32581 + Interview Questions in Mathematics Page 234 InterviewSolution

11651.	Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.
Answer» Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

Discussion

11652.	A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.
Answer» A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

Discussion

11653.	The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.
Answer» The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

Discussion

11654.	Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomialy^2+3/2 under root 5y -5
Answer» Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomial y^2+3/2 under root 5y -5

Discussion

11655.	Prove the following trigonometric identities.1+tan2A+1+1tan2A=1sin2A-sin4A
Answer» Prove the following trigonometric identities. $(1 + \tan^{2} A) + (1 + \frac{1}{\tan^{2} A}) = \frac{1}{\sin^{2} A - \sin^{4} A}$

Discussion

11656.	Using Euclid's algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2, and 3 respectively.
Answer» Using Euclid's algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2, and 3 respectively.

Discussion

11657.	22. From a pack of 52 playing cards half of the card are randomly removed without looking at them form remaining cards 3 cards are drawn randomly the probability that all are king
Answer» 22. From a pack of 52 playing cards half of the card are randomly removed without looking at them form remaining cards 3 cards are drawn randomly the probability that all are king

Discussion

11658.	Mark the correct alternative in each of the following:Given that x, y and b are real numbers and x<y, b>0, then(a) xb<yb(b) xb≤yb(c) xb>yb(d) xb≥yb
Answer» Mark the correct alternative in each of the following: Given that x, y and b are real numbers and x $<$ y, b $>$ 0, then (a) $\frac{x}{b < \frac{y}{b}}$ (b) $\frac{x}{b \leq \frac{y}{b}}$ (c) $\frac{x}{b > \frac{y}{b}}$ (d) $\frac{x}{b \geq \frac{y}{b}}$

Discussion

11659.	Find the value of k for which the following equations has a unique solution:x-ky-2=03x+2y+5=0
Answer» Find the value of k for which the following equations has a unique solution: $x - k y - 2 = 0 3 x + 2 y + 5 = 0$

Discussion

11660.	Solve for u and v,where u, v≠02(3u−v)=5uv2(u+3v)=5uv
Answer» Solve for u and v, where u, v $\neq 0$ $2 (3 u - v) = 5 u v 2 (u + 3 v) = 5 u v$

Discussion

11661.	Which of the following denotes the ratio of the sum and the product of the roots of 5x2–14x+8=0?
Answer» Which of the following denotes the ratio of the sum and the product of the roots of $5 x^{2} - 14 x + 8 = 0$ ?

Discussion

11662.	Question 14If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11,-9) and has diameter 10√2 units.
Answer» Question 14 If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11,-9) and has diameter $10 \sqrt{2}$ units.

Discussion

11663.	A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60∘. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30∘. Find the height of the tower and the width of the canal.
Answer» A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the canal.

Discussion

11664.	how many solutions does the equation 3a+b=7 have?
Answer» how many solutions does the equation 3a+b=7 have?

Discussion

11665.	prove that sin square theta + sin square 120 - theta + sin square 240 + theta is equal to 1 minus sin square theta
Answer» prove that sin square theta + sin square 120 - theta + sin square 240 + theta is equal to 1 minus sin square theta

Discussion

11666.	A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm.Find the rise in the level of water.
Answer» A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm.Find the rise in the level of water.

Discussion

11667.	Solve the following quadratic equations by factorization:(2x + 3)(3x − 7) = 0
Answer» Solve the following quadratic equations by factorization: (2x + 3)(3x − 7) = 0

Discussion

11668.	If the zeroes of the polynomial x3−3x2+x+1 are m – n, m and m + n, find m and n.
Answer» If the zeroes of the polynomial $x^{3} - 3 x^{2} + x + 1$ are m – n, m and m + n, find m and n.

Discussion

11669.	A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48,60 and 72 km a day, round the field. When will they meet again?
Answer» A circular field has a circumference of $360$ km. Three cyclists start together and can cycle 48,60 and 72 km a day, round the field. When will they meet again?

Discussion

11670.	In the figure, P and Q are the points of intersection of two circles with centres O and O′. If straight lines, APB and CQD are parallel to OO′, then what is the ratio of OO′ and AB?
Answer» In the figure, $P$ and $Q$ are the points of intersection of two circles with centres $O$ and $O^{'} .$ If straight lines, $A P B$ and $C Q D$ are parallel to $O O^{'},$ then what is the ratio of $O O^{'}$ and $A B ?$

11670.

