32581 + Interview Questions in Mathematics

1.	Solve the following pair of linear equation 1) px+qy=p-q qx-py=p+q
Answer» Solve the following pair of linear equation 1) px+qy=p-q qx-py=p+q

1.

Solve the following pair of linear equation 1) px+qy=p-q qx-py=p+q

Answer»

Solve the following pair of linear equation

1) px+qy=p-q

qx-py=p+q

2.	sin18∘cos72∘___
Answer» $\frac{s i n 18^{\circ}}{c o s 72^{\circ}}$ ___

Discussion

3.	In fig. 8, the vertices of ΔABC are A(4,6), B(1,5) and C(7,2). A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that ADAB=AEAC=13. Calculate the area of ΔADE and compare it with area of ΔABC.
Answer» In fig. 8, the vertices of $Δ A B C$ are $A (4, 6), B (1, 5)$ and $C (7, 2)$ . A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that $\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{3}$ . Calculate the area of $Δ A D E$ and compare it with area of $Δ A B C$ .

Discussion

4.	Solve each of the following systems of equations by using the method of cross multiplication: ax−by=0,ab2x+a2by=(a2+b2),where x≠0 and y≠0.
Answer» Solve each of the following systems of equations by using the method of cross multiplication: $\frac{a}{x} - \frac{b}{y} = 0, \frac{a b^{2}}{x} + \frac{a^{2} b}{y} = (a^{2} + b^{2}), w h e r e x \neq 0 a n d y \neq 0.$

4.

Solve each of the following systems of equations by using the method of cross multiplication: ax−by=0,ab2x+a2by=(a2+b2),where x≠0 and y≠0.

Answer»

Solve each of the following systems of equations by using the method of cross multiplication:

$\frac{a}{x} - \frac{b}{y} = 0, \frac{a b^{2}}{x} + \frac{a^{2} b}{y} = (a^{2} + b^{2}), w h e r e x \neq 0 a n d y \neq 0.$

Discussion

5.	Prove the following identities: cos A cosec A−sin A sec Acos A+sin A=cosec A−sec A
Answer» Prove the following identities: $\frac{c o s A c o s e c A - s i n A s e c A}{c o s A + s i n A} = c o s e c A - s e c A$

5.

Prove the following identities: cos A cosec A−sin A sec Acos A+sin A=cosec A−sec A

Answer»

Prove the following identities:

$\frac{c o s A c o s e c A - s i n A s e c A}{c o s A + s i n A} = c o s e c A - s e c A$

Discussion

6.	On increasing the diameter of a circle by 40%, its area will be increased by (a) 40% (b) 80 % (c) 96 % (d) 82%
Answer» On increasing the diameter of a circle by 40%, its area will be increased by (a) 40% (b) 80 % (c) 96 % (d) 82%

6.

On increasing the diameter of a circle by 40%, its area will be increased by (a) 40% (b) 80 % (c) 96 % (d) 82%

Answer»

On increasing the diameter of a circle by 40%, its area will be increased by

(a) 40% (b) 80 % (c) 96 % (d) 82%

Discussion

7.	Insert the missing number : 5261984311?5
Answer» Insert the missing number : $\begin{matrix} 5 & 26 & 1 9 & 84 & 3 11 & ? & 5 \end{matrix}$

7.

Insert the missing number : 5261984311?5

Answer»

Insert the missing number :

$\begin{matrix} 5 & 26 & 1 9 & 84 & 3 11 & ? & 5 \end{matrix}$

Discussion

8.	If a secθ+b tanθ+c=0 and psecθ+qtanθ+r=θ, prove that (br−qc)2−(pc−ar)2=(ap−bp)2
Answer» If $a s e c θ + b t a n θ + c = 0$ and $p s e c θ + q t a n θ + r = θ$ , prove that $(b r - q c)^{2} - (p c - a r)^{2} = (a p - b p)^{2}$

Discussion

9.	10 times the numerator exceeds 5 times the denominator by 30. The equation satisfying the statement is
Answer» 10 times the numerator exceeds 5 times the denominator by 30. The equation satisfying the statement is

Discussion

10.	While covering a distance of 30 km.Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.
Answer» While covering a distance of 30 km.Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.

