32581 + Interview Questions in Mathematics

1.	Is it possible to design a rectangle mango grove whose length is twice it's breadth and the area is 800 m2 ?find length and breadth
Answer» Is it possible to design a rectangle mango grove whose length is twice it's breadth and the area is 800 m2 ?find length and breadth

Discussion

2.	A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.
Answer» A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Discussion

3.	It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find the radius of the vessel.
Answer» It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $R s 20 p e r m^{2}$ , find the radius of the vessel.

Discussion

4.	In the picture below, the radius of the circle is 15 cm. ∠QOR=120°. Select the statements that are true.
Answer» In the picture below, the radius of the circle is 15 cm. $∠ Q O R = 120 °$ . Select the statements that are true.

4.

In the picture below, the radius of the circle is 15 cm. ∠QOR=120°. Select the statements that are true.

Answer»

In the picture below, the radius of the circle is 15 cm. $∠ Q O R = 120 °$ . Select the statements that are true.

Discussion

5.	Out of a collection of hats which contains red and blue hat 2 hats are drawn at random. The number of hats belong to the set {1,2,3,4............13).The probability that they have different color is 12.Possible number of blue hats is?
Answer» Out of a collection of hats which contains red and blue hat 2 hats are drawn at random. The number of hats belong to the set {1,2,3,4............13).The probability that they have different color is $\frac{1}{2}$ .Possible number of blue hats is?

Discussion

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

Discussion

7.	If a, b ϵ R+ [ R+ denote real positive numbers] then aba+b is
Answer» If a, b $ϵ$ $R^{+}$ [ $R^{+}$ denote real positive numbers] then $\frac{a b}{a + b}$ is

Discussion

8.	Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
Answer» Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Discussion

9.	Prove that the lengths of two tangents drawn from an external point to a circle are equal.
Answer» Prove that the lengths of two tangents drawn from an external point to a circle are equal.

Discussion

10.	A company with 10,000 shares of Rs.100 each declares a dividend of 5%
Answer» A company with 10,000 shares of Rs.100 each declares a dividend of 5%

Discussion

11.	Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
Answer» Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.

Discussion

12.	While finding the height of a tower from a place 200 meters away from the tower. The angle of elevation of the top of the tower was found to be 30.12 degree. If the actual measure of angle of elevation is 30 degree, then the error in measurement of the height is _____
Answer» While finding the height of a tower from a place 200 meters away from the tower. The angle of elevation of the top of the tower was found to be 30.12 degree. If the actual measure of angle of elevation is 30 degree, then the error in measurement of the height is _____

Discussion

13.	A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of the base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? (Use π=227) [4 MARKS]
Answer» A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of the base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? $(U s e π = \frac{22}{7})$ [4 MARKS]

Discussion

14.	Nilay purchases an item from the manufacturer for Rs 216 which he sells to Rahul, Rahul sells it to Naman and Naman sells it to Harshil who sells it to the customer. The VAT rate is 10% and the profit is Rs 20 at each stage of the selling chain. Find: i) amount of VAT deposited to the Government ii) total price paid by the customer for the item
Answer» Nilay purchases an item from the manufacturer for Rs 216 which he sells to Rahul, Rahul sells it to Naman and Naman sells it to Harshil who sells it to the customer. The VAT rate is 10% and the profit is Rs 20 at each stage of the selling chain. Find: i) amount of VAT deposited to the Government ii) total price paid by the customer for the item

14.

Nilay purchases an item from the manufacturer for Rs 216 which he sells to Rahul, Rahul sells it to Naman and Naman sells it to Harshil who sells it to the customer. The VAT rate is 10% and the profit is Rs 20 at each stage of the selling chain. Find: i) amount of VAT deposited to the Government ii) total price paid by the customer for the item

Answer»

Nilay purchases an item from the manufacturer for Rs 216 which he sells to Rahul, Rahul sells it to Naman and Naman sells it to Harshil who sells it to the customer. The VAT rate is 10% and the profit is Rs 20 at each stage of the selling chain. Find:

i) amount of VAT deposited to the Government

ii) total price paid by the customer for the item

Discussion

15.	A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?
Answer» A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?

