24740 + Interview Questions in Mathematics

1.	Which of the following are two rational numbers between √5 and √6
Answer» Which of the following are two rational numbers between $\sqrt{5}$ and $\sqrt{6}$

Discussion

2.	Question 5A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and its longer diagonal is 48m, how much area of grass field will each cow be getting?
Answer» Question 5 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and its longer diagonal is 48m, how much area of grass field will each cow be getting?

Discussion

3.	In trapezium ABCD, side AB \|\| side PQ \|\| side ∆C, AP = 15, PD = 12, QC = 14, Find BQ.
Answer» In trapezium ABCD, side AB \|\| side PQ \|\| side ∆C, AP = 15, PD = 12, QC = 14, Find BQ.

Discussion

4.	ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC is 30∘ and AB = BC, find ∠ECD.
Answer» ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 70^{\circ}, ∠ B A C is 30^{\circ}$ and AB = BC, find $∠ E C D$ .

Discussion

5.	If an integer is chosen at random and squared, then the probability that the last digit of the square is either 1 or 5, is
Answer» If an integer is chosen at random and squared, then the probability that the last digit of the square is either $1$ or $5,$ is

Discussion

6.	On the plane of a graph paper draw X'OX and YOY' as coordinate axes and plot each of the following points.(i) A(5, 3)(ii) B(6, 2)(iii) C(–5, 3)(iv) D(4, –6)(v) E(–3, –2)(vi) F(–4, 4)(vii) G(3, –4)(viii) H(5, 0)(ix) I(0, 6)(x) J(–3, 0)(xi) K(0, –2)(xii) O(0, 0)
Answer» On the plane of a graph paper draw X'OX and YOY' as coordinate axes and plot each of the following points. (i) A(5, 3) (ii) B(6, 2) (iii) C(–5, 3) (iv) D(4, –6) (v) E(–3, –2) (vi) F(–4, 4) (vii) G(3, –4) (viii) H(5, 0) (ix) I(0, 6) (x) J(–3, 0) (xi) K(0, –2) (xii) O(0, 0)

Discussion

7.	1,2,3,4,5......The above set of numbers are known as _______.
Answer» 1,2,3,4,5...... The above set of numbers are known as _______.

Discussion

8.	the length of the sides of a triangle are 8 cm,15 cm and 17 cm . Perpendicular length from the opposite vertex to the side whose length is 17 cm i
Answer» the length of the sides of a triangle are 8 cm,15 cm and 17 cm . Perpendicular length from the opposite vertex to the side whose length is 17 cm i

Discussion

9.	In Δ ABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?
Answer» In $Δ$ ABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

Discussion

10.	On 31st March, 2019, the total assets and external liabilities were ₹ 2,00,000 and ₹ 6,000 respectively. During the year, the proprietor had introduced capital of ₹ 20,000 and withdrawn ₹ 12,000 for personal use. He made a profit of ₹ 20,000 during the year. Calculate the capital as on 1st April, 2018.
Answer» On 31st March, 2019, the total assets and external liabilities were ₹ 2,00,000 and ₹ 6,000 respectively. During the year, the proprietor had introduced capital of ₹ 20,000 and withdrawn ₹ 12,000 for personal use. He made a profit of ₹ 20,000 during the year. Calculate the capital as on 1st April, 2018.

Discussion

11.	In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that:(i) ΔMBC ≅ ΔABD(ii) (iii) (iv) ΔFCB ≅ ΔACE(v) (vi) (vii) Note: Result (vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in class X.
Answer» In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that: (i) ΔMBC ≅ ΔABD (ii) (iii) (iv) ΔFCB ≅ ΔACE (v) (vi) (vii) Note: Result (vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in class X.

11.

In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that:(i) ΔMBC ≅ ΔABD(ii) (iii) (iv) ΔFCB ≅ ΔACE(v) (vi) (vii) Note: Result (vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in class X.

Answer»

In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that:

(i) ΔMBC ≅ ΔABD

(ii)

(iii)

(iv) ΔFCB ≅ ΔACE

(v)

(vi)

(vii)

Note: Result (vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in class X.

Discussion

12.	In the above figure, ABCD is a square and BCE is an equilateral triangle, what is the measure of angle DEC?
Answer» In the above figure, ABCD is a square and BCE is an equilateral triangle, what is the measure of angle DEC?