Discussion

11.	Sum of the areas of two squares is 400cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
Answer» Sum of the areas of two squares is $400 c m^{2}$ . If the difference of their perimeters is 16 cm, find the sides of the two squares.

Discussion

12.	In ΔABC, AC=15 cm and DE∥BC. If ABAD=3, find EC.
Answer» In $Δ A B C, A C = 15 c m$ and $D E ∥ B C$ . If $\frac{A B}{A D} = 3$ , find EC.

Discussion

13.	A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is ___ cm.
Answer» A circle is inscribed in a triangle with sides $3, 4$ and $5 c m .$ The radius of the circle is ___ $c m .$

13.

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is ___ cm.

Answer»

A circle is inscribed in a triangle with sides $3, 4$ and $5 c m .$ The radius of the circle is ___ $c m .$

Discussion

14.	Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.
Answer» Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.

Discussion

15.	If 5!=5×4×3×2×1 8!=8×7×6×5×4×3×2×1 then what is −8!=? and −5!=? What is the elongation of -ve factorial?
Answer» If $5! = 5 \times 4 \times 3 \times 2 \times 1$ $8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ then what is $- 8! =$ ? and $- 5! =$ ? What is the elongation of -ve factorial?

Discussion

16.	Solve the following quadratic equation for x: x2−2ax−(4b2−a2)=0
Answer» Solve the following quadratic equation for $x$ : $x^{2} - 2 a x - (4 b^{2} - a^{2}) = 0$

Discussion

17.	If two circles with radius a cm and b cm meet externally., then the distance between their centres is equal to ______ cm.
Answer» If two circles with radius a cm and b cm meet externally., then the distance between their centres is equal to ______ cm.

Discussion

18.	The number of distinct elements in a given set A is called the ___ of A.
Answer» The number of distinct elements in a given set A is called the ___ of A.

Discussion

19.	A cone of radius 3 cm and slant height 5 cm has a curved surface area of ___ cm2.
Answer» A cone of radius 3 cm and slant height 5 cm has a curved surface area of ___ $c m^{2}$ .

Discussion

20.	Find the values of k for which the following equations have real and equal roots. (i)x2−2(k+1)x+k2=0(ii)k2x2−2(2k−1)x+4=0(iii)(k+1)x2−2(k−1)x+1=0(iv)x2+k(2x+k−1)+2=0
Answer» Find the values of k for which the following equations have real and equal roots. $(i) x^{2} - 2 (k + 1) x + k^{2} = 0 (i i) k^{2} x^{2} - 2 (2 k - 1) x + 4 = 0 (i i i) (k + 1) x^{2} - 2 (k - 1) x + 1 = 0 (i v) x^{2} + k (2 x + k - 1) + 2 = 0$

Discussion

21.	Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is (a) 1 : √2 (b) √2:1 (c) 1 : 2 (d) 1 : 4
Answer» Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is (a) 1 : $\sqrt{2}$ (b) $\sqrt{2} : 1$ (c) 1 : 2 (d) 1 : 4

21.

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is (a) 1 : √2 (b) √2:1 (c) 1 : 2 (d) 1 : 4

Answer»

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is

(a) 1 : $\sqrt{2}$ (b) $\sqrt{2} : 1$ (c) 1 : 2 (d) 1 : 4

Discussion

22.	Solve each of the following systems of equations by using the method of cross multiplication: 2ax+3by=(a+2b),3ax+2by=(2a+b)
Answer» Solve each of the following systems of equations by using the method of cross multiplication: $2 a x + 3 b y = (a + 2 b), 3 a x + 2 b y = (2 a + b)$

22.

