32581 + Interview Questions in Mathematics

1.	If y is the mean proportional between x and z prove that xyz(x+y+z)^3=(xy+yz+zx)^3
Answer» If y is the mean proportional between x and z prove that xyz(x+y+z)^3=(xy+yz+zx)^3

1.

If y is the mean proportional between x and z prove that xyz(x+y+z)^3=(xy+yz+zx)^3

Answer»

If y is the mean proportional between x and z prove that

xyz(x+y+z)^3=(xy+yz+zx)^3

Discussion

2.	If 2 is a zero of both the polynomial, 3x2+ax−14 and 2x−b, then value of (a−2b) is,
Answer» If $2$ is a zero of both the polynomial, $3 x^{2} + a x - 14$ and $2 x - b$ , then value of $(a - 2 b)$ is,

2.

If 2 is a zero of both the polynomial, 3x2+ax−14 and 2x−b, then value of (a−2b) is,

Answer»

If $2$ is a zero of both the polynomial, $3 x^{2} + a x - 14$ and $2 x - b$ , then value of $(a - 2 b)$ is,

Discussion

3.	What is the percentage interest on the capital invested in 9% shares, when Rs 10 shares cost Rs 12?
Answer» What is the percentage interest on the capital invested in $9 %$ shares, when Rs 10 shares cost Rs 12?

Discussion

4.	Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(1, 1), B(5, 3) and C(2, 7). (ii) Construct the locus of points equidistant from A and B. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length(approximately) of PA in cm is
Answer» Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(1, 1), B(5, 3) and C(2, 7). (ii) Construct the locus of points equidistant from A and B. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length(approximately) of PA in cm is

4.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(1, 1), B(5, 3) and C(2, 7). (ii) Construct the locus of points equidistant from A and B. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length(approximately) of PA in cm is

Answer»

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC.

Then the length(approximately) of PA in cm is

Discussion

5.	in the given figure,DE∥BC and ADDB=35Calculate:(i)ar(△ADE)ar(△ABC)(ii)Area of trapezium DECBar(△ABC)
Answer» $i n t h e g i v e n f i g u r e, D E ∥ B C a n d \frac{A D}{D B} = \frac{3}{5} C a l c u l a t e : (i) \frac{a r (△ A D E)}{a r (△ A B C)} (i i) \frac{A r e a o f t r a p e z i u m D E C B}{a r (△ A B C)}$

5.

in the given figure,DE∥BC and ADDB=35Calculate:(i)ar(△ADE)ar(△ABC)(ii)Area of trapezium DECBar(△ABC)

Answer»

$i n t h e g i v e n f i g u r e, D E ∥ B C a n d \frac{A D}{D B} = \frac{3}{5} C a l c u l a t e : (i) \frac{a r (△ A D E)}{a r (△ A B C)} (i i) \frac{A r e a o f t r a p e z i u m D E C B}{a r (△ A B C)}$

Discussion

6.	Which of the following statements is correct
Answer» Which of the following statements is correct

Discussion

7.	If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies. Marks0−1010−3030−6060−8080−90Number of students5f130f22
Answer» If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies. $\begin{matrix} M a r k s & 0 - 10 & 10 - 30 & 30 - 60 & 60 - 80 & 80 - 90 N u m b e r o f s t u d e n t s & 5 & f_{1} & 30 & f_{2} & 2 \end{matrix}$

Discussion

8.	For the following set of data the median will be 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9 and 15
Answer» For the following set of data the median will be 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9 and 15

Discussion

9.	In a class, there are 2 seats for students in each row. There are 12 such rows. The total number of seats in that class is .
Answer» In a class, there are 2 seats for students in each row. There are 12 such rows. The total number of seats in that class is .

Discussion

10.	The sum of the first 20 term of the sqeuence 0, 7, 0.77, 0.777,...., is
Answer» The sum of the first 20 term of the sqeuence 0, 7, 0.77, 0.777,...., is

Discussion

11.	Question 7 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 53 times the corresponding sides of the given triangle.
Answer» Question 7 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.