Discussion

13.	Question 6 A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6 m. For how many days will the water of this tank last?
Answer» Question 6 A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring $20 m \times 15 m \times 6 m$ . For how many days will the water of this tank last?

13.

Question 6 A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6 m. For how many days will the water of this tank last?

Answer»

Question 6
A village, having a population of 4000, requires 150 litres of water per head per day.

It has a tank measuring $20 m \times 15 m \times 6 m$ . For how many days will the water of this tank last?

Discussion

14.	28. If the point P (a2,a) lies in the region corresponding to the acute angle between the lines 2y = x and 4y = x, then (A) a (2,6) (B) a (4,6) (C) a (2,4) (D) None of these
Answer» 28. If the point P (a2,a) lies in the region corresponding to the acute angle between the lines 2y = x and 4y = x, then (A) a (2,6) (B) a (4,6) (C) a (2,4) (D) None of these

Discussion

15.	In the given figure, AB \|\| PQ. Find the values of x and y.
Answer» In the given figure, AB \|\| PQ. Find the values of x and y.

15.

In the given figure, AB || PQ. Find the values of x and y.

Answer»

In the given figure, AB || PQ. Find the values of x and y.

Discussion

16.	State whether the statements are True or False. Question 34The Y-coordinate of any point lying on the X-axis will be zero.
Answer» State whether the statements are True or False. Question 34 The Y-coordinate of any point lying on the X-axis will be zero.

Discussion

17.	The given table shows the marks obtained and the frequency. The cumulative frequency is ________ MarksFrequency10−20420−30930−40640−5010
Answer» The given table shows the marks obtained and the frequency. The cumulative frequency is ________ $\begin{matrix} Marks & Frequency 10 - 20 & 4 20 - 30 & 9 30 - 40 & 6 40 - 50 & 10 \end{matrix}$

17.

The given table shows the marks obtained and the frequency. The cumulative frequency is ________ MarksFrequency10−20420−30930−40640−5010

Answer»

The given table shows the marks obtained and the frequency. The cumulative frequency is ________

$\begin{matrix} Marks & Frequency 10 - 20 & 4 20 - 30 & 9 30 - 40 & 6 40 - 50 & 10 \end{matrix}$

Discussion

18.	If P=⎡⎢⎣1c3133244⎤⎥⎦ is the adjoint of a 3×3 matrix Q and detQ=4, then the value of c is
Answer» If $P = ⎡ ⎢ ⎣ \begin{matrix} 1 & c & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦$ is the adjoint of a $3 \times 3$ matrix $Q$ and $det Q = 4$ , then the value of $c$ is

Discussion

19.	The diameter of a cylinder is 28 cm and its height is 40 cm .Find the curved surface area, total surface area and the volume of the cylinder.
Answer» The diameter of a cylinder is 28 cm and its height is 40 cm .Find the curved surface area, total surface area and the volume of the cylinder.

Discussion

20.	What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?
Answer» What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?

Discussion

21.	Question 21 There is a mistake in each of the following ray diagrams given as Fig. (a), (b), and (c). Make the necessary correction(s).
Answer» Question 21 There is a mistake in each of the following ray diagrams given as Fig. (a), (b), and (c). Make the necessary correction(s).

21.

Question 21 There is a mistake in each of the following ray diagrams given as Fig. (a), (b), and (c). Make the necessary correction(s).

Answer»

Question 21

There is a mistake in each of the following ray diagrams given as Fig. (a), (b), and (c). Make the necessary correction(s).

Discussion

22.	A student is given three sticks of length 15 CM 8 cm and 5 cm respectively his friend asked him to make a triangle with the help of these sticks and then find its area
Answer» A student is given three sticks of length 15 CM 8 cm and 5 cm respectively his friend asked him to make a triangle with the help of these sticks and then find its area

Discussion

23.	The algebraic sum of the deviations of a set of n values from their mean is(a) 0(b) n − 1(c) n(d) n + 1
Answer» The algebraic sum of the deviations of a set of n values from their mean is (a) 0 (b) n − 1 (c) n (d) n + 1

Discussion

24.	If α,β are the zeroes of the polynomial x2−px+36 and α2+β2 = 9, then what is the value of p?
Answer» If $α, β$ are the zeroes of the polynomial $x^{2} - p x + 36$ and $α^{2}$ + $β^{2}$ = 9, then what is the value of p?