Solve each of the following systems of equations by using the method of cross multiplication: 2ax+3by=(a+2b),3ax+2by=(2a+b)

Answer»

Solve each of the following systems of equations by using the method of cross multiplication:

$2 a x + 3 b y = (a + 2 b), 3 a x + 2 b y = (2 a + b)$

Discussion

23.	If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of the point P such that AP = 37 AB, where P lies on the line segment AB.
Answer» If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of the point P such that AP = $\frac{3}{7}$ AB, where P lies on the line segment AB.

Discussion

24.	In the given figure the radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle. BD is the tangent to the smaller circle touching it at D. Find the length AD
Answer» In the given figure the radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle. BD is the tangent to the smaller circle touching it at D. Find the length AD

Discussion

25.	The point P (x, y) is first reflected in the x-axis and then reflected in teh origin to P'. If P' has co-ordinats (-8, 5); evaluate x and y.
Answer» The point P (x, y) is first reflected in the x-axis and then reflected in teh origin to P'. If P' has co-ordinats (-8, 5); evaluate x and y.

Discussion

26.	For what value of p are 2p+1,13,5p-3 three consecutive terms of an A.P.?
Answer» For what value of p are 2p+1,13,5p-3 three consecutive terms of an A.P.?

Discussion

27.	Question 156 Sanchay put a 1 cm stick of gum through a (1×3−2) machine. How long was the stick when it came out ?
Answer» Question 156 Sanchay put a 1 cm stick of gum through a $(1 \times 3^{- 2})$ machine. How long was the stick when it came out ?

27.

Question 156 Sanchay put a 1 cm stick of gum through a (1×3−2) machine. How long was the stick when it came out ?

Answer»

Question 156

Sanchay put a 1 cm stick of gum through a $(1 \times 3^{- 2})$ machine. How long was the stick when it came out ?

Discussion

28.	Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices.
Answer» Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices.

Discussion

29.	The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take π=3.14)
Answer» The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take $π = 3.14$ )

29.

The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take π=3.14)

Answer»

The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take $π = 3.14$ )

Discussion

30.	A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest for first three years and find the sum of the interest for first three years.
Answer» A sum of Rs 1000 is invested at 8 $%$ simple interest per year. Calculate the interest for first three years and find the sum of the interest for first three years.

Discussion

31.	A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.
Answer» A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

31.

A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Answer»

A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Discussion

32.	In triangle ABC, ∠CAB=40∘, AC = 6 cm, AB = 7 cm. The length BC is equal to_____. [sin 40∘=0.67, cos 40∘=0.76]
Answer» In triangle ABC, $∠ C A B = 40^{\circ}$ , AC = 6 cm, AB = 7 cm. The length BC is equal to_____. $[s i n 40^{\circ} = 0.67, c o s 40^{\circ} = 0.76]$

32.

In triangle ABC, ∠CAB=40∘, AC = 6 cm, AB = 7 cm. The length BC is equal to_____. [sin 40∘=0.67, cos 40∘=0.76]

Answer»

In triangle ABC, $∠ C A B = 40^{\circ}$ , AC = 6 cm, AB = 7 cm. The length BC is equal to_____. $[s i n 40^{\circ} = 0.67, c o s 40^{\circ} = 0.76]$

Discussion

33.	Question 11. If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1 ? Given reasons.
Answer» Question 11. If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1 ? Given reasons.

Discussion

34.	If √2 is a zero of 6x3+√2x2−10x−4√2 find the other zeroes.
Answer» If $\sqrt{2}$ is a zero of $6 x^{3} + \sqrt{2} x^{2} - 10 x - 4 \sqrt{2}$ find the other zeroes.

Discussion

35.	AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, the radius of the circle is
Answer» AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, the radius of the circle is

Discussion

36.	In the given figure, PT is a tangent to the circle. If PA=5 cm and PT=10 cm, then the radius of the circle is ___ cm.
Answer» In the given figure, $P T$ is a tangent to the circle. If $P A = 5 c m$ and $P T = 10 c m,$ then the radius of the circle is ___ $c m .$

36.

In the given figure, PT is a tangent to the circle. If PA=5 cm and PT=10 cm, then the radius of the circle is ___ cm.