Discussion

16.	How does the banking system link investors and savers in modern society?
Answer» How does the banking system link investors and savers in modern society?

Discussion

17.	If xg+1xa is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial? ___
Answer» If $x^{g}$ + $\frac{1}{x^{a}}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial? ___

17.

If xg+1xa is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial? ___

Answer»

If $x^{g}$ + $\frac{1}{x^{a}}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial?

___

Discussion

18.	A two digit number is four times the sum of the digits . It is also equal to 3 times the product of digits . Find the number .
Answer» A two digit number is four times the sum of the digits . It is also equal to 3 times the product of digits . Find the number .

Discussion

19.	A is a point on -axis, B is a point on -axis. The coordinate of the midpoint of AB is (6, 8). Find the length of AB.
Answer» A is a point on -axis, B is a point on -axis. The coordinate of the midpoint of AB is (6, 8). Find the length of AB.

Discussion

20.	A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls thus formed.
Answer» A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls thus formed.

Discussion

21.	$\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~~~\text{quadrilateral whose side AB is a diameter}\\ ~~~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___$
Answer» $\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~~~\text{quadrilateral whose side AB is a diameter}\\ ~~~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___$

Discussion

22.	The students of a class are made to stand in rows. If 3 students are more in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of students in the class.
Answer» The students of a class are made to stand in rows. If 3 students are more in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of students in the class.

Discussion

23.	Without using trigonometric tables, prove that: (i) sin 53∘ cos 37∘+cos 53∘ sin 37∘=1 (ii) cos 54∘ cos 36∘−sin 54∘ sin 36∘=0 (iii) sec 70∘ sin 20∘+cos 20∘ cosec 70∘=2 (iv) sin 35∘ sin 55∘−cos 35∘ cos 55∘=0 (v) (sin 72∘+cos 18∘)(sin 72∘−cos 18∘)=0 (vi) tan 48∘ tan 23∘ tan 42∘ tan 67∘=1
Answer» Without using trigonometric tables, prove that: (i) $s i n 53^{\circ} c o s 37^{\circ} + c o s 53^{\circ} s i n 37^{\circ} = 1$ (ii) $c o s 54^{\circ} c o s 36^{\circ} - s i n 54^{\circ} s i n 36^{\circ} = 0$ (iii) $s e c 70^{\circ} s i n 20^{\circ} + c o s 20^{\circ} c o s e c 70^{\circ} = 2$ (iv) $s i n 35^{\circ} s i n 55^{\circ} - c o s 35^{\circ} c o s 55^{\circ} = 0$ (v) $(s i n 72^{\circ} + c o s 18^{\circ}) (s i n 72^{\circ} - c o s 18^{\circ}) = 0$ (vi) $t a n 48^{\circ} t a n 23^{\circ} t a n 42^{\circ} t a n 67^{\circ} = 1$

23.

Without using trigonometric tables, prove that: (i) sin 53∘ cos 37∘+cos 53∘ sin 37∘=1 (ii) cos 54∘ cos 36∘−sin 54∘ sin 36∘=0 (iii) sec 70∘ sin 20∘+cos 20∘ cosec 70∘=2 (iv) sin 35∘ sin 55∘−cos 35∘ cos 55∘=0 (v) (sin 72∘+cos 18∘)(sin 72∘−cos 18∘)=0 (vi) tan 48∘ tan 23∘ tan 42∘ tan 67∘=1

Answer»

Without using trigonometric tables, prove that:

(i) $s i n 53^{\circ} c o s 37^{\circ} + c o s 53^{\circ} s i n 37^{\circ} = 1$

(ii) $c o s 54^{\circ} c o s 36^{\circ} - s i n 54^{\circ} s i n 36^{\circ} = 0$

(iii) $s e c 70^{\circ} s i n 20^{\circ} + c o s 20^{\circ} c o s e c 70^{\circ} = 2$

