32581 + Interview Questions in Mathematics Page 292 InterviewSolution

14551.	Question 11Which of the nets given below will generate a cone?
Answer» Question 11 Which of the nets given below will generate a cone?

Discussion

14552.	Q20. March 6, 2005 is Monday. What was the day of the week on March 7, 2004?
Answer» Q20. March 6, 2005 is Monday. What was the day of the week on March 7, 2004?

Discussion

14553.	The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.
Answer» The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

Discussion

14554.	With reference to the figure given, a metal container in the form of a cylinder is surmounted by a hemisphere of same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate
Answer» With reference to the figure given, a metal container in the form of a cylinder is surmounted by a hemisphere of same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate

14554.

With reference to the figure given, a metal container in the form of a cylinder is surmounted by a hemisphere of same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate

Answer»

With reference to the figure given, a metal container in the form of a cylinder is surmounted by a hemisphere of same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate

Discussion

14555.	ABC is a triangle and G is its centroid. If AD=12 cm, then find the length of AG.
Answer» ABC is a triangle and G is its centroid. If AD=12 cm, then find the length of AG.

Discussion

14556.	A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is 30∘.
Answer» A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

14557.	The minute hand of a clock is 14 cm long. How far does the tip of the minute handmove in 60 minutes?(a) 22 cm (b) 44 cm (c) 33 cm (d) 88 cm
Answer» The minute hand of a clock is 14 cm long. How far does the tip of the minute hand move in 60 minutes? (a) 22 cm (b) 44 cm (c) 33 cm (d) 88 cm

Discussion

14558.	The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB.
Answer» The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{A X}{A B}$ .

14558.

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB.

Answer»

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{A X}{A B}$ .

Discussion

14559.	Given P (–3, 2) and Q (4, 5), and the join of PQ is intersected by -axis at R. Find the coordinates of R.
Answer» Given P (–3, 2) and Q (4, 5), and the join of PQ is intersected by -axis at R. Find the coordinates of R.

Discussion

14560.	A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m and the string makes an angle 30∘ with the ground.
Answer» A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m and the string makes an angle $30^{\circ}$ with the ground.

Discussion

14561.	The roots of the equation ax2+bx+c=0 will be reciprocal of each other if(a) a = b(b) b= c(c) c = a(d) none of these
Answer» The roots of the equation $a x^{2} + b x + c = 0$ will be reciprocal of each other if (a) a = b (b) b= c (c) c = a (d) none of these

Discussion

14562.	Find (x,y) if x =2y and (x,y) is a solution of 7x - 3y = 8.
Answer» Find (x,y) if x =2y and (x,y) is a solution of 7x - 3y = 8.

Discussion

14563.	A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
Answer» A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.

Discussion

14564.	Half the Perimeter of a rectangular garden whose length is4 meter more than its width is36 meter. Find the dimensions of the garden
Answer» Half the Perimeter of a rectangular garden whose length is4 meter more than its width is36 meter. Find the dimensions of the garden

Discussion

14565.	Prove that: tan theta - cot theta = 2sin2theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta
Answer» Prove that: tan theta - cot theta = 2sin²theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta

14565.

Prove that: tan theta - cot theta = 2sin2theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta

Answer»

Prove that:

tan theta - cot theta = 2sin²theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta

Discussion

14566.	250 students of class X of a school appeared in a test of 100 marks and the data about the marks secured is a below Marks securedNumber of students0−202020−403540−606560−806080−10070Find the modal vlaue of the above data.
Answer» 250 students of class X of a school appeared in a test of 100 marks and the data about the marks secured is a below $\begin{matrix} M a r k s s e c u r e d & N u m b e r o f s t u d e n t s 0 - 20 & 20 20 - 40 & 35 40 - 60 & 65 60 - 80 & 60 80 - 100 & 70 \end{matrix}$ Find the modal vlaue of the above data.

Discussion

14567.	Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, then find the distance between the two ships.
Answer» Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, then find the distance between the two ships.

Discussion

14568.	A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of √3m and is inclined at an angle of 60∘ to the ground. What should be the length of the slide?
Answer» A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of √3m and is inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide?

Discussion

14569.	5. In triangle ABC right angled at vertex B, a point O is chosen on the side BC such that the circle γ centered at O of radius OB touches the side AC. Let AB = 63 and BC = 16, and the radius of γ be of the form m/nwhere m, n are relatively prime positive integers. Find the value of m + n.
Answer» 5. In triangle ABC right angled at vertex B, a point O is chosen on the side BC such that the circle γ centered at O of radius OB touches the side AC. Let AB = 63 and BC = 16, and the radius of γ be of the form m/nwhere m, n are relatively prime positive integers. Find the value of m + n.

