32581 + Interview Questions in Mathematics Page 152 InterviewSolution

7551.	3 tan x/2 = cosecx -sinx Prove that tan(x/2) = -2\pm 5
Answer» 3 tan x/2 = cosecx -sinx Prove that tan(x/2) = -2\pm 5

Discussion

7552.	Find the number of nodes, arcs and regions in the following networks.(i) (ii) (iii)(iv)
Answer» Find the number of nodes, arcs and regions in the following networks. (i) (ii) (iii) (iv)

7552.

Find the number of nodes, arcs and regions in the following networks.(i) (ii) (iii)(iv)

Answer»

Find the number of nodes, arcs and regions in the following networks.

(i)

(ii)

(iii)

(iv)

Discussion

7553.	Question 5Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Answer» Question 5 Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Discussion

7554.	Find the mean and variance and standard deviation using short-cut method. Height in cms) (no.of children) 70-75. 3 75-80. 4 80-85. 7 85-90. 7 90-95. 15 95-100. 9 100-105. 6 105-110. 6 110-115. 3
Answer» Find the mean and variance and standard deviation using short-cut method. Height in cms) (no.of children) 70-75. 3 75-80. 4 80-85. 7 85-90. 7 90-95. 15 95-100. 9 100-105. 6 105-110. 6 110-115. 3

Discussion

7555.	The sum of the first n terms of an AP is given by Sn=3n2−4n. Determine the AP and the 12th term.
Answer» The sum of the first n terms of an AP is given by $S_{n} = 3 n^{2} - 4 n$ . Determine the AP and the $12^{t h}$ term.

Discussion

7556.	A ladder leans against a wall with its foot 2 metres away from the wall and it makes a 40° angle with the ground. How high is the top of the ladder from the ground?
Answer» A ladder leans against a wall with its foot 2 metres away from the wall and it makes a 40° angle with the ground. How high is the top of the ladder from the ground?

Discussion

7557.	Choose the correct alternative answers for the following questions.(i) If 3x + 5y = 9 and 5x + 3y= 7 then What is the value of x + y ?(A) 2 (B) 16 (C) 9 (D) 7(ii) 'When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26.' What is the mathematical form of the statement ?(A) x - y = 8 (B) x + y = 8 (C) x + y = 23 (D) 2x + y = 21(iii) Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age ?(A) 20 (B) 15 (C) 10 (D) 5
Answer» Choose the correct alternative answers for the following questions. (i) If 3x + 5y = 9 and 5x + 3y= 7 then What is the value of x + y ? (A) 2 (B) 16 (C) 9 (D) 7 (ii) 'When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26.' What is the mathematical form of the statement ? (A) x $-$ y = 8 (B) x + y = 8 (C) x + y = 23 (D) 2x + y = 21 (iii) Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age ? (A) 20 (B) 15 (C) 10 (D) 5

Discussion

7558.	If (m+1)th term of an A.P. is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.
Answer» If (m+1)th term of an A.P. is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.

Discussion

7559.	Write the value of k for which the system of equations x + y − 4 = 0 and 2x + ky − 3 = 0 has no solution.
Answer» Write the value of k for which the system of equations x + y − 4 = 0 and 2x + ky − 3 = 0 has no solution.

Discussion

7560.	In the figure given above, AX = 5. AB is a tangent at B, AB = 20. Find XC.
Answer» In the figure given above, AX = 5. AB is a tangent at B, AB = 20. Find XC.

7560.

In the figure given above, AX = 5. AB is a tangent at B, AB = 20. Find XC.

Answer»

In the figure given above, AX = 5. AB is a tangent at B, AB = 20. Find XC.

Discussion

7561.	Find the class marks of classes 10-25 and 35-55.
Answer» Find the class marks of classes 10-25 and 35-55.

Discussion

7562.	If cot θ=3, find the value of cosec2 θ+cot2 θcosec2 θ-sec2 θ.
Answer» If $\cot θ = \sqrt{3}$ , find the value of $\frac{\cos e c^{2} θ + \cot^{2} θ}{{cosec}^{2} θ - \sec^{2} θ}$ .

Discussion

7563.	Find the roots of the following quadratic equations by factorisation:
Answer» Find the roots of the following quadratic equations by factorisation:

7563.

Find the roots of the following quadratic equations by factorisation:

Answer»

Find the roots of the following quadratic equations by factorisation:

Discussion

7564.	what is the meaning of tan theta?
Answer» what is the meaning of tan theta?