(iv) $s i n 35^{\circ} s i n 55^{\circ} - c o s 35^{\circ} c o s 55^{\circ} = 0$

(v) $(s i n 72^{\circ} + c o s 18^{\circ}) (s i n 72^{\circ} - c o s 18^{\circ}) = 0$

(vi) $t a n 48^{\circ} t a n 23^{\circ} t a n 42^{\circ} t a n 67^{\circ} = 1$

Discussion

24.	If tan(a2)=m, then the value of 1−2sin2(a2)1+sin a will be
Answer» If $t a n (\frac{a}{2}) = m$ , then the value of $\frac{1 - 2 s i n^{2} (\frac{a}{2})}{1 + s i n a}$ will be

Discussion

25.	A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs.75 per m2.
Answer» A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs.75 per $m^{2}$ .

Discussion

26.	Solve each of the following quadratic equations: 12abx2−(9a2−8b2)x−6ab=0
Answer» Solve each of the following quadratic equations: $12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

Discussion

27.	Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
Answer» Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

Discussion

28.	A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles? __
Answer» A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles? __

Discussion

29.	Question 17 State whether the given statements are true (T) or false (F). 4 : 7 = 20 : 35
Answer» Question 17 State whether the given statements are true (T) or false (F). 4 : 7 = 20 : 35

29.

Question 17 State whether the given statements are true (T) or false (F). 4 : 7 = 20 : 35

Answer»

Question 17

State whether the given statements are true (T) or false (F).

4 : 7 = 20 : 35

Discussion

30.	Show that the value of sin 45∘−sin 30∘cos 45∘+cos 60∘ and sec 45∘−tan 45∘cosec 45∘+cot 45∘ are equal
Answer» Show that the value of $\frac{s i n 45^{\circ} - s i n 30^{\circ}}{c o s 45^{\circ} + c o s 60^{\circ}}$ and $\frac{s e c 45^{\circ} - t a n 45^{\circ}}{c o s e c 45^{\circ} + c o t 45^{\circ}}$ are equal

Discussion

31.	A factory has two machines A and B. Past record shows that machine A produced 60% of the item of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was prodcued by machine B?
Answer» A factory has two machines A and B. Past record shows that machine A produced 60% of the item of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was prodcued by machine B?

Discussion

32.	Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. Find the approximate values of the length and breadth of the rectangular plot.
Answer» Taylor purchased a rectangular plot of area $634 m^{2}$ . The length of the plot is 2 m more than thrice its breadth. Find the approximate values of the length and breadth of the rectangular plot.

Discussion

33.	Using euclid's division algorithm find whether the pair of numbers 847 2160 are coprime or not
Answer» Using euclid's division algorithm find whether the pair of numbers 847 2160 are coprime or not

Discussion

34.	x + 2y = 5 and 4x + 4y - 6 = 0 are two linear equations whose graphical lines meet at a point (-2, 3.5). The pair of equations is
Answer» x + 2y = 5 and 4x + 4y - 6 = 0 are two linear equations whose graphical lines meet at a point (-2, 3.5). The pair of equations is

Discussion

35.	An integer is choosen at random between 1 and 100.Find the probability that it is( 1). divisible by a 8. (2.) not divisible by 8.
Answer» An integer is choosen at random between 1 and 100.Find the probability that it is( 1). divisible by a 8. (2.) not divisible by 8.

Discussion

36.	Evaluate ddx{(x+1)5−1}
Answer» Evaluate $\frac{d}{d x} {(x + 1)^{5} - 1}$

Discussion

37.	Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it. [2 MARKS]
Answer» Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it. [2 MARKS]

Discussion

38.	When the rate of sale tax decreased from 9% to 6% for a laptop, a man saves Rs. 783 on buying the laptop. The marked price of the T.V is
Answer» When the rate of sale tax decreased from 9% to 6% for a laptop, a man saves Rs. 783 on buying the laptop. The marked price of the T.V is

Discussion

39.	If roots of polynomial ax^3+3bx^2+3cx+d are in A.p. prove that 2b^3-3abc+a^2d=0
Answer» If roots of polynomial ax^3+3bx^2+3cx+d are in A.p. prove that 2b^3-3abc+a^2d=0

Discussion

40.	The sum of the first 'm' terms of an AP is 4msquare - m. if it's nth term is 107. Find the value of n and 21st term.
Answer» The sum of the first 'm' terms of an AP is 4msquare - m. if it's nth term is 107. Find the value of n and 21st term.

