centimetres and the angle between them is 35°. What are the lengths of its diagonals?
Answer» Two sides of a parallelogram are of length 6 centimetres and 4 centimetres and the angle between them is 35°. What are the lengths of its diagonals?

Discussion

20.	A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.
Answer» A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

20.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

Answer»

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

Discussion

21.	Find the number that is to be added to x2+12x to make it a perfect square.36
Answer» Find the number that is to be added to $x^{2} + 12 x$ to make it a perfect square. 36

Discussion

22.	As shown in the figure, a square is drawn sharing one corner with a right triangle and the other three corners on the sides of this triangle. Calculate the length of a side of the square.
Answer» As shown in the figure, a square is drawn sharing one corner with a right triangle and the other three corners on the sides of this triangle. Calculate the length of a side of the square.

Discussion

23.	1. What lenght of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra lenght of material that will be required for stitching margins and wastage in cutting is approximately 20 cm ( use pie= 3.14).
Answer» 1. What lenght of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra lenght of material that will be required for stitching margins and wastage in cutting is approximately 20 cm ( use pie= 3.14).

Discussion

24.	A natural number when increased by 84 equals 160 times its reciprocal. Find the number
Answer» A natural number when increased by 84 equals 160 times its reciprocal. Find the number

Discussion

25.	Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………
Answer» Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

25.

Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Answer»

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

Discussion

26.	In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?
Answer» In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

26.

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

Answer»

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

Discussion

27.	A. Find (a) (b) (c) B. (a) If ∑ n = 55 find n (b) If ∑ n = 210 find n.C. Find the sum of all natural numbers below 50 which are divisible by 7?
Answer» A. Find (a) (b) (c) B. (a) If ∑ n = 55 find n (b) If ∑ n = 210 find n. C. Find the sum of all natural numbers below 50 which are divisible by 7?

27.

A. Find (a) (b) (c) B. (a) If ∑ n = 55 find n (b) If ∑ n = 210 find n.C. Find the sum of all natural numbers below 50 which are divisible by 7?

Answer»

A. Find (a) (b) (c)

B. (a) If ∑ n = 55 find n (b) If ∑ n = 210 find n.

C. Find the sum of all natural numbers below 50 which are divisible by 7?

Discussion

28.	The zero of the polynomial x - 3 is
Answer» The zero of the polynomial x - 3 is

Discussion

29.	The total number of possible paths from A to D without crossing the same point twice are:
Answer» The total number of possible paths from A to D without crossing the same point twice are:

29.

The total number of possible paths from A to D without crossing the same point twice are:

Answer»

The total number of possible paths from A to D without crossing the same point twice are:

Discussion

30.	Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Answer» Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

30.

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Answer»

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Discussion

31.

The marks scored by 750 students in an examination are given in the form of a frequency distribution table: Marks No. of student Marks No. of students 600−640 640−680 680−720 720−760 16 45 156 284 760−800 800−840 840−880 172 59 18 Prepare a cumulative frequency table by less than method and draw an ogive.

Answer» The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks	No. of student	Marks	No. of students
600−640 640−680 680−720 720−760	16 45 156 284	760−800 800−840 840−880	172 59 18

Prepare a cumulative frequency table by less than method and draw an ogive.