Answer»

In the given figure, $P T$ is a tangent to the circle. If $P A = 5 c m$ and $P T = 10 c m,$ then the radius of the circle is ___ $c m .$

Discussion

37.	The unit’s digit in the expansion (2317)759 is:
Answer» The unit’s digit in the expansion $(2317)^{759}$ is:

Discussion

38.	If the roots of the equation(a-b)x2+(b-c)x+(c-a)=0 are equal,prove that b+c=2a.
Answer» If the roots of the equation(a-b)x²+(b-c)x+(c-a)=0 are equal,prove that b+c=2a.

Discussion

39.	BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP , AB/AC = BP/PC , AP is the bisector of angle BAC.
Answer» BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP , AB/AC = BP/PC , AP is the bisector of angle BAC.

39.

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP , AB/AC = BP/PC , AP is the bisector of angle BAC.

Answer»

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP ,

AB/AC = BP/PC , AP is the bisector of angle BAC.

Discussion

40.	If a parallelogram ABCD is drawn are shown in fig then find the coordinates of 'D'
Answer» If a parallelogram ABCD is drawn are shown in fig then find the coordinates of 'D'

40.

If a parallelogram ABCD is drawn are shown in fig then find the coordinates of 'D'

Answer»

If a parallelogram ABCD is drawn are shown in fig then find the coordinates of 'D'

Discussion

41.	A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
Answer» A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

Discussion

42.	HOTS: In an AP the first term is 2 and the sum of the first 5 terms is 1/4 of the sum of the of the next 5 terms. Show that the 20th term is -112
Answer» HOTS: In an AP the first term is 2 and the sum of the first 5 terms is 1/4 of the sum of the of the next 5 terms. Show that the 20th term is -112

Discussion

43.	A carpet of size 5m×2m has 25 cm wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?
Answer» A carpet of size $5 m \times 2 m$ has $25 c m$ wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

43.

A carpet of size 5m×2m has 25 cm wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

Answer»

A carpet of size $5 m \times 2 m$ has $25 c m$ wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

Discussion

44.	Question 1 (ii) In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine: (ii) sin C, cos C
Answer» Question 1 (ii) In $Δ$ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine: (ii) sin C, cos C

Discussion

45.	Let d be the HCF of 24 and 36. Find two numbers a and b such that d= 24a + 36b
Answer» Let d be the HCF of 24 and 36. Find two numbers a and b such that d= 24a + 36b

Discussion

46.	Find the whether 0(zero) is a term of the A.P. 40,37,34,31,...
Answer» Find the whether 0(zero) is a term of the A.P. 40,37,34,31,...

Discussion

47.	Which term of the AP 121, 117, 113,... is its first negative term?
Answer» Which term of the AP 121, 117, 113,... is its first negative term?

Discussion

48.	The digits of a positive number have 3digits which are in A.P. and their sum is 18. The number obtained by reversing digits is 594 less than the original number. Find the number.
Answer» The digits of a positive number have 3digits which are in A.P. and their sum is 18. The number obtained by reversing digits is 594 less than the original number. Find the number.

48.

The digits of a positive number have 3digits which are in A.P. and their sum is 18. The number obtained by reversing digits is 594 less than the original number. Find the number.

Answer»

The digits of a positive number have 3digits which are in A.P. and their sum is 18.

The number obtained by reversing digits is 594 less than the original number.

Find the number.

Discussion

49.	The mean of five number is 18. On excluding one number,the mean becomes 16. find the excluded number .
Answer» The mean of five number is 18. On excluding one number,the mean becomes 16. find the excluded number .

Discussion

50.	Question 18 Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?
Answer» Question 18 Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following pair of linear equation 1) px+qy=p-q qx-py=p+q

sin18∘cos72∘___

In fig. 8, the vertices of ΔABC are A(4,6), B(1,5) and C(7,2). A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that ADAB=AEAC=13. Calculate the area of ΔADE and compare it with area of ΔABC.

Solve each of the following systems of equations by using the method of cross multiplication: ax−by=0,ab2x+a2by=(a2+b2),where x≠0 and y≠0.