Discussion

41.	If Sn denotes the sum of the first n terms of an AP, prove that S12=3(S8−S4)
Answer» If $S_{n}$ denotes the sum of the first $n$ terms of an AP, prove that $S_{12} = 3 (S_{8} - S_{4})$

Discussion

42.	175 men can dig a 3150 m long canal in 36 days. How many more men are required to dig a canal 3900 m long in 24 days?
Answer» 175 men can dig a 3150 m long canal in 36 days. How many more men are required to dig a canal 3900 m long in 24 days?

Discussion

43.	If-5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k
Answer» If-5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k

Discussion

44.	Solve for a, b and c; if (i) [−45+532]=[b+423c−1] (ii)[aa−bb+c0]=[3−100]
Answer» Solve for a, b and c; if (i) $[\begin{matrix} - 4 & 5 + 5 3 & 2 \end{matrix}] = [\begin{matrix} b + 4 & 2 3 & c - 1 \end{matrix}]$ (ii) $[\begin{matrix} a & a - b b + c & 0 \end{matrix}] = [\begin{matrix} 3 & - 1 0 & 0 \end{matrix}]$

44.

Solve for a, b and c; if (i) [−45+532]=[b+423c−1] (ii)[aa−bb+c0]=[3−100]

Answer»

Solve for a, b and c; if
(i) $[\begin{matrix} - 4 & 5 + 5 3 & 2 \end{matrix}] = [\begin{matrix} b + 4 & 2 3 & c - 1 \end{matrix}]$

(ii) $[\begin{matrix} a & a - b b + c & 0 \end{matrix}] = [\begin{matrix} 3 & - 1 0 & 0 \end{matrix}]$

Discussion

45.	Solve the following equation: 2xx−3+12x+3+3x+9(x−3)(2x+3)=0; x≠3,x≠−32
Answer» Solve the following equation: $\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0; x \neq 3, x \neq - \frac{3}{2}$

45.

Solve the following equation: 2xx−3+12x+3+3x+9(x−3)(2x+3)=0; x≠3,x≠−32

Answer»

Solve the following equation:

$\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0; x \neq 3, x \neq - \frac{3}{2}$

Discussion

46.	HCF of x6y4z2, x6y4z6 and x7y9z4 is xaybzc. a-b-c = ___
Answer» HCF of $x^{6} y^{4} z^{2}$ , $x^{6} y^{4} z^{6}$ and $x^{7} y^{9} z^{4}$ is $x^{a} y^{b} z^{c}$ . a-b-c = ___

Discussion

47.	Let A = {a, b, c, d} and B = {4, 8, 16, 32). If the total number of relations from A to B is 2x find the value of (x)2? ___
Answer» Let A = {a, b, c, d} and B = {4, 8, 16, 32). If the total number of relations from A to B is $2^{x}$ find the value of $\frac{(x)}{2}$ ? ___

Discussion

48.	In an A.P., first term is 1, last term is 11 and sum of n terms is 36, then n=
Answer» In an A.P., first term is 1, last term is 11 and sum of n terms is 36, then n=

Discussion

49.	Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.
Answer» Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.

Discussion

50.	How many three digits number have exactly three factor
Answer» How many three digits number have exactly three factor

Discussion

21.	\(\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~~~\text{quadrilateral whose side AB is a diameter}\\ ~~~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___\)
Answer» \(\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~~~\text{quadrilateral whose side AB is a diameter}\\ ~~~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___\)

Explore topic-wise InterviewSolutions in Current Affairs.