In the figure, P and Q are the points of intersection of two circles with centres O and O′. If straight lines, APB and CQD are parallel to OO′, then what is the ratio of OO′ and AB?

Answer»

In the figure, $P$ and $Q$ are the points of intersection of two circles with centres $O$ and $O^{'} .$ If straight lines, $A P B$ and $C Q D$ are parallel to $O O^{'},$ then what is the ratio of $O O^{'}$ and $A B ?$

Discussion

11671.	Choose the correct answer of the following question:sec30°cosec60°=?a 23 b 32 c 3 d1
Answer» $Choose the correct answer of the following question : \frac{\sec 30 °}{cosec 60 °} = ? (a) \frac{2}{\sqrt{3}} (b) \frac{\sqrt{3}}{2} (c) \sqrt{3} (d) 1$

Discussion

11672.	In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find:(i) the circumference of the circle(ii) the area of the circle(iii) the length of the arc AB,(iv) the area of the sector OAB.
Answer» In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find: (i) the circumference of the circle (ii) the area of the circle (iii) the length of the arc AB, (iv) the area of the sector OAB.

Discussion

11673.	A box contains 12 balls out of which x are blue. If one ball is drawn at random from the box, what is the probability that it will be a blue ball ? If 6 more blue balls are put in the box , the probability of drawing a black ball is now double of what it was before . Find x
Answer» A box contains 12 balls out of which $x$ are blue. If one ball is drawn at random from the box, what is the probability that it will be a blue ball ? If 6 more blue balls are put in the box , the probability of drawing a black ball is now double of what it was before . Find $x$

Discussion

11674.	Find r if : (a) 13Pr = 156 (b) 8Pr = 336
Answer» Find r if : (a) ¹³P_r = 156 (b) ⁸P_r = 336

Discussion

11675.	Question 25 (i) Is the following argument correct? Give reasons for your answer. If two coins are tossed simultaneously there are three possible outcomes – two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 13.
Answer» Question 25 (i) Is the following argument correct? Give reasons for your answer. If two coins are tossed simultaneously there are three possible outcomes – two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$ .

Discussion

11676.	List-II gives distance between pair of points given in List-I, match them correctly. List−I List II(P)(−5,7),(−1,3)(1)5(Q)(5,6),(1,3)(2)√8(R)(√3+1,1),(0,√3)(3)√6(S)(0,0),(−√3,√3)(4)4√2
Answer» List-II gives distance between pair of points given in List-I, match them correctly. $\begin{matrix} L i s t - I & L i s t I I (P) & (- 5, 7), (- 1, 3) & (1) & 5 (Q) & (5, 6), (1, 3) & (2) & \sqrt{8} (R) & (\sqrt{3} + 1, 1), (0, \sqrt{3}) & (3) & \sqrt{6} (S) & (0, 0), (- \sqrt{3}, \sqrt{3}) & (4) & 4 \sqrt{2} \end{matrix}$

Discussion

11677.	What is the highest value of sin theta × cos theta
Answer» What is the highest value of sin theta × cos theta

Discussion

11678.	Evaluate:sin30°cos45°+cot45°sec60°−sin60°tan45°+cos30°sin90°
Answer» Evaluate: $\frac{sin 30 °}{cos 45 °} + \frac{cot 45 °}{sec 60 °} - \frac{sin 60 °}{tan 45 °} + \frac{cos 30 °}{sin 90 °}$

Discussion

11679.	Question 1 (i) In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A
Answer» Question 1 (i) In $Δ$ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A

Discussion

11680.	39. The points A(4,7) , B(p,3) and C(7,3) are vertices of right triangle, right angled at B. Find the value of'p'.
Answer» 39. The points A(4,7) , B(p,3) and C(7,3) are vertices of right triangle, right angled at B. Find the value of'p'.

Discussion

11681.	Cot(1358°)+tan(3608°)=?
Answer» Cot(1358°)+tan(3608°)=?

Discussion

11682.	A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.(Use π=22/7).
Answer» A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere, calculate the height of the cone and the surface area of the toy. (Use $π = 22 / 7$ ).