Discussion

7565.	In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If ∠PRQ=l and ∠OPQ=m, then find l+m.
Answer» In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If $∠ P R Q = l$ and $∠ O P Q = m,$ then find $l + m$ .

Discussion

7566.	A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.
Answer» A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Discussion

7567.	Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue coloured square is the right angle. If the largest side is 5 cm, then find the sum of the areas of the yellow square and brown square.
Answer» Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue coloured square is the right angle. If the largest side is 5 cm, then find the sum of the areas of the yellow square and brown square.

Discussion

7568.	Slant height of cone is 25 cm and it's CSA is 550 cm find its height.
Answer» Slant height of cone is 25 cm and it's CSA is 550 cm find its height.

Discussion

7569.	Prove that 11+sinθ+11-sinθ=2sec2θ
Answer» Prove that $\frac{1}{(1 + \sin θ)} + \frac{1}{(1 - \sin θ)} = 2 \sec^{2} θ$

Discussion

7570.	A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is __________.
Answer» A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is __________.

Discussion

7571.	Determine whether the triangle having sides (a − 1) cm, 2a cm and (a + 1) cm is a right angled triangle.
Answer» Determine whether the triangle having sides (a − 1) cm, $2 \sqrt{a} cm$ and (a + 1) cm is a right angled triangle.

Discussion

7572.	The sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.
Answer» The sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.

Discussion

7573.	In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here? [CBSE 2014]
Answer» In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here? [CBSE 2014]

Discussion

7574.	a) Solve the following equation and calculate the answer correct to two decimal places: x2−5x−10=0. b) Without solving the following quadratic equation, find the value of 'p' for which the given equation has real and equal roots: x2+(p−3)x+p=0. [6 MARKS]
Answer» a) Solve the following equation and calculate the answer correct to two decimal places: $x^{2} - 5 x - 10 = 0$ . b) Without solving the following quadratic equation, find the value of 'p' for which the given equation has real and equal roots: $x^{2} + (p - 3) x + p = 0$ . [6 MARKS]

Discussion

7575.	Karan took a loan from a bank at the rate of 12% p.a. simple interest. After a period of 3 years, he had to pay Rs. 5400 as interest. What was the principal amount borrowed by him?
Answer» Karan took a loan from a bank at the rate of 12% p.a. simple interest. After a period of 3 years, he had to pay Rs. 5400 as interest. What was the principal amount borrowed by him?

Discussion

7576.	Consider the above figure where O is the center of the circle, AB = CD and ∠AOB=30∘. Find ∠AED and ∠COD.
Answer» Consider the above figure where O is the center of the circle, AB = CD and $∠ A O B = 30^{\circ} .$ Find $∠ A E D$ and $∠ C O D$ .

Discussion

7577.	There are 20 cards numbered from 1 to 20. Krishna selects a card at random from these cards. What is the probability that this card selected at random is a multiple of 3?
Answer» There are 20 cards numbered from 1 to 20. Krishna selects a card at random from these cards. What is the probability that this card selected at random is a multiple of 3?

Discussion

7578.	ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of ∆FBE = 108 cm2, find the length of AC.
Answer» ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of ∆FBE = 108 cm², find the length of AC.

Discussion

7579.	There is a grouped data distribution for which mean is to be found by step deviation method. Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200D......100−20039150B.....E.....200−3003425000300−400303501001400−50045450C.....F......TotalA=∑fi=...... Find the value of A, B, C, D, E and F respectively.
Answer» There is a grouped data distribution for which mean is to be found by step deviation method. $\begin{matrix} C l a s s I n t e r v a l & N u m b e r o f F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & D . . . . . . 100 - 200 & 39 & 150 & B . . . . . & E . . . . . 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & C . . . . . & F . . . . . . T o t a l & A = \sum f_{i} = . . . . . . \end{matrix}$ Find the value of A, B, C, D, E and F respectively.

7579.

There is a grouped data distribution for which mean is to be found by step deviation method. Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200D......100−20039150B.....E.....200−3003425000300−400303501001400−50045450C.....F......TotalA=∑fi=...... Find the value of A, B, C, D, E and F respectively.

Answer»

There is a grouped data distribution for which mean is to be found by step deviation method.

$\begin{matrix} C l a s s I n t e r v a l & N u m b e r o f F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & D . . . . . . 100 - 200 & 39 & 150 & B . . . . . & E . . . . . 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & C . . . . . & F . . . . . . T o t a l & A = \sum f_{i} = . . . . . . \end{matrix}$

Find the value of A, B, C, D, E and F respectively.