Is it possible to design a rectangle mango grove whose length is twice it's breadth and the area is 800 m2 ?find length and breadth

A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find the radius of the vessel.

In the picture below, the radius of the circle is 15 cm. ∠QOR=120°. Select the statements that are true.

Out of a collection of hats which contains red and blue hat 2 hats are drawn at random. The number of hats belong to the set {1,2,3,4............13).The probability that they have different color is 12.Possible number of blue hats is?

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

If a, b ϵ R+ [ R+ denote real positive numbers] then aba+b is

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Prove that the lengths of two tangents drawn from an external point to a circle are equal.

A company with 10,000 shares of Rs.100 each declares a dividend of 5%

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.

While finding the height of a tower from a place 200 meters away from the tower. The angle of elevation of the top of the tower was found to be 30.12 degree. If the actual measure of angle of elevation is 30 degree, then the error in measurement of the height is _____

A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of the base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? (Use π=227) [4 MARKS]

A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?

How does the banking system link investors and savers in modern society?

If xg+1xa is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial? ___

A two digit number is four times the sum of the digits . It is also equal to 3 times the product of digits . Find the number .

A is a point on -axis, B is a point on -axis. The coordinate of the midpoint of AB is (6, 8). Find the length of AB.

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls thus formed.

\(\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~~~\text{quadrilateral whose side AB is a diameter}\\ ~~~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___\)

The students of a class are made to stand in rows. If 3 students are more in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of students in the class.

If tan(a2)=m, then the value of 1−2sin2(a2)1+sin a will be

A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs.75 per m2.

Solve each of the following quadratic equations: 12abx2−(9a2−8b2)x−6ab=0

Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles? __

Question 17 State whether the given statements are true (T) or false (F). 4 : 7 = 20 : 35

Show that the value of sin 45∘−sin 30∘cos 45∘+cos 60∘ and sec 45∘−tan 45∘cosec 45∘+cot 45∘ are equal

Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. Find the approximate values of the length and breadth of the rectangular plot.

Using euclid's division algorithm find whether the pair of numbers 847 2160 are coprime or not

x + 2y = 5 and 4x + 4y - 6 = 0 are two linear equations whose graphical lines meet at a point (-2, 3.5). The pair of equations is

An integer is choosen at random between 1 and 100.Find the probability that it is( 1). divisible by a 8. (2.) not divisible by 8.

Evaluate ddx{(x+1)5−1}

Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it. [2 MARKS]

When the rate of sale tax decreased from 9% to 6% for a laptop, a man saves Rs. 783 on buying the laptop. The marked price of the T.V is

If roots of polynomial ax^3+3bx^2+3cx+d are in A.p. prove that 2b^3-3abc+a^2d=0

The sum of the first 'm' terms of an AP is 4msquare - m. if it's nth term is 107. Find the value of n and 21st term.

If Sn denotes the sum of the first n terms of an AP, prove that S12=3(S8−S4)

175 men can dig a 3150 m long canal in 36 days. How many more men are required to dig a canal 3900 m long in 24 days?

If-5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k

Solve for a, b and c; if (i) [−45+532]=[b+423c−1] (ii)[aa−bb+c0]=[3−100]

Solve the following equation: 2xx−3+12x+3+3x+9(x−3)(2x+3)=0; x≠3,x≠−32

HCF of x6y4z2, x6y4z6 and x7y9z4 is xaybzc. a-b-c = ___

Let A = {a, b, c, d} and B = {4, 8, 16, 32). If the total number of relations from A to B is 2x find the value of (x)2? ___

In an A.P., first term is 1, last term is 11 and sum of n terms is 36, then n=

Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.

How many three digits number have exactly three factor

\(\text{In given figure, ABCD is a cyclic} (q)~ 65^\circ\\ ~\text{quadrilateral whose side AB is a diameter}\\ ~ \text{of the circle through A, B, C, D.}\\ ~~~\text{If} ~\angle ADC = 130^\circ, \text{then find}~ \angle BAC = ___\)