Discussion

12.	The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is increased by 2, then the median of the new set
Answer» The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is increased by 2, then the median of the new set

Discussion

13.	If cosec(A+B)=2√3, sec(A−B)=2√3, 0∘<A+B≤90∘, Find A and B.
Answer» If $c o s e c (A + B) = \frac{2}{\sqrt{3}}$ , $s e c (A - B) = \frac{2}{\sqrt{3}}$ , $0^{\circ} < A + B \leq 90^{\circ}$ , Find A and B.

13.

If cosec(A+B)=2√3, sec(A−B)=2√3, 0∘<A+B≤90∘, Find A and B.

Answer»

If $c o s e c (A + B) = \frac{2}{\sqrt{3}}$ , $s e c (A - B) = \frac{2}{\sqrt{3}}$ ,

$0^{\circ} < A + B \leq 90^{\circ}$ ,

Find A and B.

Discussion

14.	Solve the following quadric equations by factorization method only 9x2+4=0
Answer» Solve the following quadric equations by factorization method only $9 x^{2} + 4 = 0$

Discussion

15.	show that square of an odd positive integer is of the form 8m+1, for some whole number m
Answer» show that square of an odd positive integer is of the form 8m+1, for some whole number m

Discussion

16.	Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.
Answer» Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.

Discussion

17.	Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.
Answer» Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

Discussion

18.	The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is (a) 60π cm2 (b) 65π cm2 (c) 30π cm2 (d) none of these
Answer» The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is (a) $60 π c m^{2}$ (b) $65 π c m^{2}$ (c) $30 π c m^{2}$ (d) none of these

18.

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is (a) 60π cm2 (b) 65π cm2 (c) 30π cm2 (d) none of these

Answer»

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is

(a) $60 π c m^{2}$ (b) $65 π c m^{2}$ (c) $30 π c m^{2}$ (d) none of these

Discussion

19.	Suppose that 90% of people are right handed. What is the probability that alomost 6 of random sample of 10 people are right handed?
Answer» Suppose that $90 %$ of people are right handed. What is the probability that alomost 6 of random sample of 10 people are right handed?

Discussion

20.	If the roots of the equation (a2+b2)x2−2(ac+bd)x+(c2+d2)=0 are equal, prove that ab=cd
Answer» If the roots of the equation $(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + (c^{2} + d^{2}) = 0$ are equal, prove that $\frac{a}{b} = \frac{c}{d}$

Discussion

21.	Find: (i) 10th term of the A.P. 1,4,7,10,... (ii) 18th term of the A.P. √2,3√2,5√2,... (iii) nth term of the A.P. 13,8,3,-2,... (iv) 10th term of the A.P. -40,-15,10,35,... (v) 8th term of the A.P. 117,104,91,78,... (vi) 11th term of the A.P. 10.0,10.5,11.0,11.5,... (vii) 9th term of the A.P. 34,54,74,94,...
Answer» Find: (i) 10th term of the A.P. 1,4,7,10,... (ii) 18th term of the A.P. $\sqrt{2}, 3 \sqrt{2}, 5 \sqrt{2}$ ,... (iii) nth term of the A.P. 13,8,3,-2,... (iv) 10th term of the A.P. -40,-15,10,35,... (v) 8th term of the A.P. 117,104,91,78,... (vi) 11th term of the A.P. 10.0,10.5,11.0,11.5,... (vii) 9th term of the A.P. $\frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{9}{4}$ ,...

Discussion

22.	If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation is
Answer» If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation is

Discussion

23.	Find the mean for the following data. Class0−2020−4040−6060−8080−100Frequency51112139
Answer» Find the mean for the following data. $\begin{matrix} C l a s s & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 F r e q u e n c y & 5 & 11 & 12 & 13 & 9 \end{matrix}$

Discussion

24.	A square ABCD is inscribed in a circle of radius r. Find the area of the square.
Answer» A square ABCD is inscribed in a circle of radius r. Find the area of the square.