Discussion

25.	Find the median of first 10 prime numbers.
Answer» Find the median of first 10 prime numbers.

Discussion

26.	In triangle ABC, D is a point in AB such that AC =CD =DB. If ∠ B = 280, find the angle ACD.
Answer» In triangle ABC, D is a point in AB such that AC =CD =DB. If $∠$ B = $28^{0}$ , find the angle ACD.

Discussion

27.	A triangular tent is 12 ft. high . The diagonal length between the top and the pegs of the tent is 15 ft. Find the base width of the tent if it is given that the height of the tent bisects the base width at right angle.
Answer» A triangular tent is 12 ft. high . The diagonal length between the top and the pegs of the tent is 15 ft. Find the base width of the tent if it is given that the height of the tent bisects the base width at right angle.

Discussion

28.	If A={1,2,{3,4}}, then the number of elements in P(P(A)) is (where P(A) is the power set of A)
Answer» If $A = {1, 2, {3, 4}}$ , then the number of elements in $P (P (A))$ is (where $P (A)$ is the power set of $A)$

Discussion

29.	Question 21 Rani ate 27 part of a cake while her brother Ravi ate 45 of the remaining. Part of the cake left is ___.
Answer» Question 21 Rani ate $\frac{2}{7}$ part of a cake while her brother Ravi ate $\frac{4}{5}$ of the remaining. Part of the cake left is ___.

29.

Question 21 Rani ate 27 part of a cake while her brother Ravi ate 45 of the remaining. Part of the cake left is ___.

Answer»

Question 21

Rani ate $\frac{2}{7}$ part of a cake while her brother Ravi ate $\frac{4}{5}$ of the remaining. Part of the cake left is ___.

Discussion

30.	Find the area remaining if 6 circle are placed in a hexagon of side length 8cm each touching 2 other circle.
Answer» Find the area remaining if 6 circle are placed in a hexagon of side length 8cm each touching 2 other circle.

Discussion

31.	ABC is a triangle where AM\|BC and AN bisects angle A.If ABC is 70° and acb is 20° find man
Answer» ABC is a triangle where AM\|BC and AN bisects angle A.If ABC is 70° and acb is 20° find man

Discussion

32.	Factorise: 2√3x2+x−5√3
Answer» Factorise: $2 \sqrt{3} x^{2} + x - 5 \sqrt{3}$

32.

Factorise: 2√3x2+x−5√3

Answer»

Factorise:

$2 \sqrt{3} x^{2} + x - 5 \sqrt{3}$

Discussion

33.	Construct a frequency distribution table from the following cumulative frequency distribution:-(i)Class IntervalCumulative Frequency10−19820−291930−392340−4930(ii)Class IntervalCumulative Frequency5−101810−153015−204620−257325−3090
Answer» Construct a frequency distribution table from the following cumulative frequency distribution:- (i) $\begin{matrix} Class Interval & Cumulative Frequency 10 - 19 & 8 20 - 29 & 19 30 - 39 & 23 40 - 49 & 30 \end{matrix}$ (ii) $\begin{matrix} Class Interval & Cumulative Frequency 5 - 10 & 18 10 - 15 & 30 15 - 20 & 46 20 - 25 & 73 25 - 30 & 90 \end{matrix}$

Discussion

34.	Rachna borrows Rs.12,000 at 10 per cent per annum interest compounded half-yearly. She repays Rs. 4,000 at the end of every six months. Calculate the third payment she has to make at the end of 18 months in order to clear the entire loan.
Answer» Rachna borrows Rs.12,000 at 10 per cent per annum interest compounded half-yearly. She repays Rs. 4,000 at the end of every six months. Calculate the third payment she has to make at the end of 18 months in order to clear the entire loan.

Discussion

35.	If →r×→b=→c×→b and →r.→a=0 where →a=2^i+3^j−^k,→b=3^i−^j+^k and →c=^i+^j+3^k, then →r is equal to
Answer» If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Discussion

36.	If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a (a) rhombus (b) kite (c) trapezium (d) parallelogram
Answer» If $∠ A, ∠ B, ∠ C a n d ∠ D$ of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a (a) rhombus (b) kite (c) trapezium (d) parallelogram

36.