Discussion

7580.	A school has 3 sections each from class 1 to 12. Students of this school plant tree in the school campus to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class in which they are studying. How many plants were planted by the students?
Answer» A school has 3 sections each from class 1 to 12. Students of this school plant tree in the school campus to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class in which they are studying. How many plants were planted by the students?

Discussion

7581.	The line segment joining any two points on the boundary of a circle is called a ___ of the circle.
Answer» The line segment joining any two points on the boundary of a circle is called a ___ of the circle.

Discussion

7582.	Which among these is a measure of central tendency?
Answer» Which among these is a measure of central tendency?

Discussion

7583.	If two adjacent vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5) then find the coordinates of the other two vertices. [CBSE 2017]
Answer» If two adjacent vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5) then find the coordinates of the other two vertices. [CBSE 2017]

Discussion

7584.	Find the value of a for which (x + 1) is a factor of (ax3 + x2 – 2x + 4a – 9).
Answer» Find the value of a for which (x + 1) is a factor of (ax³+ x² – 2x + 4a – 9).

Discussion

7585.	Reena has pend and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.
Answer» Reena has pend and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

Discussion

7586.	The surface area of a sphere is 2464 cm2. If its radius be doubled, then what will be the surface area of the new sphere?
Answer» The surface area of a sphere is 2464 cm². If its radius be doubled, then what will be the surface area of the new sphere?

Discussion

7587.	Find the roots of the equation 5x2–6x–2=0 by the method of completing the square.
Answer» Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square.

Discussion

7588.	x2-(x+2)(x-2) ÷x+3 =1÷2
Answer» x²-(x+2)(x-2) ÷x+3 =1÷2

Discussion

7589.	If the solution of 20x−4x≥8 and x>0 is x≤k, where k is a variable, then k=2
Answer» If the solution of $\frac{20}{x} - \frac{4}{x} \geq 8$ and $x > 0$ is $x \leq k$ , where $k$ is a variable, then $k =$ 2

Discussion

7590.	The greatest number which divides 134 and 167 leaving 2 as remainder in each case is(a) 14(b) 19(c) 33(d) 17
Answer» The greatest number which divides 134 and 167 leaving 2 as remainder in each case is (a) 14 (b) 19 (c) 33 (d) 17

Discussion

7591.	If the perimeter of a circle is equal to that of a square, then the ratio of area of circle to the square is ______.
Answer» If the perimeter of a circle is equal to that of a square, then the ratio of area of circle to the square is ______.

Discussion

7592.	write the standard form of y = 7x- 4 , and whats a,b,c
Answer» write the standard form of y = 7x- 4 , and whats a,b,c

Discussion

7593.	Solve the following quadratic equations by factorization:x2-3+1x+3=0
Answer» Solve the following quadratic equations by factorization: $x^{2} - (\sqrt{3} + 1) x + \sqrt{3} = 0$

Discussion

7594.	In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?
Answer» In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?

7594.

In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?

Answer»

In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?

Discussion

7595.	Two dice are thrown simultaneously, what is the probability of not getting the sum of the digits on the dice as '2'?
Answer» Two dice are thrown simultaneously, what is the probability of not getting the sum of the digits on the dice as '2'?

Discussion

7596.	The ratio between the areas of two similar triangles is 16 : 25. Find the ratio between their : (i) perimeters. (ii) altitudes. (iii) medians.
Answer» The ratio between the areas of two similar triangles is 16 : 25. Find the ratio between their : (i) perimeters. (ii) altitudes. (iii) medians.

Discussion

7597.	In Fig. 14.46, the area of ΔABC (in square units) is(a) 15 (b) 10 (c) 7.5 (d) 2.5 [CBSE 2013]
Answer» In Fig. 14.46, the area of ΔABC (in square units) is (a) 15 (b) 10 (c) 7.5 (d) 2.5 [CBSE 2013]

Discussion

7598.	Indians , Egyptians , Europeans and Australians are resided in a village of area 200km2. If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?
Answer» Indians , Egyptians , Europeans and Australians are resided in a village of area 200 $k m^{2}$ . If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?

Discussion

7599.	In an A. P a = 22, nth term is -11 and sum of first n terms is 66 . Find n and d
Answer» In an A. P a = 22, n^th term is -11 and sum of first n terms is 66 . Find n and d

Discussion

7600.	There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first 2 customers. It is given that Ram is allotted one locker in the 235th shelf. What is the probability that Arjun also is allotted a locker in the 235th shelf?
Answer» There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first 2 customers. It is given that Ram is allotted one locker in the $235^{t h}$ shelf. What is the probability that Arjun also is allotted a locker in the $235^{t h}$ shelf?

