32581 + Interview Questions in Mathematics

1.

Find the missing frequency, if mean is 62. C.I 0-40 40-80 80-120 120-160 Frequency 6 9 ? 2

Answer» Find the missing frequency, if mean is 62.

C.I	0-40	40-80	80-120	120-160
Frequency	6	9	?	2

Discussion

2.	Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, −1 and − 3 respectively.
Answer» Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, −1 and − 3 respectively.

Discussion

3.	What is the value of the expression tan 1∘tan 89∘.tan 2∘.tan 88∘?
Answer» What is the value of the expression $tan 1^{\circ} tan 89^{\circ} . tan 2^{\circ} . tan 88^{\circ}$ ?

Discussion

4.	If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.
Answer» If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

Discussion

5.	Construct a ∆ABC in which AB = 6 cm, ∠A = 30º and ∠B = 60º. Construct another ∆AB'C' similar to ∆ABC with baseAB' = 8 cm. [CBSE 2015]
Answer» Construct a ∆ABC in which AB = 6 cm, $∠$ A = 30º and $∠$ B = 60º. Construct another ∆AB'C' similar to ∆ABC with base AB' = 8 cm. [CBSE 2015]

Discussion

6.	Select the factors of 6.
Answer» Select the factors of 6.

Discussion

7.	Match the following to their roots.
Answer» Match the following to their roots.

Discussion

8.	In the given figure, the measure of side DC is ___ .
Answer» In the given figure, the measure of side DC is ___ .

8.

In the given figure, the measure of side DC is ___ .

Answer»

In the given figure, the measure of side DC is ___ .

Discussion

9.	The factors of the polynomial equation P(x) = 4x3+x2+5x+8 is
Answer» The factors of the polynomial equation P(x) = $4 x^{3} + x^{2} + 5 x + 8$ is

Discussion

10.	Is the fomula or finding the area of an equipaequil triangle is √3/4 × (Side)²
Answer» Is the fomula or finding the area of an equipaequil triangle is √3/4 × (Side)²

Discussion

11.	If x cosec2 30° sec2 45°8 cos2 45° sin2 60°=tan2 60°-tan2 30°, then x =(a) 1(b) −1(c) 2(d) 0
Answer» If $\frac{x {cosec}^{2} 30 ° \sec^{2} 45 °}{8 \cos^{2} 45 ° \sin^{2} 60 °} = \tan^{2} 60 ° - \tan^{2} 30 °$ , then x = (a) 1 (b) −1 (c) 2 (d) 0

Discussion

12.	18.A straight line L with negative slope passes through the point (8,2) and cuts positive coordinate axes at the points P and Q. Find the minimum value of OP +OQ as L varies ,where O is origin
Answer» 18.A straight line L with negative slope passes through the point (8,2) and cuts positive coordinate axes at the points P and Q. Find the minimum value of OP +OQ as L varies ,where O is origin

Discussion

13.	Shakti Enterprises Ltd. issued 30,000;8% Debentures of ₹ 100 each on 1st October ,2014 redeemable in five equal annual installments starting with 31st March, 2018. The Board decides to transfer to Debentures Redemption Reserve ₹ 50,000 and ₹ 4,00,000 on 31st March 2015 and 2016 respectively and balance required to be transferred to Debentures Redemption Reserve on 31st March, 2017.Pass journal entries.
Answer» Shakti Enterprises Ltd. issued 30,000;8% Debentures of ₹ 100 each on 1st October ,2014 redeemable in five equal annual installments starting with 31st March, 2018. The Board decides to transfer to Debentures Redemption Reserve ₹ 50,000 and ₹ 4,00,000 on 31st March 2015 and 2016 respectively and balance required to be transferred to Debentures Redemption Reserve on 31st March, 2017. Pass journal entries.

Discussion

14.