Discussion

25.	What is the greatest possible perimeter of a right angle triangle with integer side lengths if one of the sides has length 12?
Answer» What is the greatest possible perimeter of a right angle triangle with integer side lengths if one of the sides has length 12?

Discussion

26.	If A = {1,2,3}, B = {a,b,c}, which of the following is a function?
Answer» If A = {1,2,3}, B = {a,b,c}, which of the following is a function?

Discussion

27.	If sin 3θ= cos(θ-26∘), where 3θ and(θ-26∘) are acute angles then find the value of θ.
Answer» If sin 3 $θ$ = cos( $θ$ - $26^{\circ}$ ), where 3 $θ$ and( $θ$ - $26^{\circ}$ ) are acute angles then find the value of $θ$ .

Discussion

28.	(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5. (ii) AB meets the x-axis at A and y-axis at B. Calculate the area of triangle OAB, where O is the origin.
Answer» (i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5. (ii) AB meets the x-axis at A and y-axis at B. Calculate the area of triangle OAB, where O is the origin.

28.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5. (ii) AB meets the x-axis at A and y-axis at B. Calculate the area of triangle OAB, where O is the origin.

Answer»

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.

(ii) AB meets the x-axis at A and y-axis at B. Calculate the area of triangle OAB, where O is the origin.

Discussion

29.	The angle of elevation of a cloud from a point 60 m above a lake is 30∘ and the angle of depression of the reflection of cloud in the lake is 60∘. Find the height of the cloud.
Answer» The angle of elevation of a cloud from a point 60 m above a lake is $30^{\circ}$ and the angle of depression of the reflection of cloud in the lake is $60^{\circ}$ . Find the height of the cloud.

Discussion

30.	PQR is a triangle right-angled at P and M is a point on QR such that PM⊥QR. Show that PM2=QM×MR [3 MARKS]
Answer» PQR is a triangle right-angled at P and M is a point on QR such that $P M ⊥ Q R$ . Show that $P M^{2} = Q M \times M R$ [3 MARKS]

Discussion

31.	The sum of three consecutive terms of an A. P. is 21 and the sum of their squares is 165. Find these terms.
Answer» The sum of three consecutive terms of an A. P. is 21 and the sum of their squares is 165. Find these terms.

Discussion

32.	In Δ ABC, DE \|\| BC. If AD = x - 5, DB = 3x - 19, AE = 3 and EC = x - 3. Then which of the following could be the value of x?
Answer» In $Δ$ ABC, DE \|\| BC. If AD = x - 5, DB = 3x - 19, AE = 3 and EC = x - 3. Then which of the following could be the value of x?

Discussion

33.	Match the following columns: Column I Column II(a) Theradii of circular ends of(p) 2418π a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is ..... cm3. [Take π=227.](b) The radii of the circular ends(q) 22000 of a conical bucket of height 15 cm are 20 cm and 12 cm respectively. The slant height of the bucket is.... cm.(c) The radii of the circular ends(r) 12 of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is ..... cm2.(d) Three solid metallic spheres of(s) 17 radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ...... cm. The correct answer is (a)−........, (b)−........, (c)−........, (d)−.........
Answer» Match the following columns: $\begin{matrix} C o l u m n I & C o l u m n I I (a) T h e r a d i i o f c i r c u l a r e n d s o f & (p) 2418 π a b u c k e t i n t h e f o r m o f f r u s t u m o f a c o n e o f h e i g h t 30 c m a r e 20 c m a n d 10 c m r e s p e c t i v e l y . T h e c a p a c i t y o f t h e b u c k e t i s . . . . . c m^{3} . [T a k e π = \frac{22}{7} .] (b) T h e r a d i i o f t h e c i r c u l a r e n d s & (q) 22000 o f a c o n i c a l b u c k e t o f h e i g h t 15 c m a r e 20 c m a n d 12 c m r e s p e c t i v e l y . T h e s l a n t h e i g h t o f t h e b u c k e t i s . . . . c m . (c) T h e r a d i i o f t h e c i r c u l a r e n d s & (r) 12 o f a s o l i d f r u s t u m o f a c o n e a r e 33 c m a n d 27 c m a n d i t s s l a n t h e i g h t i s 10 c m . T h e t o t a l s u r f a c e a r e a o f t h e b u c k e t i s . . . . . c m^{2} . (d) T h r e e s o l i d m e t a l l i c s p h e r e s o f & (s) 17 r a d i i 3 c m, 4 c m a n d 5 c m a r e m e l t e d t o f o r m a s i n g l e s o l i d s p h e r e . T h e d i a m e t e r o f t h e r e s u l t i n g s p h e r e i s . . . . . . c m . \end{matrix}$ The correct answer is $(a) -_{. . . . . . . .,}$ $(b) -_{. . . . . . . .,}$ $(c) -_{. . . . . . . .,}$ $(d) -_{. . . . . . . . .}$