Discussion

14570.	Question 7The point at which the two coordinate axes meet is called theA) AbscissaB) OrdinateC) OriginD) Quadrant
Answer» Question 7 The point at which the two coordinate axes meet is called the A) Abscissa B) Ordinate C) Origin D) Quadrant

Discussion

14571.	The angle of depression of a car parked on the road from the top of a 150 m high tower is 30º. The distance of the car from the tower (in metres) is(a) 503 (b) 1503 (c) 1502 (d) 75 [CBSE 2014]
Answer» The angle of depression of a car parked on the road from the top of a 150 m high tower is 30º. The distance of the car from the tower (in metres) is (a) $50 \sqrt{3}$ (b) $150 \sqrt{3}$ (c) $150 \sqrt{2}$ (d) 75 [CBSE 2014]

Discussion

14572.	21. Express the following function as set of ordered pair and determine the range: g \| A --> N, g(x) = 2x, where A = {x \| x ∈ N, x ≤ 10
Answer» 21. Express the following function as set of ordered pair and determine the range: g \| A --> N, g(x) = 2x, where A = {x \| x ∈ N, x ≤ 10

Discussion

14573.	What is the next term in the following sequence? 1T2, 3R5, 8P13, 21N34, 55L89, ?
Answer» What is the next term in the following sequence? $1T2, 3R5, 8P13, 21N34, 55L89, ?$

Discussion

14574.	The cost of 4 pens and 4 pencil boxes is ₹100 . Three times the cost of a pen is ₹15 more than the cost of a pencil box . Form the pair of linear equations for the above situation . Find the cost of a pen and a pencil box.
Answer» The cost of 4 pens and 4 pencil boxes is ₹100 . Three times the cost of a pen is ₹15 more than the cost of a pencil box . Form the pair of linear equations for the above situation . Find the cost of a pen and a pencil box.

Discussion

14575.	If 1 is a root of the equation x2 + px + q = 0 find p + q
Answer» If 1 is a root of the equation $x^{2}$ + px + q = 0 find p + q

Discussion

14576.	Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?
Answer» Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

14576.

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

Answer»

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

Discussion

14577.	If -1, 1 & 3 are the zeroes of a cubic polynomial, then the correct expression of the polynomial is .
Answer» If -1, 1 & 3 are the zeroes of a cubic polynomial, then the correct expression of the polynomial is .

Discussion

14578.	Factorise : x2−3ax−88a2
Answer» Factorise : $x^{2} - 3 a x - 88 a^{2}$

14578.

Factorise : x2−3ax−88a2

Answer»

Factorise :

$x^{2} - 3 a x - 88 a^{2}$

Discussion

14579.	Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5). [CBSE 2017]
Answer» Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5). [CBSE 2017]

Discussion

14580.	Sanjeev is 4 times as old as his son. After 16 years he will be twice as old as his son. Find their present ages
Answer» Sanjeev is 4 times as old as his son. After 16 years he will be twice as old as his son. Find their present ages

Discussion

14581.	What rule should be followed while solving inequality ( not equal to sign)equations
Answer» What rule should be followed while solving inequality ( not equal to sign) equations

Discussion

14582.	Find the area of a triangle whose sides are 12cm,35cm,37cm.
Answer» Find the area of a triangle whose sides are $12 c m, 35 c m, 37 c m$ .

14582.

Find the area of a triangle whose sides are 12cm,35cm,37cm.

Answer»

Find the area of a triangle whose sides are $12 c m, 35 c m, 37 c m$ .

Discussion

14583.	Find the probability of finding a red marble out of a bag consisting of 8 green, 5 red and 4 white marbles?
Answer» Find the probability of finding a red marble out of a bag consisting of 8 green, 5 red and 4 white marbles?

Discussion

14584.	The nth term of a sequence is 8 - 5n . Show that the sequence is an A. P.
Answer» The $n^{t h}$ term of a sequence is 8 - 5n . Show that the sequence is an A. P.

Discussion

14585.	If X = {10, 11, 12……. 19} and ‘a’ represents any element of X, then write the set which satisfies the condition a – 2 = 11 , a ∈ X
Answer» If X = {10, 11, 12……. 19} and ‘a’ represents any element of X, then write the set which satisfies the condition a – 2 = 11 , a $\in$ X

Discussion

14586.	Question 4Find two consecutive positive integers, sum of whose squares is 365.
Answer» Question 4 Find two consecutive positive integers, sum of whose squares is 365.