Record the following transactions in the Journal of Ashoka Furniture Traders, Ludhiana (Punjab): 2018 ₹ Jan. 1 Started business with cash 50,000 Jan. 2 Opened a Current Account by personal cheque 3,50,000 Jan. 10 Purchased machinery against cheque 1,00,000 Jan. 15 Paid wages for installation of machinery 2,000 Jan. 20 Purchased timber from Singh & Co., Ludhiana (Punjab) of the list price of ₹ 20,000, allowed 10% trade discount Jan. 25 Out of the above, timber used for furnishing the office 5,000 Jan. 31 Sold timber to Rakesh of the list price of ₹ 10,000 and allowed him 10% trade discount Feb.10 Issued to Singh &Co. a cheque in full settlement 21,000 Feb. 15 Received from Rakesh in full and final settlement 10,220 Feb. 20 Paid Wages 15,000 Feb. 28 Issued a cheque for ₹ 5,000 in favour of the landlord for rent of February CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Answer» Record the following transactions in the Journal of Ashoka Furniture Traders, Ludhiana (Punjab):

2018		₹
Jan. 1	Started business with cash	50,000
Jan. 2	Opened a Current Account by personal cheque	3,50,000
Jan. 10	Purchased machinery against cheque	1,00,000
Jan. 15	Paid wages for installation of machinery	2,000
Jan. 20	Purchased timber from Singh & Co., Ludhiana (Punjab) of the list price of ₹ 20,000, allowed 10% trade discount
Jan. 25	Out of the above, timber used for furnishing the office	5,000
Jan. 31	Sold timber to Rakesh of the list price of ₹ 10,000 and allowed him 10% trade discount
Feb.10	Issued to Singh &Co. a cheque in full settlement	21,000
Feb. 15	Received from Rakesh in full and final settlement	10,220
Feb. 20	Paid Wages	15,000
Feb. 28	Issued a cheque for ₹ 5,000 in favour of the landlord for rent of February

CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Discussion

15.	The condition for the equation bx2+cx+a=0, where a, b, c are real numbers, to be quadratic is:
Answer» The condition for the equation $b x^{2} + c x + a = 0$ , where a, b, c are real numbers, to be quadratic is:

Discussion

16.

During the medical check up of 35 students of a class, their weights were recorded as follows: Weight (in kg) Number of students Less than 38 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52 0 3 5 9 14 28 32 35 Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula.

Answer» During the medical check up of 35 students of a class, their weights were recorded as follows:

Weight (in kg)	Number of students
Less than 38 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52	0 3 5 9 14 28 32 35

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula.

Discussion

17.	Find the discriminant of the quadratic equation 33x2+10x+3=0.
Answer» Find the discriminant of the quadratic equation $3 \sqrt{3} x^{2} + 10 x + \sqrt{3} = 0$ .

Discussion

18.	Solve 9x−7<––28+4x;x ϵ W
Answer» Solve $9 x - 7 < - - 28 + 4 x; x ϵ W$

Discussion

19.	If p(x)=2x3+5x2−3x−2 is divided by x−1, then find the remainder.
Answer» $If p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2 is divided by x - 1, then find the remainder.$

Discussion

20.	Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of 50∘ and its top at an angle of elevation of 25∘. The height of the bigger building will be [Tan 50∘=1.2 Tan 25∘=0.46]
Answer» Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of $50^{\circ}$ and its top at an angle of elevation of $25^{\circ} .$ The height of the bigger building will be $[T a n 50^{\circ} = 1.2 T a n 25^{\circ} = 0.46]$

Discussion

21.	AB is a line segment which is 8 cm long. CD and EF are parallel to AB, at a distance of 4 cm from it. GH is a line segment parallel to AB, at a distance of 2 cm from it. PQ is the perpendicular bisector of AB which intersects CD, GH, AB and EF at M, N, O and P respectively. The point/s which is/are always at a distance of 4 cm from the line AB and equidistant from A and B is/are
Answer» AB is a line segment which is 8 cm long. CD and EF are parallel to AB, at a distance of 4 cm from it. GH is a line segment parallel to AB, at a distance of 2 cm from it. PQ is the perpendicular bisector of AB which intersects CD, GH, AB and EF at M, N, O and P respectively. The point/s which is/are always at a distance of 4 cm from the line AB and equidistant from A and B is/are

21.

AB is a line segment which is 8 cm long. CD and EF are parallel to AB, at a distance of 4 cm from it. GH is a line segment parallel to AB, at a distance of 2 cm from it. PQ is the perpendicular bisector of AB which intersects CD, GH, AB and EF at M, N, O and P respectively. The point/s which is/are always at a distance of 4 cm from the line AB and equidistant from A and B is/are

Answer»

AB is a line segment which is 8 cm long. CD and EF are parallel to AB, at a distance of 4 cm from it. GH is a line segment parallel to AB, at a distance of 2 cm from it. PQ is the perpendicular bisector of AB which intersects CD, GH, AB and EF at M, N, O and P respectively.

The point/s which is/are always at a distance of 4 cm from the line AB and equidistant from A and B is/are

Discussion

22.	In the given figure, ∆ACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).
Answer» In the given figure, ∆ACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).