Prove the following identities: cos A cosec A−sin A sec Acos A+sin A=cosec A−sec A

On increasing the diameter of a circle by 40%, its area will be increased by (a) 40% (b) 80 % (c) 96 % (d) 82%

Insert the missing number : 5261984311?5

If a secθ+b tanθ+c=0 and psecθ+qtanθ+r=θ, prove that (br−qc)2−(pc−ar)2=(ap−bp)2

10 times the numerator exceeds 5 times the denominator by 30. The equation satisfying the statement is

While covering a distance of 30 km.Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.

Sum of the areas of two squares is 400cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.

In ΔABC, AC=15 cm and DE∥BC. If ABAD=3, find EC.

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is ___ cm.

Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.

If 5!=5×4×3×2×1 8!=8×7×6×5×4×3×2×1 then what is −8!=? and −5!=? What is the elongation of -ve factorial?

Solve the following quadratic equation for x: x2−2ax−(4b2−a2)=0

If two circles with radius a cm and b cm meet externally., then the distance between their centres is equal to ______ cm.

The number of distinct elements in a given set A is called the ___ of A.

A cone of radius 3 cm and slant height 5 cm has a curved surface area of ___ cm2.

Find the values of k for which the following equations have real and equal roots. (i)x2−2(k+1)x+k2=0(ii)k2x2−2(2k−1)x+4=0(iii)(k+1)x2−2(k−1)x+1=0(iv)x2+k(2x+k−1)+2=0

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is (a) 1 : √2 (b) √2:1 (c) 1 : 2 (d) 1 : 4

Solve each of the following systems of equations by using the method of cross multiplication: 2ax+3by=(a+2b),3ax+2by=(2a+b)

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of the point P such that AP = 37 AB, where P lies on the line segment AB.

In the given figure the radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle. BD is the tangent to the smaller circle touching it at D. Find the length AD

The point P (x, y) is first reflected in the x-axis and then reflected in teh origin to P'. If P' has co-ordinats (-8, 5); evaluate x and y.

For what value of p are 2p+1,13,5p-3 three consecutive terms of an A.P.?

Question 156 Sanchay put a 1 cm stick of gum through a (1×3−2) machine. How long was the stick when it came out ?

Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices.

The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take π=3.14)

A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest for first three years and find the sum of the interest for first three years.

A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

In triangle ABC, ∠CAB=40∘, AC = 6 cm, AB = 7 cm. The length BC is equal to_____. [sin 40∘=0.67, cos 40∘=0.76]

Question 11. If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1 ? Given reasons.

If √2 is a zero of 6x3+√2x2−10x−4√2 find the other zeroes.

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, the radius of the circle is

In the given figure, PT is a tangent to the circle. If PA=5 cm and PT=10 cm, then the radius of the circle is ___ cm.

The unit’s digit in the expansion (2317)759 is:

If the roots of the equation(a-b)x2+(b-c)x+(c-a)=0 are equal,prove that b+c=2a.

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP , AB/AC = BP/PC , AP is the bisector of angle BAC.

If a parallelogram ABCD is drawn are shown in fig then find the coordinates of 'D'

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

HOTS: In an AP the first term is 2 and the sum of the first 5 terms is 1/4 of the sum of the of the next 5 terms. Show that the 20th term is -112

A carpet of size 5m×2m has 25 cm wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

Question 1 (ii) In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine: (ii) sin C, cos C

Let d be the HCF of 24 and 36. Find two numbers a and b ​​​​​such that d= 24a + 36b

Find the whether 0(zero) is a term of the A.P. 40,37,34,31,...

Which term of the AP 121, 117, 113,... is its first negative term?

The digits of a positive number have 3digits which are in A.P. and their sum is 18. The number obtained by reversing digits is 594 less than the original number. Find the number.

The mean of five number is 18. On excluding one number,the mean becomes 16. find the excluded number .

Question 18 Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Let d be the HCF of 24 and 36. Find two numbers a and b such that d= 24a + 36b