Discussion

32.	Babita, Chetan and David are partners in a firm sharing profits in the ratio of 2 : 1 : 1 respectively. Firm closes its accounts on 31st March every year. Chetan died on 30th September, 2012. There was a balance of ₹ 1,25,000 in Chetan's Capital Account in the beginning of the year. In the event of death of any partner, the Partnership Deed provides for the following:(a) Interest on capital will be calculated at the rate of 6% p.a.(b) The executor of deceased partner shall be paid ₹ 24,000 for his share of goodwill.(c) His share of Reserve Fund of ₹ 12,000, shall be paid to his executor.(d) His share of profit till the date of death will be calculated on the basis of sales. It is also specified that the sales during the year 2011-12 were ₹ 4,00,000. The sales from 1st April, 2012 to 30th September, 2012 were ₹ 1,20,000. The profit of the firm for the year ending 31st March, 2012 was ₹ 2,00,000.Prepare Chetan's Capital Account to be presented to his executor.
Answer» Babita, Chetan and David are partners in a firm sharing profits in the ratio of 2 : 1 : 1 respectively. Firm closes its accounts on 31st March every year. Chetan died on 30th September, 2012. There was a balance of ₹ 1,25,000 in Chetan's Capital Account in the beginning of the year. In the event of death of any partner, the Partnership Deed provides for the following: (a) Interest on capital will be calculated at the rate of 6% p.a. (b) The executor of deceased partner shall be paid ₹ 24,000 for his share of goodwill. (c) His share of Reserve Fund of ₹ 12,000, shall be paid to his executor. (d) His share of profit till the date of death will be calculated on the basis of sales. It is also specified that the sales during the year 2011-12 were ₹ 4,00,000. The sales from 1st April, 2012 to 30th September, 2012 were ₹ 1,20,000. The profit of the firm for the year ending 31st March, 2012 was ₹ 2,00,000. Prepare Chetan's Capital Account to be presented to his executor.

Discussion

33.	The sum of two numbers is 50 and their difference is 16. Find the numbers. ?
Answer» The sum of two numbers is 50 and their difference is 16. Find the numbers. ?

Discussion

34.	54. Let ABCD be a quadrilateral with area 18,with side AB parallel to the side CD and AB=2CD . Let AD be perpendicular to AD and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is (A) 3 (B) 2 (C) 3/2 (D)1
Answer» 54. Let ABCD be a quadrilateral with area 18,with side AB parallel to the side CD and AB=2CD . Let AD be perpendicular to AD and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is (A) 3 (B) 2 (C) 3/2 (D)1

Discussion

35.	Question 12 (ii)A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at an odd number?
Answer» Question 12 (ii) A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at an odd number?

Discussion

36.	If A=[10234264], then find the fourth element of second column of AT.
Answer» If $A = [\begin{matrix} 1 & 0 & 2 & 3 4 & 2 & 6 & 4 \end{matrix}]$ , then find the fourth element of second column of $A^{T} .$

Discussion

37.	If the equation px2 - 6x - 2 = 0 has real roots then, ________
Answer» If the equation px² - 6x - 2 = 0 has real roots then, ________

Discussion

38.	Face Value (FV) of a share is also called its
Answer» Face Value (FV) of a share is also called its

Discussion

39.	Prove that ∑1/\sqrt n+\sqrt{n+1}=\sqrt{n+1}-1,where n is positive integer.
Answer» Prove that ∑1/\sqrt n+\sqrt{n+1}=\sqrt{n+1}-1,where n is positive integer.

Discussion

40.	Question 1 (iii)Find the square roots of each of the following numbers by Division method:3481
Answer» Question 1 (iii) Find the square roots of each of the following numbers by Division method: 3481

40.

Question 1 (iii)Find the square roots of each of the following numbers by Division method:3481

Answer»

Question 1 (iii)

Find the square roots of each of the following numbers by Division method:

3481

Discussion

41.	X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:
Answer» X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

Discussion

42.	27. If the perimeter of a semicircular protactor is 36cm,find its diameter
Answer» 27. If the perimeter of a semicircular protactor is 36cm,find its diameter

Discussion

43.	The incircle of triangle ABC touches sides AB, BC and CA at P, Q and R respectively. If AP = BQ = CR = 2 cm, then which of the following statements are true?
Answer» The incircle of triangle ABC touches sides AB, BC and CA at P, Q and R respectively. If AP = BQ = CR = 2 cm, then which of the following statements are true?

43.

The incircle of triangle ABC touches sides AB, BC and CA at P, Q and R respectively. If AP = BQ = CR = 2 cm, then which of the following statements are true?

Answer»

The incircle of triangle ABC touches sides AB, BC and CA at P, Q and R respectively. If AP = BQ = CR = 2 cm, then which of the following statements are true?