Discussion

11683.	Find the equation of the straight lines each passing through the point (6,-2) and whose sum of the intercept is 5.
Answer» Find the equation of the straight lines each passing through the point (6,-2) and whose sum of the intercept is 5.

Discussion

11684.

Find the mode of the given data: [CBSE 2015] Class interval 0−20 20−40 40−60 60−80 Frequency 15 6 18 10

Answer» Find the mode of the given data: [CBSE 2015]

Class interval	0−20	20−40	40−60	60−80
Frequency	15	6	18	10

Discussion

11685.	A is not equal to I, B3=I,AB=BA2 and Ak=I then the least value of k is
Answer» A is not equal to I, $B^{3} = I, A B = B A^{2}$ and $A^{k} = I$ then the least value of k is

Discussion

11686.	If sinθ=12and θ is acute,then find the value of (3cosθ−4cos3θ).
Answer» $If s i n θ = \frac{1}{2}$ and $θ$ is acute, $then find the value of (3 c o s θ - 4 c o s^{3} θ) .$

Discussion

11687.	In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following.p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)
Answer» In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following. p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)

11687.

In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following.p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)

Answer»

In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following.

p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)

Discussion

11688.	Find the volume of : [2 MARKS]
Answer» Find the volume of : [2 MARKS]

11688.

Find the volume of : [2 MARKS]

Answer»

Find the volume of : [2 MARKS]

Discussion

11689.	If p and q are the roots of the equation a2+2a−3=0, which of these could be the quadratic equation in ‘a’ whose roots are (p + q) and (p - q).
Answer» If p and q are the roots of the equation $a^{2} + 2 a - 3 = 0$ , which of these could be the quadratic equation in ‘a’ whose roots are (p + q) and (p - q).

Discussion

11690.	If cos θ=45, find all other trigonometric ratios of angle θ
Answer» If $c o s θ = \frac{4}{5}$ , find all other trigonometric ratios of angle $θ$

Discussion

11691.	If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .
Answer» If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .

Discussion

11692.	In a blood donation camp following was the observation of 15 people's blood group. A, B, AB, A, B, A, A, B, O, A, AB, B, A, B, AB. Make an ungrouped frequency distribution and find the rarest blood group.
Answer» In a blood donation camp following was the observation of 15 people's blood group. A, B, AB, A, B, A, A, B, O, A, AB, B, A, B, AB. Make an ungrouped frequency distribution and find the rarest blood group.

Discussion

11693.	How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?
Answer» How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

Discussion

11694.	In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is
Answer» In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

11694.

In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

Answer»

In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

Discussion

11695.	A man on top of a building observes a car at an angle of depression α, where tan α=1√5 and sees that it is moving towards the base of the building. Ten minutes later the angle of depression of the car is found to be β where tan β=√5. If the car is moving with an uniform speed, then how much more time will it take to reach the base of the tower?
Answer» A man on top of a building observes a car at an angle of depression $α$ , where $t a n α = \frac{1}{\sqrt{5}}$ and sees that it is moving towards the base of the building. Ten minutes later the angle of depression of the car is found to be $β$ where tan $β = \sqrt{5}$ . If the car is moving with an uniform speed, then how much more time will it take to reach the base of the tower?

Discussion

11696.	limn→∞1+2+3+...+nn2+100 _________________________.
Answer» $\lim_{n \to \infty} \frac{1 + 2 + 3 + . . . + n}{n^{2} + 100}_________________________.$

Discussion

11697.	If ax3+bx2+x-6 has a factor and leaves remainder 4when divided by x-2.Find the value of a and b.
Answer» If ax³+bx²+x-6 has a factor and leaves remainder 4when divided by x-2.Find the value of a and b.

Discussion

11698.	The first term of the G.P is 1 . If (p+q)th term of G.P. is `a` and it's (p−q)th term is `b` where a, b ∈ R+ then it's pth term is:
Answer» The first term of the G.P is 1 . If ${(p + q)}^{t h}$ term of G.P. is `a` and it's ${(p - q)}^{t h}$ term is `b` where a, b ∈ $R^{+}$ then it's $p^{t h}$ term is:

Discussion

11699.	Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.
Answer» Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

Discussion

11700.	Graphically , solve the following pair of equations:2x + y = 62x - y + 2 =0Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.
Answer» Graphically , solve the following pair of equations: $2 x + y = 6 2 x - y + 2 = 0$ Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Discussion

Explore topic-wise InterviewSolutions in .

Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomialy^2+3/2 under root 5y -5

Prove the following trigonometric identities.1+tan2A+1+1tan2A=1sin2A-sin4A

Using Euclid's algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2, and 3 respectively.

22. From a pack of 52 playing cards half of the card are randomly removed without looking at them form remaining cards 3 cards are drawn randomly the probability that all are king

Mark the correct alternative in each of the following:Given that x, y and b are real numbers and x&lt;y, b&gt;0, then(a) xb&lt;yb(b) xb≤yb(c) xb&gt;yb(d) xb≥yb

Find the value of k for which the following equations has a unique solution:x-ky-2=03x+2y+5=0

Solve for u and v,where u, v≠02(3u−v)=5uv2(u+3v)=5uv

Which of the following denotes the ratio of the sum and the product of the roots of 5x2–14x+8=0?

Question 14If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11,-9) and has diameter 10√2 units.

how many solutions does the equation 3a+b=7 have?

prove that sin square theta + sin square 120 - theta + sin square 240 + theta is equal to 1 minus sin square theta

A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm.Find the rise in the level of water.

Solve the following quadratic equations by factorization:(2x + 3)(3x − 7) = 0

If the zeroes of the polynomial x3−3x2+x+1 are m – n, m and m + n, find m and n.

A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48,60 and 72 km a day, round the field. When will they meet again?

In the figure, P and Q are the points of intersection of two circles with centres O and O′. If straight lines, APB and CQD are parallel to OO′, then what is the ratio of OO′ and AB?

Choose the correct answer of the following question:sec30°cosec60°=?a 23 b 32 c 3 d1

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find:(i) the circumference of the circle(ii) the area of the circle(iii) the length of the arc AB,(iv) the area of the sector OAB.

A box contains 12 balls out of which x are blue. If one ball is drawn at random from the box, what is the probability that it will be a blue ball ? If 6 more blue balls are put in the box , the probability of drawing a black ball is now double of what it was before . Find x

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

Question 25 (i) Is the following argument correct? Give reasons for your answer. If two coins are tossed simultaneously there are three possible outcomes – two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 13.

List-II gives distance between pair of points given in List-I, match them correctly. List−I List II(P)(−5,7),(−1,3)(1)5(Q)(5,6),(1,3)(2)√8(R)(√3+1,1),(0,√3)(3)√6(S)(0,0),(−√3,√3)(4)4√2

What is the highest value of sin theta × cos theta

Evaluate:sin30°cos45°+cot45°sec60°−sin60°tan45°+cos30°sin90°

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

39. The points A(4,7) , B(p,3) and C(7,3) are vertices of right triangle, right angled at B. Find the value of'p'.

Cot(1358°)+tan(3608°)=?

Find the equation of the straight lines each passing through the point (6,-2) and whose sum of the intercept is 5.

Find the mode of the given data: [CBSE 2015] Class interval 0−20 20−40 40−60 60−80 Frequency 15 6 18 10

A is not equal to I, B3=I,AB=BA2 and Ak=I then the least value of k is

If sinθ=12and θ is acute,then find the value of (3cosθ−4cos3θ).

In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following.p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)

Find the volume of : [2 MARKS]

If p and q are the roots of the equation a2+2a−3=0, which of these could be the quadratic equation in ‘a’ whose roots are (p + q) and (p - q).

If cos θ=45, find all other trigonometric ratios of angle θ

If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .

In a blood donation camp following was the observation of 15 people's blood group. A, B, AB, A, B, A, A, B, O, A, AB, B, A, B, AB. Make an ungrouped frequency distribution and find the rarest blood group.

How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

limn→∞1+2+3+...+nn2+100 _________________________.

If ax3+bx2+x-6 has a factor and leaves remainder 4when divided by x-2.Find the value of a and b.

The first term of the G.P is 1 . If (p+q)th term of G.P. is `a` and it's (p−q)th term is `b` where a, b ∈ R+ then it's pth term is:

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

Graphically , solve the following pair of equations:2x + y = 62x - y + 2 =0Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Mark the correct alternative in each of the following:Given that x, y and b are real numbers and x<y, b>0, then(a) xb<yb(b) xb≤yb(c) xb>yb(d) xb≥yb