33.

Match the following columns: Column I Column II(a) Theradii of circular ends of(p) 2418π a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is ..... cm3. [Take π=227.](b) The radii of the circular ends(q) 22000 of a conical bucket of height 15 cm are 20 cm and 12 cm respectively. The slant height of the bucket is.... cm.(c) The radii of the circular ends(r) 12 of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is ..... cm2.(d) Three solid metallic spheres of(s) 17 radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ...... cm. The correct answer is (a)−........, (b)−........, (c)−........, (d)−.........

Answer»

Match the following columns:

$\begin{matrix} C o l u m n I & C o l u m n I I (a) T h e r a d i i o f c i r c u l a r e n d s o f & (p) 2418 π a b u c k e t i n t h e f o r m o f f r u s t u m o f a c o n e o f h e i g h t 30 c m a r e 20 c m a n d 10 c m r e s p e c t i v e l y . T h e c a p a c i t y o f t h e b u c k e t i s . . . . . c m^{3} . [T a k e π = \frac{22}{7} .] (b) T h e r a d i i o f t h e c i r c u l a r e n d s & (q) 22000 o f a c o n i c a l b u c k e t o f h e i g h t 15 c m a r e 20 c m a n d 12 c m r e s p e c t i v e l y . T h e s l a n t h e i g h t o f t h e b u c k e t i s . . . . c m . (c) T h e r a d i i o f t h e c i r c u l a r e n d s & (r) 12 o f a s o l i d f r u s t u m o f a c o n e a r e 33 c m a n d 27 c m a n d i t s s l a n t h e i g h t i s 10 c m . T h e t o t a l s u r f a c e a r e a o f t h e b u c k e t i s . . . . . c m^{2} . (d) T h r e e s o l i d m e t a l l i c s p h e r e s o f & (s) 17 r a d i i 3 c m, 4 c m a n d 5 c m a r e m e l t e d t o f o r m a s i n g l e s o l i d s p h e r e . T h e d i a m e t e r o f t h e r e s u l t i n g s p h e r e i s . . . . . . c m . \end{matrix}$

The correct answer is

$(a) -_{. . . . . . . .,}$ $(b) -_{. . . . . . . .,}$ $(c) -_{. . . . . . . .,}$ $(d) -_{. . . . . . . . .}$

Discussion

34.	If the mean of the data is 60, find the value of p Class intervalfrequency25−351235−451645−55p55−651565−75875−851985−9513
Answer» If the mean of the data is 60, find the value of p $\begin{matrix} C l a s s i n t e r v a l & f r e q u e n c y 25 - 35 & 12 35 - 45 & 16 45 - 55 & p 55 - 65 & 15 65 - 75 & 8 75 - 85 & 19 85 - 95 & 13 \end{matrix}$

Discussion

35.	if one zero of a polynomial 3x2- 8 x + 2 k + 1 is 7 times the other find the value of k
Answer» if one zero of a polynomial 3x²- 8 x + 2 k + 1 is 7 times the other find the value of k

Discussion

36.	The product of two fractions is (2526) and their quotient is (1332), find the larger fraction?
Answer» The product of two fractions is $(\frac{25}{26})$ and their quotient is $(\frac{13}{32})$ , find the larger fraction?