Discussion

44.	43. A rectangle PQRS joins the points P, Q, R, S.Co-ordinates of P and R be (2, 3) and (8, 11) respectively. The line QS is known to be parallel to the y-axis. Then coordinates of Q and S are: (1). (0, 7) and (10, 7) (2). (5, 2) and (5, 12) (3). (7, 6) and (7, 10) (4). (7, 2) and (7, 12)
Answer» 43. A rectangle PQRS joins the points P, Q, R, S.Co-ordinates of P and R be (2, 3) and (8, 11) respectively. The line QS is known to be parallel to the y-axis. Then coordinates of Q and S are: (1). (0, 7) and (10, 7) (2). (5, 2) and (5, 12) (3). (7, 6) and (7, 10) (4). (7, 2) and (7, 12)

Discussion

45.	Calculate the mean of the distribution given below using the short cut method Marks11−2021−3031−4041−5051−6061−7071−80No. of students261012974
Answer» Calculate the mean of the distribution given below using the short cut method $\begin{matrix} M a r k s & 11 - 20 & 21 - 30 & 31 - 40 & 41 - 50 & 51 - 60 & 61 - 70 & 71 - 80 N o . o f s t u d e n t s & 2 & 6 & 10 & 12 & 9 & 7 & 4 \end{matrix}$

Discussion

46.	Question 9Simplify the following (i)√45−3√20+4√5(ii)√248+√549(iii)4√12×7√6(iv)4√28+3√7+3√7(v)3√3+2√27+7√3(vi)(√3−√2)2(vii)4√81−83√216+155√32+√225(viii)3√8+1√2(ix)2√33−√36
Answer» Question 9 Simplify the following $(i) \sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} (i i) \frac{\sqrt{24}}{8} + \frac{\sqrt{54}}{9} (i i i) 4 \sqrt{12} \times 7 \sqrt{6} (i v) 4 \sqrt{28} + 3 \sqrt{7} + \sqrt[3]{7} (v) 3 \sqrt{3} + 2 \sqrt{27} + \frac{7}{\sqrt{3}} (v i) (\sqrt{3} - \sqrt{2})^{2} (v i i) \sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225} (v i i i) \frac{3}{\sqrt{8}} + \frac{1}{\sqrt{2}} (i x) \frac{2 \sqrt{3}}{3} - \frac{\sqrt{3}}{6}$

Discussion

47.	47. Prove: tan 6 . tan 42 . tan 66 . tan 78 = 1
Answer» 47. Prove: tan 6 . tan 42 . tan 66 . tan 78 = 1

Discussion

48.	Represent 1 + √9.3 on number line
Answer» Represent 1 + √9.3 on number line

Discussion

49.	Rohit walks 80 m towards left and then turns right. How much distance should he walk now so that the minimum distance between the initial and final point is 100 m?
Answer» Rohit walks 80 m towards left and then turns right. How much distance should he walk now so that the minimum distance between the initial and final point is 100 m?

Discussion

50.	Choose the correct answer of the following question:If sec4A=cosecA-10° and 4A is acute, then ∠A=?a 20° b 30° c 40° d 50°
Answer» $Choose the correct answer of the following question : If \sec 4 A = cosec (A - 10 °) and 4 A is acute, then ∠ A = ? (a) 20 ° (b) 30 ° (c) 40 ° (d) 50 °$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If 2f(x)=f(xy)+f(x/y) for all positive values of x and y, f(1)=0 and f'(1)=1,find the value of f(e).

Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :3x − 4y − 1 = 02x-83y+5=0

Sort the following in increasing order.

Which of the following is not a geometric progression?

A purchases an article for ₹ 3,100 and sells it to B for ₹ 4250. B in turn sells it to C for ₹ 5000. If VAT is 10%, find the VAT levied on A and B.

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh2r + h.

If the numerical value of total surface area and volume of a hemisphere are equal, then the volume of the smallest cubical box in which it can be placed is.