If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a (a) rhombus (b) kite (c) trapezium (d) parallelogram

Answer»

If $∠ A, ∠ B, ∠ C a n d ∠ D$ of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a

(a) rhombus

(b) kite

(c) trapezium

(d) parallelogram

Discussion

37.	Find five rational numbers between 35 and 45.
Answer» Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .

Discussion

38.	Simplify x234 and express the result in the exponential form of x.
Answer» Simplify $\sqrt[4]{\sqrt[3]{x^{2}}}$ and express the result in the exponential form of x.

Discussion

39.	The rate of change of the surface are of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is _________________.
Answer» The rate of change of the surface are of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is _________________.

Discussion

40.	How many theorems did Euclid give in his book - Elements?
Answer» How many theorems did Euclid give in his book - Elements?

Discussion

41.	The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be
Answer» The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

Discussion

42.	If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =(a) 3(b) −3(c) 9(d) −9
Answer» If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x = (a) 3 (b) −3 (c) 9 (d) −9

Discussion

43.	In Fig. 7, a small indoor green house is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. What is the area of the glass? How much tape is required for all the 12 edges?
Answer» In Fig. 7, a small indoor green house is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. What is the area of the glass? How much tape is required for all the 12 edges?

Discussion

44.	In a Right-angled triangle, one angle is 60°. If hypotenuse measures 12cm, then the sides of the triangle are
Answer» In a Right-angled triangle, one angle is 60°. If hypotenuse measures 12cm, then the sides of the triangle are

Discussion

45.	It costs Rs. 2200 to paint outer surface of a closed cylindrical tank of height 6.5 m , painting at Rs. 10 per sq. m. The volume of kerosene that can be filled in this tank is
Answer» It costs Rs. 2200 to paint outer surface of a closed cylindrical tank of height 6.5 m , painting at Rs. 10 per sq. m. The volume of kerosene that can be filled in this tank is

Discussion

46.	a point m is equal distance from two lines PQ and QR intersecting at point Q show that the line MQ bisect the angle between them
Answer» a point m is equal distance from two lines PQ and QR intersecting at point Q show that the line MQ bisect the angle between them

Discussion

47.	Polynomials bx2 + x + 5 and bx3 -2x + 5 are divided by polynomial x-3 and the remainders are m and n respectively. If m- n = 0 then find the value of b.
Answer» Polynomials bx²+ x + 5 and bx³ $-$ 2x + 5 are divided by polynomial x $-$ 3 and the remainders are m and n respectively. If m $-$ n = 0 then find the value of b.

Discussion

48.	If θ = 30∘, prove that cos 2θ = cos2 θ - sin2 θ
Answer» If θ = $30^{\circ}$ , prove that cos 2θ = cos² θ - sin² θ

Discussion

49.	Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5m. Also find the area of the iron sheet required to make the cistern.
Answer» Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5m. Also find the area of the iron sheet required to make the cistern.

Discussion

50.	Question 8In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX⊥DE meets BC at Y. Show that:(i) ΔMBC≅ΔABD(ii) area(BYXD)=2area(ΔMBC)(iii) ar(BYXD)=ar(ABMN)(iv) ΔFCB≅ΔACE(v) ar(CYXE)=2ar(ΔFCB)(vi) ar(ACFG)=ar(CYXE)(vii) ar (BCED) = ar(ABMN) + ar(ACFG)
Answer» Question 8 In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment $A X ⊥ D E$ meets BC at Y. Show that: (i) $Δ M B C ≅ Δ A B D$ (ii) $a r e a (B Y X D) = 2 a r e a (Δ M B C)$ (iii) $a r (B Y X D) = a r (A B M N)$ (iv) $Δ F C B ≅ Δ A C E$ (v) $a r (C Y X E) = 2 a r (Δ F C B)$ (vi) $a r (A C F G) = a r (C Y X E)$ (vii) ar (BCED) = ar(ABMN) + ar(ACFG)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Which of the following are two rational numbers between √5 and √6

Question 5A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and its longer diagonal is 48m, how much area of grass field will each cow be getting?

In trapezium ABCD, side AB || side PQ || side ∆C, AP = 15, PD = 12, QC = 14, Find BQ.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC is 30∘ and AB = BC, find ∠ECD.