Discussion

23.	A frustum of a uniform solid cone has base radius R and height H as shown. Radius of top surface is R2. If height of centre of mass of frustum is 11H4n from base then n will be.
Answer» A frustum of a uniform solid cone has base radius R and height H as shown. Radius of top surface is $\frac{R}{2}$ . If height of centre of mass of frustum is $\frac{11 H}{4 n}$ from base then $n$ will be.

Discussion

24.

A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method. Production (Thousand rupees) 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 No. of Customers 20 25 15 10 10

Answer» A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method.

Production (Thousand rupees)	25 - 30	30 - 35	35 - 40	40 - 45	45 - 50
No. of Customers	20	25	15	10	10

Discussion

25.	If the volume of a hemisphere is four times its total surface area, what is its radius?
Answer» If the volume of a hemisphere is four times its total surface area, what is its radius?

Discussion

26.	The three sides of a triangle are given.The figure similar to this triangle is _____
Answer» The three sides of a triangle are given. The figure similar to this triangle is _____

Discussion

27.	One is asked to select a two -digit number. What is the probability of getting the first digit greater than the second digit ?
Answer» One is asked to select a two -digit number. What is the probability of getting the first digit greater than the second digit ?

Discussion

28.	There are 2 men X and Y who were born in the same year. If X's date of birth is on 19thDecember 1990, how many dates are possible for Y to be born such that he doesn't have the same birthday as X?
Answer» There are 2 men X and Y who were born in the same year. If X's date of birth is on $19^{t h}$ December 1990, how many dates are possible for Y to be born such that he doesn't have the same birthday as X?

Discussion

29.	Question 5 (vii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vii) (sinθ−2sin3θ)(2cos3θ−cosθ)=tanθ
Answer» Question 5 (vii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vii) $\frac{(s i n θ - 2 s i n^{3} θ)}{(2 c o s^{3} θ - c o s θ)} = t a n θ$

Discussion

30.	In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?
Answer» In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ Statement 1 : This is an inconsistent pair of linear equations. Statement 2 : There exists infinitely many solutions. Statement 3 : The lines representing these linese are parallel. Which of the above statements is/are true?

30.

In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?

Answer»

In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?

Discussion

31.	If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then the value of its 18th term is ________.
Answer» If 7 times the 7^th term of an A.P. is equal to 11 times its 11^th term, then the value of its 18^th term is ________.

Discussion

32.	A circular garden of radius 10 m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in m2? It is given that cos53∘=35.
Answer» A circular garden of radius $10 m$ has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of $6 m$ from the centre of the garden. What is the walking area in $m^{2}$ ? It is given that $cos 53^{\circ} = \frac{3}{5}$ .

Discussion

33.	Question 5A metallic right circular cone 20 cm high and whose vertical angle is 60∘ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 116 cm, find the length of the wire.
Answer» Question 5 A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.

Discussion

34.	A(→a), B(→b), C(→c) are the vertices of a triangle ABC and R(→r) is any point in the plane of triangle ABC, then →r.(→a×→b+→b×→c+→c×→a) is always equal to
Answer» $A (\to a), B (\to b), C (\to c)$ are the vertices of a triangle ABC and $R (\to r)$ is any point in the plane of triangle ABC, then $\to r . (\to a \times \to b + \to b \times \to c + \to c \times \to a)$ is always equal to

Discussion

35.	If set A has p element and set B has q elements, then the number of element in set (A × B) is _____.
Answer» If set A has p element and set B has q elements, then the number of element in set (A $\times$ B) is _____.

Discussion

36.	\begin{vmatrix}(y+z)^2&xy &zx xy&(x+z)^2&yz zx&yz&(x+y)^2\end{vmatrix} evaluate
Answer» \begin{vmatrix}(y+z)^2&xy &zx xy&(x+z)^2&yz zx&yz&(x+y)^2\end{vmatrix} evaluate

Discussion

37.	Find the value of sin50°cos40°+cosec40°sec50°-4cos50° cosec40°.
Answer» $Find the value of \frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 ° .$

Discussion

38.	Question 12Aruna has only Rs. 1 and Rs.2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs.75, then the number of Rs. 1 and Rs. 2 coins are, respectively(A) 35 and 15(B) 35 and 20(C) 15 and 35(D) 25 and 25
Answer» Question 12 Aruna has only Rs. 1 and Rs.2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs.75, then the number of Rs. 1 and Rs. 2 coins are, respectively (A) 35 and 15 (B) 35 and 20 (C) 15 and 35 (D) 25 and 25

Discussion

39.	A box contains two pairs of socks of two colours (black and white). I have picked out a white sock first and latter if I pick one more with my eyes closed, what is the probability that it will make a pair?
Answer» A box contains two pairs of socks of two colours (black and white). I have picked out a white sock first and latter if I pick one more with my eyes closed, what is the probability that it will make a pair?