Discussion

37.	at an annual function, each student gives gift to every other student. if no. of gifts is 1980. find no. of students
Answer» at an annual function, each student gives gift to every other student. if no. of gifts is 1980. find no. of students

Discussion

38.	What is the value of sin263∘+sin227∘cos217∘+cos273∘ ?
Answer» What is the value of $\frac{s i n^{2} 63^{\circ} + s i n^{2} 27^{\circ}}{c o s^{2} 17^{\circ} + c o s^{2} 73^{\circ}}$ ?

Discussion

39.	A manufacturer sells a washing machine to a wholesaler for Rs 15000. The wholesaler sells it to a trader at a profit of Rs 1200 and the trader in turn sells it to a consumer at a profit of Rs 1800. If the rate of VAT is 8% find the amount of VAT received by the State Government on the sale of this machine from the wholesaler.
Answer» A manufacturer sells a washing machine to a wholesaler for Rs 15000. The wholesaler sells it to a trader at a profit of Rs 1200 and the trader in turn sells it to a consumer at a profit of Rs 1800. If the rate of VAT is 8% find the amount of VAT received by the State Government on the sale of this machine from the wholesaler.

Discussion

40.	The list of numbers 5, - 2, -9, -16 ... is an AP with d = 7.
Answer» The list of numbers 5, - 2, -9, -16 ... is an AP with d = 7.

Discussion

41.	A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. [4 MARKS]
Answer» A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. [4 MARKS]

Discussion

42.	A right-angled triangle having its height and base equal to 24 cm and 7 cm respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.
Answer» A right-angled triangle having its height and base equal to 24 cm and 7 cm respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

Discussion

43.	Choose the correct option: (cosec θ+cot θ)×(1−cos θ)=
Answer» Choose the correct option: $(c o s e c θ + c o t θ) \times (1 - c o s θ) =$

Discussion

44.	What is the value of tanθ in △ABC, if θ is increased by 30∘.
Answer» What is the value of $t a n θ$ in $△$ ABC, if $θ$ is increased by $30^{\circ}$ .

Discussion

45.	A bag contains 3 red balls, 5 black balls, and 4 white balls. A ball is drawn at random from the bag. What is the probability of not getting a black ball?
Answer» A bag contains 3 red balls, 5 black balls, and 4 white balls. A ball is drawn at random from the bag. What is the probability of not getting a black ball?

Discussion

46.	Question 11. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?
Answer» Question 11. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

Discussion

47.	In the given figure, O is the centre of the circle and ∠ AOC is 60∘, then the value of X is .
Answer» In the given figure, O is the centre of the circle and $∠ A O C$ is $60^{\circ}$ , then the value of X is .

Discussion

48.	The volume of a hemisphere is 2425 12cm3. Find its curved surface area. [Use =227 ]
Answer» The volume of a hemisphere is 2425 $\frac{1}{2} c m^{3}$ . Find its curved surface area. [Use $= \frac{22}{7}$ ]

Discussion

49.	What is the factorization of 2x2−7x−15?
Answer» What is the factorization of $2 x^{2} - 7 x - 15$ ?

Discussion

50.	In triangle DEF, GH is a line parallel to EF cutting DE in G and DF in H. If DE=16.5, DH=5, HF=6 GE=?
Answer» In triangle DEF, GH is a line parallel to EF cutting DE in G and DF in H. If DE=16.5, DH=5, HF=6 GE=?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If y is the mean proportional between x and z prove that xyz(x+y+z)^3=(xy+yz+zx)^3

If 2 is a zero of both the polynomial, 3x2+ax−14 and 2x−b, then value of (a−2b) is,

What is the percentage interest on the capital invested in 9% shares, when Rs 10 shares cost Rs 12?

in the given figure,DE∥BC and ADDB=35Calculate:(i)ar(△ADE)ar(△ABC)(ii)Area of trapezium DECBar(△ABC)

Which of the following statements is correct

If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies. Marks0−1010−3030−6060−8080−90Number of students5f130f22

For the following set of data the median will be 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9 and 15

In a class, there are 2 seats for students in each row. There are 12 such rows. The total number of seats in that class is .