Discussion

Explore topic-wise InterviewSolutions in .

3 tan x/2 = cosecx -sinx Prove that tan(x/2) = -2\pm 5

Find the number of nodes, arcs and regions in the following networks.(i) (ii) (iii)(iv)

Question 5Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Find the mean and variance and standard deviation using short-cut method. Height in cms) (no.of children) 70-75. 3 75-80. 4 80-85. 7 85-90. 7 90-95. 15 95-100. 9 100-105. 6 105-110. 6 110-115. 3

The sum of the first n terms of an AP is given by Sn=3n2−4n. Determine the AP and the 12th term.

A ladder leans against a wall with its foot 2 metres away from the wall and it makes a 40° angle with the ground. How high is the top of the ladder from the ground?

If (m+1)th term of an A.P. is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.

Write the value of k for which the system of equations x + y − 4 = 0 and 2x + ky − 3 = 0 has no solution.

In the figure given above, AX = 5. AB is a tangent at B, AB = 20. Find XC.

Find the class marks of classes 10-25 and 35-55.

If cot θ=3, find the value of cosec2 θ+cot2 θcosec2 θ-sec2 θ.

Find the roots of the following quadratic equations by factorisation:

what is the meaning of tan theta?

In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If ∠PRQ=l and ∠OPQ=m, then find l+m.

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Slant height of cone is 25 cm and it's CSA is 550 cm find its height.

Prove that 11+sinθ+11-sinθ=2sec2θ

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is __________.

Determine whether the triangle having sides (a − 1) cm, 2a cm and (a + 1) cm is a right angled triangle.

The sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.

In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here? [CBSE 2014]

a) Solve the following equation and calculate the answer correct to two decimal places: x2−5x−10=0. b) Without solving the following quadratic equation, find the value of 'p' for which the given equation has real and equal roots: x2+(p−3)x+p=0. [6 MARKS]

Karan took a loan from a bank at the rate of 12% p.a. simple interest. After a period of 3 years, he had to pay Rs. 5400 as interest. What was the principal amount borrowed by him?

Consider the above figure where O is the center of the circle, AB = CD and ∠AOB=30∘. Find ∠AED and ∠COD.

There are 20 cards numbered from 1 to 20. Krishna selects a card at random from these cards. What is the probability that this card selected at random is a multiple of 3?

ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of ∆FBE = 108 cm2, find the length of AC.

The line segment joining any two points on the boundary of a circle is called a ___ of the circle.

Which among these is a measure of central tendency?

If two adjacent vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5) then find the coordinates of the other two vertices. [CBSE 2017]

Find the value of a for which (x + 1) is a factor of (ax3 + x2 – 2x + 4a – 9).

Reena has pend and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

The surface area of a sphere is 2464 cm2. If its radius be doubled, then what will be the surface area of the new sphere?

Find the roots of the equation 5x2–6x–2=0 by the method of completing the square.

x​​​​​​2​​​​​-(x+2)(x-2) ÷x+3 =1÷2

If the solution of 20x−4x≥8 and x&gt;0 is x≤k, where k is a variable, then k=2

The greatest number which divides 134 and 167 leaving 2 as remainder in each case is(a) 14(b) 19(c) 33(d) 17

If the perimeter of a circle is equal to that of a square, then the ratio of area of circle to the square is ______.

write the standard form of y = 7x- 4 , and whats a,b,c

Solve the following quadratic equations by factorization:x2-3+1x+3=0

In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?

Two dice are thrown simultaneously, what is the probability of not getting the sum of the digits on the dice as '2'?

The ratio between the areas of two similar triangles is 16 : 25. Find the ratio between their : (i) perimeters. (ii) altitudes. (iii) medians.

In Fig. 14.46, the area of ΔABC (in square units) is(a) 15 (b) 10 (c) 7.5 (d) 2.5 [CBSE 2013]

Indians , Egyptians , Europeans and Australians are resided in a village of area 200km2. If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?

In an A. P a = 22, nth term is -11 and sum of first n terms is 66 . Find n and d

There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first 2 customers. It is given that Ram is allotted one locker in the 235th shelf. What is the probability that Arjun also is allotted a locker in the 235th shelf?

x2-(x+2)(x-2) ÷x+3 =1÷2

If the solution of 20x−4x≥8 and x>0 is x≤k, where k is a variable, then k=2