Discussion

40.	A tree s†an ding on a horizontal plane is leaning toward west. At two points situated at dis†an ces of m and n exactly due east of it,the angles of elevation of the top are α1 and α2 respectively. find the height of the top of the tree from the ground
Answer» A tree s†an ding on a horizontal plane is leaning toward west. At two points situated at dis†an ces of m and n exactly due east of it,the angles of elevation of the top are α1 and α2 respectively. find the height of the top of the tree from the ground

Discussion

41.	Question 93 (i)Refer to the given map to answer the following question.What is the built-up area of Govt. Model School I?
Answer» Question 93 (i) Refer to the given map to answer the following question. What is the built-up area of Govt. Model School I?

Discussion

42.	What are the roots of the quadratic equation ax2+bx+c=0 ?
Answer» What are the roots of the quadratic equation $a x^{2} + b x + c = 0 ?$

Discussion

43.	The time (in seconds) taken by 15 athletes to run a 110 m hurdle race are tabulated below:Class13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of athletes who completed the race in less than or equal to 14 seconds is _______.2
Answer» The time (in seconds) taken by 15 athletes to run a 110 m hurdle race are tabulated below: $\begin{matrix} Class & 13.8 - 14 & 14 - 14.2 & 14.2 - 14.4 & 14.4 - 14.6 & 14.6 - 14.8 & 14.8 - 15 Frequency & 2 & 4 & 5 & 71 & 48 & 20 \end{matrix}$ The number of athletes who completed the race in less than or equal to 14 seconds is _______. 2

43.

The time (in seconds) taken by 15 athletes to run a 110 m hurdle race are tabulated below:Class13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of athletes who completed the race in less than or equal to 14 seconds is _______.2

Answer»

The time (in seconds) taken by 15 athletes to run a 110 m hurdle race are tabulated below:

$\begin{matrix} Class & 13.8 - 14 & 14 - 14.2 & 14.2 - 14.4 & 14.4 - 14.6 & 14.6 - 14.8 & 14.8 - 15 Frequency & 2 & 4 & 5 & 71 & 48 & 20 \end{matrix}$

The number of athletes who completed the race in less than or equal to 14 seconds is _______.

2

Discussion

44.	If f(x) is a polynomial satisfying f(x)⋅f(1x)=f(x)+f(1x) and f(2)=17, then the value of f(3) is
Answer» If $f (x)$ is a polynomial satisfying $f (x) \cdot f (\frac{1}{x}) = f (x) + f (\frac{1}{x})$ and $f (2) = 17$ , then the value of $f (3)$ is

Discussion

45.

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method. Milk Sold (Litre) 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6 No. of Customers 17 13 10 7 3

Answer» A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.

Milk Sold (Litre)	1 - 2	2 - 3	3 - 4	4 - 5	5 - 6
No. of Customers	17	13	10	7	3

Discussion

46.	77.A 25 m ladder placed against a vertical wall of a building. The foot of the ladder is 7m from the base of the building. If the top of the ladder slips 4m. Then find the foot of the ladder side.
Answer» 77.A 25 m ladder placed against a vertical wall of a building. The foot of the ladder is 7m from the base of the building. If the top of the ladder slips 4m. Then find the foot of the ladder side.

Discussion

47.	If r1 and r2 denote the radii of the circular bases of the frustum of a cone such that r1 > r2, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.
Answer» If r₁ and r₂ denote the radii of the circular bases of the frustum of a cone such that r₁ > r₂, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.

Discussion

48.	A number is selected at random from the numbers 1 to 30. The probability that it is a prime number
Answer» A number is selected at random from the numbers 1 to 30. The probability that it is a prime number

Discussion

49.	Explain trigonometry identities
Answer» Explain trigonometry identities

Discussion

50.

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

Answer»

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the missing frequency, if mean is 62. C.I 0-40 40-80 80-120 120-160 Frequency 6 9 ? 2

Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, −1 and − 3 respectively.