The sum of the first 20 term of the sqeuence 0, 7, 0.77, 0.777,...., is

Question 7 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 53 times the corresponding sides of the given triangle.

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is increased by 2, then the median of the new set

If cosec(A+B)=2√3, sec(A−B)=2√3, 0∘&lt;A+B≤90∘, Find A and B.

Solve the following quadric equations by factorization method only 9x2+4=0

show that square of an odd positive integer is of the form 8m+1, for some whole number m

Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.

Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is (a) 60π cm2 (b) 65π cm2 (c) 30π cm2 (d) none of these

Suppose that 90% of people are right handed. What is the probability that alomost 6 of random sample of 10 people are right handed?

If the roots of the equation (a2+b2)x2−2(ac+bd)x+(c2+d2)=0 are equal, prove that ab=cd

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation is

Find the mean for the following data. Class0−2020−4040−6060−8080−100Frequency51112139

A square ABCD is inscribed in a circle of radius r. Find the area of the square.

What is the greatest possible perimeter of a right angle triangle with integer side lengths if one of the sides has length 12?

If A = {1,2,3}, B = {a,b,c}, which of the following is a function?

If sin 3θ= cos(θ-26∘), where 3θ and(θ-26∘) are acute angles then find the value of θ.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5. (ii) AB meets the x-axis at A and y-axis at B. Calculate the area of triangle OAB, where O is the origin.

The angle of elevation of a cloud from a point 60 m above a lake is 30∘ and the angle of depression of the reflection of cloud in the lake is 60∘. Find the height of the cloud.

PQR is a triangle right-angled at P and M is a point on QR such that PM⊥QR. Show that PM2=QM×MR [3 MARKS]

The sum of three consecutive terms of an A. P. is 21 and the sum of their squares is 165. Find these terms.

In Δ ABC, DE || BC. If AD = x - 5, DB = 3x - 19, AE = 3 and EC = x - 3. Then which of the following could be the value of x?

If the mean of the data is 60, find the value of p Class intervalfrequency25−351235−451645−55p55−651565−75875−851985−9513

if one zero of a polynomial 3x2- 8 x + 2 k + 1 is 7 times the other find the value of k

The product of two fractions is (2526) and their quotient is (1332), find the larger fraction?

at an annual function, each student gives gift to every other student. if no. of gifts is 1980. find no. of students

What is the value of sin263∘+sin227∘cos217∘+cos273∘ ?

The list of numbers 5, - 2, -9, -16 ... is an AP with d = 7.

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. [4 MARKS]

A right-angled triangle having its height and base equal to 24 cm and 7 cm respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

Choose the correct option: (cosec θ+cot θ)×(1−cos θ)=

What is the value of tanθ in △ABC, if θ is increased by 30∘.

A bag contains 3 red balls, 5 black balls, and 4 white balls. A ball is drawn at random from the bag. What is the probability of not getting a black ball?

In the given figure, O is the centre of the circle and ∠ AOC is 60∘, then the value of X is .

The volume of a hemisphere is 2425 12cm3. Find its curved surface area. [Use =227 ]

What is the factorization of 2x2−7x−15?

In triangle DEF, GH is a line parallel to EF cutting DE in G and DF in H. If DE=16.5, DH=5, HF=6 GE=?

If cosec(A+B)=2√3, sec(A−B)=2√3, 0∘<A+B≤90∘, Find A and B.