Discussion

14587.	How many years was the income more than the average income of the given years?
Answer» How many years was the income more than the average income of the given years?

Discussion

14588.	Choose the correct answer of the following question:Each side of an equilateral triangle is 63 cm. The altitude of the triangle is(a) 8 cm (b) 9 cm (c) 33 cm (d) 6 cm
Answer» Choose the correct answer of the following question: Each side of an equilateral triangle is $6 \sqrt{3}$ cm. The altitude of the triangle is (a) 8 cm (b) 9 cm (c) $3 \sqrt{3}$ cm (d) 6 cm

Discussion

14589.	Solve this equation H3Po4+3Ca(OH2)=HOH+Ca3(Po4)
Answer» Solve this equation H3Po4+3Ca(OH2)=HOH+Ca3(Po4)

Discussion

14590.	x sq. - 2 sq.root 3 x + 3 =0
Answer» x sq. - 2 sq.root 3 x + 3 =0

Discussion

14591.	Solve each of the following quadratic equations:2x2+ax-a2=0 [CBSE 2015]
Answer» Solve each of the following quadratic equations: $2 x^{2} + a x - a^{2} = 0$ [CBSE 2015]

Discussion

14592.	Solve: x+5>4x−10
Answer» Solve: $x + 5 > 4 x - 10$

Discussion

14593.	The L.C.M. of 9x2+6x+1,3x2+7x+2 and 2x2+3x−2 is (x+a)(2x−b)(3x+c)2. Then a−b−c= _____
Answer» The L.C.M. of $9 x^{2} + 6 x + 1, 3 x^{2} + 7 x + 2$ and $2 x^{2} + 3 x - 2$ is $(x + a) (2 x - b) (3 x + c)^{2}$ . Then $a - b - c =$ _____

Discussion

14594.	In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show that ∠OTS=∠OST=30∘.
Answer» In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If $O P = 2 r$ , show that $∠ O T S = ∠ O S T = 30^{\circ}$ .

Discussion

14595.	The LCM and HCF of two numbers are 432 and 72 respectively. If one of the numbers is 216, what is the other ?
Answer» The LCM and HCF of two numbers are 432 and 72 respectively. If one of the numbers is 216, what is the other ?

Discussion

14596.	If one of the zero of the quadratic polynomial kx2+3x+k is 2 then find the value of k.
Answer» If one of the zero of the quadratic polynomial $k x^{2} + 3 x + k$ is $2$ then find the value of $k$ .

Discussion

14597.	(cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.
Answer» (cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.

Discussion

14598.	If ΔABC ~ ΔQRP, arΔABCarΔPQR=94, AB = 18 cm and BC = 15 cm, then PR = _________.
Answer» If ΔABC ~ ΔQRP, $\frac{a r (Δ A B C)}{a r (Δ P Q R)} = \frac{9}{4}, A B$ = 18 cm and BC = 15 cm, then PR = _________.

Discussion

14599.	A two-digit number is 3 more than 4 times the sum of its digits. If 8 is added to the number, the digits are reversed. Find the number.
Answer» A two-digit number is 3 more than 4 times the sum of its digits. If 8 is added to the number, the digits are reversed. Find the number.

Discussion

14600.	A card is picked from a well shuffled deck of 52 cards.if a face card comes up, then a die is rolled once and if a non face card comes up, then a coin is tossed. Find the probability of getting a perfect number on the die or a tail.
Answer» A card is picked from a well shuffled deck of 52 cards.if a face card comes up, then a die is rolled once and if a non face card comes up, then a coin is tossed. Find the probability of getting a perfect number on the die or a tail.

Discussion

Explore topic-wise InterviewSolutions in .

Question 11Which of the nets given below will generate a cone?

Q20. March 6, 2005 is Monday. What was the day of the week on March 7, 2004?

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

With reference to the figure given, a metal container in the form of a cylinder is surmounted by a hemisphere of same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate

ABC is a triangle and G is its centroid. If AD=12 cm, then find the length of AG.

A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is 30∘.

The minute hand of a clock is 14 cm long. How far does the tip of the minute handmove in 60 minutes?(a) 22 cm (b) 44 cm (c) 33 cm (d) 88 cm

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB.

Given P (–3, 2) and Q (4, 5), and the join of PQ is intersected by -axis at R. Find the coordinates of R.