What is the value of the expression tan 1∘tan 89∘.tan 2∘.tan 88∘?

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

Construct a ∆ABC in which AB = 6 cm, ∠A = 30º and ∠B = 60º. Construct another ∆AB'C' similar to ∆ABC with baseAB' = 8 cm. [CBSE 2015]

Select the factors of 6.

Match the following to their roots.

In the given figure, the measure of side DC is ___ .

The factors of the polynomial equation P(x) = 4x3+x2+5x+8 is

Is the fomula or finding the area of an equipaequil triangle is √3/4 × (Side)²

If x cosec2 30° sec2 45°8 cos2 45° sin2 60°=tan2 60°-tan2 30°, then x =(a) 1(b) −1(c) 2(d) 0

18.A straight line L with negative slope passes through the point (8,2) and cuts positive coordinate axes at the points P and Q. Find the minimum value of OP +OQ as L varies ,where O is origin

The condition for the equation bx2+cx+a=0, where a, b, c are real numbers, to be quadratic is:

Find the discriminant of the quadratic equation 33x2+10x+3=0.

Solve 9x−7&lt;––28+4x;x ϵ W

If p(x)=2x3+5x2−3x−2 is divided by x−1, then find the remainder.

Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of 50∘ and its top at an angle of elevation of 25∘. The height of the bigger building will be [Tan 50∘=1.2 Tan 25∘=0.46]

In the given figure, ∆ACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).

A frustum of a uniform solid cone has base radius R and height H as shown. Radius of top surface is R2. If height of centre of mass of frustum is 11H4n from base then n will be.

A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method. Production (Thousand rupees) 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 No. of Customers 20 25 15 10 10

If the volume of a hemisphere is four times its total surface area, what is its radius?

The three sides of a triangle are given.The figure similar to this triangle is _____

One is asked to select a two -digit number. What is the probability of getting the first digit greater than the second digit ?

There are 2 men X and Y who were born in the same year. If X's date of birth is on 19thDecember 1990, how many dates are possible for Y to be born such that he doesn't have the same birthday as X?

Question 5 (vii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vii) (sinθ−2sin3θ)(2cos3θ−cosθ)=tanθ

In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?

If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then the value of its 18th term is ________.

Question 5A metallic right circular cone 20 cm high and whose vertical angle is 60∘ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 116 cm, find the length of the wire.

A(→a), B(→b), C(→c) are the vertices of a triangle ABC and R(→r) is any point in the plane of triangle ABC, then →r.(→a×→b+→b×→c+→c×→a) is always equal to

If set A has p element and set B has q elements, then the number of element in set (A × B) is _____.

\begin{vmatrix}(y+z)^2&xy &zx xy&(x+z)^2&yz zx&yz&(x+y)^2\end{vmatrix} evaluate

Find the value of sin50°cos40°+cosec40°sec50°-4cos50° cosec40°.

Question 12Aruna has only Rs. 1 and Rs.2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs.75, then the number of Rs. 1 and Rs. 2 coins are, respectively(A) 35 and 15(B) 35 and 20(C) 15 and 35(D) 25 and 25

A box contains two pairs of socks of two colours (black and white). I have picked out a white sock first and latter if I pick one more with my eyes closed, what is the probability that it will make a pair?

A tree s†an ding on a horizontal plane is leaning toward west. At two points situated at dis†an ces of m and n exactly due east of it,the angles of elevation of the top are α1 and α2 respectively. find the height of the top of the tree from the ground

Question 93 (i)Refer to the given map to answer the following question.What is the built-up area of Govt. Model School I?

What are the roots of the quadratic equation ax2+bx+c=0 ?

The time (in seconds) taken by 15 athletes to run a 110 m hurdle race are tabulated below:Class13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of athletes who completed the race in less than or equal to 14 seconds is _______.2

If f(x) is a polynomial satisfying f(x)⋅f(1x)=f(x)+f(1x) and f(2)=17, then the value of f(3) is

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method. Milk Sold (Litre) 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6 No. of Customers 17 13 10 7 3

77.A 25 m ladder placed against a vertical wall of a building. The foot of the ladder is 7m from the base of the building. If the top of the ladder slips 4m. Then find the foot of the ladder side.

If r1 and r2 denote the radii of the circular bases of the frustum of a cone such that r1 > r2, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.

A number is selected at random from the numbers 1 to 30. The probability that it is a prime number

Explain trigonometry identities

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

Solve 9x−7<––28+4x;x ϵ W