If an integer is chosen at random and squared, then the probability that the last digit of the square is either 1 or 5, is

On the plane of a graph paper draw X'OX and YOY' as coordinate axes and plot each of the following points.(i) A(5, 3)(ii) B(6, 2)(iii) C(–5, 3)(iv) D(4, –6)(v) E(–3, –2)(vi) F(–4, 4)(vii) G(3, –4)(viii) H(5, 0)(ix) I(0, 6)(x) J(–3, 0)(xi) K(0, –2)(xii) O(0, 0)

1,2,3,4,5......The above set of numbers are known as _______.

the length of the sides of a triangle are 8 cm,15 cm and 17 cm . Perpendicular length from the opposite vertex to the side whose length is 17 cm i

In Δ ABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

In the above figure, ABCD is a square and BCE is an equilateral triangle, what is the measure of angle DEC?

Question 6 A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6 m. For how many days will the water of this tank last?

28. If the point P (a2,a) lies in the region corresponding to the acute angle between the lines 2y = x and 4y = x, then (A) a (2,6) (B) a (4,6) (C) a (2,4) (D) None of these

In the given figure, AB || PQ. Find the values of x and y.

State whether the statements are True or False. Question 34The Y-coordinate of any point lying on the X-axis will be zero.

The given table shows the marks obtained and the frequency. The cumulative frequency is ________ MarksFrequency10−20420−30930−40640−5010

If P=⎡⎢⎣1c3133244⎤⎥⎦ is the adjoint of a 3×3 matrix Q and detQ=4, then the value of c is

The diameter of a cylinder is 28 cm and its height is 40 cm .Find the curved surface area, total surface area and the volume of the cylinder.

What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?

Question 21 There is a mistake in each of the following ray diagrams given as Fig. (a), (b), and (c). Make the necessary correction(s).

A student is given three sticks of length 15 CM 8 cm and 5 cm respectively his friend asked him to make a triangle with the help of these sticks and then find its area

The algebraic sum of the deviations of a set of n values from their mean is(a) 0(b) n − 1(c) n(d) n + 1

If α,β are the zeroes of the polynomial x2−px+36 and α2+β2 = 9, then what is the value of p?

Find the median of first 10 prime numbers.

In triangle ABC, D is a point in AB such that AC =CD =DB. If ∠ B = 280, find the angle ACD.

A triangular tent is 12 ft. high . The diagonal length between the top and the pegs of the tent is 15 ft. Find the base width of the tent if it is given that the height of the tent bisects the base width at right angle.

If A={1,2,{3,4}}, then the number of elements in P(P(A)) is (where P(A) is the power set of A)

Question 21 Rani ate 27 part of a cake while her brother Ravi ate 45 of the remaining. Part of the cake left is ___.

Find the area remaining if 6 circle are placed in a hexagon of side length 8cm each touching 2 other circle.

ABC is a triangle where AM|BC and AN bisects angle A.If ABC is 70° and acb is 20° find man

Factorise: 2√3x2+x−5√3

Construct a frequency distribution table from the following cumulative frequency distribution:-(i)Class IntervalCumulative Frequency10−19820−291930−392340−4930(ii)Class IntervalCumulative Frequency5−101810−153015−204620−257325−3090

Rachna borrows Rs.12,000 at 10 per cent per annum interest compounded half-yearly. She repays Rs. 4,000 at the end of every six months. Calculate the third payment she has to make at the end of 18 months in order to clear the entire loan.

If →r×→b=→c×→b and →r.→a=0 where →a=2^i+3^j−^k,→b=3^i−^j+^k and →c=^i+^j+3^k, then →r is equal to

If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a (a) rhombus (b) kite (c) trapezium (d) parallelogram

Find five rational numbers between 35 and 45.

Simplify x234 and express the result in the exponential form of x.

The rate of change of the surface are of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is _________________.

How many theorems did Euclid give in his book - Elements?

The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =(a) 3(b) −3(c) 9(d) −9

In Fig. 7, a small indoor green house is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. What is the area of the glass? How much tape is required for all the 12 edges?

In a Right-angled triangle, one angle is 60°. If hypotenuse measures 12cm, then the sides of the triangle are

It costs Rs. 2200 to paint outer surface of a closed cylindrical tank of height 6.5 m , painting at Rs. 10 per sq. m. The volume of kerosene that can be filled in this tank is

a point m is equal distance from two lines PQ and QR intersecting at point Q show that the line MQ bisect the angle between them

Polynomials bx2 + x + 5 and bx3 -2x + 5 are divided by polynomial x-3 and the remainders are m and n respectively. If m- n = 0 then find the value of b.

If θ = 30∘, prove that cos 2θ = cos2 θ - sin2 θ

Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5m. Also find the area of the iron sheet required to make the cistern.