A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m and the string makes an angle 30∘ with the ground.

The roots of the equation ax2+bx+c=0 will be reciprocal of each other if(a) a = b(b) b= c(c) c = a(d) none of these

Find (x,y) if x =2y and (x,y) is a solution of 7x - 3y = 8.

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.

Half the Perimeter of a rectangular garden whose length is4 meter more than its width is36 meter. Find the dimensions of the garden

Prove that: tan theta - cot theta = 2sin2theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta

250 students of class X of a school appeared in a test of 100 marks and the data about the marks secured is a below Marks securedNumber of students0−202020−403540−606560−806080−10070Find the modal vlaue of the above data.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, then find the distance between the two ships.

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of √3m and is inclined at an angle of 60∘ to the ground. What should be the length of the slide?

5. In triangle ABC right angled at vertex B, a point O is chosen on the side BC such that the circle γ centered at O of radius OB touches the side AC. Let AB = 63 and BC = 16, and the radius of γ be of the form m/nwhere m, n are relatively prime positive integers. Find the value of m + n.

Question 7The point at which the two coordinate axes meet is called theA) AbscissaB) OrdinateC) Origin​​​​​​​D)​​​​​​​ Quadrant

The angle of depression of a car parked on the road from the top of a 150 m high tower is 30º. The distance of the car from the tower (in metres) is(a) 503 (b) 1503 (c) 1502 (d) 75 [CBSE 2014]

21. Express the following function as set of ordered pair and determine the range: g | A --> N, g(x) = 2x, where A = {x | x ∈ N, x ≤ 10

What is the next term in the following sequence? 1T2, 3R5, 8P13, 21N34, 55L89, ?

The cost of 4 pens and 4 pencil boxes is ₹100 . Three times the cost of a pen is ₹15 more than the cost of a pencil box . Form the pair of linear equations for the above situation . Find the cost of a pen and a pencil box.

If 1 is a root of the equation x2 + px + q = 0 find p + q

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

If -1, 1 &amp; 3 are the zeroes of a cubic polynomial, then the correct expression of the polynomial is .

Factorise : x2−3ax−88a2

Find the coordinates of the points of trisection of the line segment joining the points A(7, –2) and B(1, –5). [CBSE 2017]

Sanjeev is 4 times as old as his son. After 16 years he will be twice as old as his son. Find their present ages

What rule should be followed while solving inequality ( not equal to sign)equations

Find the area of a triangle whose sides are 12cm,35cm,37cm.

Find the probability of finding a red marble out of a bag consisting of 8 green, 5 red and 4 white marbles?

The nth term of a sequence is 8 - 5n . Show that the sequence is an A. P.

If X = {10, 11, 12……. 19} and ‘a’ represents any element of X, then write the set which satisfies the condition a – 2 = 11 , a ∈ X

Question 4Find two consecutive positive integers, sum of whose squares is 365.

How many years was the income more than the average income of the given years?

Choose the correct answer of the following question:Each side of an equilateral triangle is 63 cm. The altitude of the triangle is(a) 8 cm (b) 9 cm (c) 33 cm (d) 6 cm

Solve this equation H3Po4+3Ca(OH2)=HOH+Ca3(Po4)

x sq. - 2 sq.root 3 x + 3 =0

Solve each of the following quadratic equations:2x2+ax-a2=0 [CBSE 2015]

Solve: x+5&gt;4x−10

The L.C.M. of 9x2+6x+1,3x2+7x+2 and 2x2+3x−2 is (x+a)(2x−b)(3x+c)2. Then a−b−c= _____

In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show that ∠OTS=∠OST=30∘.

The LCM and HCF of two numbers are 432 and 72 respectively. If one of the numbers is 216, what is the other ?

If one of the zero of the quadratic polynomial kx2+3x+k is 2 then find the value of k.

(cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.

If ΔABC ~ ΔQRP, arΔABCarΔPQR=94, AB = 18 cm and BC = 15 cm, then PR = _________.

A two-digit number is 3 more than 4 times the sum of its digits. If 8 is added to the number, the digits are reversed. Find the number.

A card is picked from a well shuffled deck of 52 cards.if a face card comes up, then a die is rolled once and if a non face card comes up, then a coin is tossed. Find the probability of getting a perfect number on the die or a tail.

Question 7The point at which the two coordinate axes meet is called theA) AbscissaB) OrdinateC) OriginD) Quadrant

If -1, 1 & 3 are the zeroes of a cubic polynomial, then the correct expression of the polynomial is .

Solve: x+5>4x−10