Divide and write the quotient and the remainder.(5x3–3x2)÷x2

Construct a triangle ABC with AB+BC+CA=12 cm ∠B=45° and ∠C = 60°

The height of the vertical pole is 3 times the length of its shadow on the ground, then angle of elevation of the sun at that time is(a) 30º (b) 60º (b) 45º (b) 75º [CBSE 2014]

3. If xcube + axsquare + bx + 6 has x-2 as a factor and leaves a remainder 3 when divided by x-3, then find the value of a and b

Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.

A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.

Match the following shapes with their volumes if each small cube is a cube of volume 1 cm3.

Tangents drawn at two ends of a diameter of a circle are _____.

x+y=a+b ax+by=a^2+b^2 find the values of a and b.

USE EUCLID'S DIVISION ALGORITHM TO FIND THE H.C.F OF 1190 AND1445 AND EXPRESS THE HCF IN THE FORM OF 1190m+1445n

Two sides of a parallelogram are of length 6 centimetres and 4 centimetres and the angle between them is 35°. What are the lengths of its diagonals?

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

Find the number that is to be added to x2+12x to make it a perfect square.36

As shown in the figure, a square is drawn sharing one corner with a right triangle and the other three corners on the sides of this triangle. Calculate the length of a side of the square.

1. What lenght of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra lenght of material that will be required for stitching margins and wastage in cutting is approximately 20 cm ( use pie= 3.14).

A natural number when increased by 84 equals 160 times its reciprocal. Find the number

Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

A. Find (a) (b) (c) B. (a) If ∑ n = 55 find n (b) If ∑ n = 210 find n.C. Find the sum of all natural numbers below 50 which are divisible by 7?

The zero of the polynomial x - 3 is

The total number of possible paths from A to D without crossing the same point twice are:

The sum of two numbers is 50 and their difference is 16. Find the numbers. ?

54. Let ABCD be a quadrilateral with area 18,with side AB parallel to the side CD and AB=2CD . Let AD be perpendicular to AD and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is (A) 3 (B) 2 (C) 3/2 (D)1

Question 12 (ii)A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at an odd number?

If A=[10234264], then find the fourth element of second column of AT.

If the equation px2 - 6x - 2 = 0 has real roots then, ________

Face Value (FV) of a share is also called its

Prove that ∑1/\sqrt n+\sqrt{n+1}=\sqrt{n+1}-1,where n is positive integer.

Question 1 (iii)Find the square roots of each of the following numbers by Division method:3481

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

27. If the perimeter of a semicircular protactor is 36cm,find its diameter

The incircle of triangle ABC touches sides AB, BC and CA at P, Q and R respectively. If AP = BQ = CR = 2 cm, then which of the following statements are true?

43. A rectangle PQRS joins the points P, Q, R, S.Co-ordinates of P and R be (2, 3) and (8, 11) respectively. The line QS is known to be parallel to the y-axis. Then coordinates of Q and S are: (1). (0, 7) and (10, 7) (2). (5, 2) and (5, 12) (3). (7, 6) and (7, 10) (4). (7, 2) and (7, 12)

Calculate the mean of the distribution given below using the short cut method Marks11−2021−3031−4041−5051−6061−7071−80No. of students261012974

Question 9Simplify the following (i)√45−3√20+4√5(ii)√248+√549(iii)4√12×7√6(iv)4√28+3√7+3√7(v)3√3+2√27+7√3(vi)(√3−√2)2(vii)4√81−83√216+155√32+√225(viii)3√8+1√2(ix)2√33−√36

47. Prove: tan 6 . tan 42 . tan 66 . tan 78 = 1

Represent 1 + √9.3 on number line

Rohit walks 80 m towards left and then turns right. How much distance should he walk now so that the minimum distance between the initial and final point is 100 m?

Choose the correct answer of the following question:If sec4A=cosecA-10° and 4A is acute, then ∠A=?a 20° b 30° c 40° d 50°