24740 + Interview Questions in Mathematics Page 94 InterviewSolution

4651.	Question 5A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall then find the distance by which the top of the ladder would slide upwards on the wall.
Answer» Question 5 A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall then find the distance by which the top of the ladder would slide upwards on the wall.

Discussion

4652.	The distances measured along the X-axis from the origin to its right, are considered _____ and the distances measured along the X-axis from the origin to its left are considered _____ by convention.
Answer» The distances measured along the X-axis from the origin to its right, are considered _____ and the distances measured along the X-axis from the origin to its left are considered _____ by convention.

Discussion

4653.	Find the value of a+b+c, if √5−√3√5+√3=a−b√c20
Answer» Find the value of $a + b + c$ , if $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}} = a - b \sqrt{c}$ 20

Discussion

4654.	Factorise :(i)7(2x+5)+3(2x+5) (ii)5a(2x+3y)–2b(2x+3y)
Answer» Factorise : $(i) 7 (2 x + 5) + 3 (2 x + 5)$ $(i i) 5 a (2 x + 3 y) - 2 b (2 x + 3 y)$

Discussion

4655.	Choose the correct answer in each of the following: If AB = QR, BC = RP and CA = PQ then which of the following holds?(a) ΔABC≅ ΔPQR (b) ΔCBA≅ ΔPQR(c) ΔCAB≅ ΔPQR (d) ΔBCA≅ ΔPQR
Answer» Choose the correct answer in each of the following: $If AB = QR, BC = RP and CA = PQ then which of the following holds? (a) Δ A B C ≅ Δ P Q R (b) Δ C B A ≅ Δ P Q R (c) Δ C A B ≅ Δ P Q R (d) Δ B C A ≅ Δ P Q R$

4655.

Choose the correct answer in each of the following: If AB = QR, BC = RP and CA = PQ then which of the following holds?(a) ΔABC≅ ΔPQR (b) ΔCBA≅ ΔPQR(c) ΔCAB≅ ΔPQR (d) ΔBCA≅ ΔPQR

Answer»

Choose the correct answer in each of the following:

$If AB = QR, BC = RP and CA = PQ then which of the following holds? (a) Δ A B C ≅ Δ P Q R (b) Δ C B A ≅ Δ P Q R (c) Δ C A B ≅ Δ P Q R (d) Δ B C A ≅ Δ P Q R$

Discussion

4656.	Find the vale of p for the following frequency distribution whose mean is 16.6x81215p202530f121620241684
Answer» Find the vale of p for the following frequency distribution whose mean is 16.6 $\begin{matrix} x & 8 & 12 & 15 & p & 20 & 25 & 30 f & 12 & 16 & 20 & 24 & 16 & 8 & 4 \end{matrix}$

Discussion

4657.	Area of rectangle is 24 sq. cm, if the length of rectangle is 8 cm, what is its width?
Answer» Area of rectangle is 24 sq. cm, if the length of rectangle is 8 cm, what is its width?

Discussion

4658.	In □ABCD , side BC \|\| side AD, side AB ≅ side DC If ∠A = 72° then find the measure of ∠B, and ∠D.
Answer» In $□$ ABCD , side BC \|\| side AD, side AB $≅$ side DC If $∠$ A = $72^{°}$ then find the measure of $∠$ B, and $∠$ D.

Discussion

4659.	When p(x) = x3 – ax2 + x is divided by (x – a), the remainder is(a) 0(b) a(c) 2a(d) 3a
Answer» When p(x) = x³– ax²+ x is divided by (x – a), the remainder is (a) 0 (b) a (c) 2a (d) 3a

Discussion

4660.	Represent 12,52,72,92 on the number line.
Answer» Represent $\frac{1}{2}, \frac{5}{2}, \frac{7}{2}, \frac{9}{2}$ on the number line.

Discussion

4661.	Find x if log10(x+1)+log10(x−1)=log1011+2log103
Answer» $Find x if$ $l o g_{10} (x + 1) + l o g_{10} (x - 1) = l o g_{10} 11 + 2 l o g_{10} 3$

Discussion

4662.	The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the parallel sides are 36 m and 20 m, then find the length of the non-parallel sides.
Answer» The area of a trapezium with equal non-parallel sides is $168 m^{2}$ . If the lengths of the parallel sides are $36 m$ and $20 m$ , then find the length of the non-parallel sides.

Discussion

4663.	What is the solution of the equation 3x+7y=30 if x=y?
Answer» What is the solution of the equation $3 x + 7 y = 30$ if $x = y$ ?

Discussion

4664.	In a quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS.
Answer» In a quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS.

Discussion

4665.	The probability for a randomly selected number out of 1, 2, 3, 4,...,1500 to be a perfect cube number is
Answer» The probability for a randomly selected number out of 1, 2, 3, 4,...,1500 to be a perfect cube number is

Discussion

4666.	In an triangle ABC with usual notations r1/bc+r2/ca+r3/ab is
Answer» In an triangle ABC with usual notations r1/bc+r2/ca+r3/ab is

Discussion

4667.	In a parallelogram ABCD, if AB=2x+5,CD=y+1,AD=y+5 and BC=3x−4, then the ratio of AB:BC is equal to
Answer» In a parallelogram ABCD, if $A B = 2 x + 5, C D = y + 1, A D = y + 5$ and $B C = 3 x - 4,$ then the ratio of $A B : B C$ is equal to

Discussion

4668.	Find the values of x and y that satisfy the below given pair of equations, where x≠0 & y≠0. 2x+3y=13 5x−4y=−2
Answer» Find the values of $x$ and $y$ that satisfy the below given pair of equations, where $x \neq 0 & y \neq 0$ . $\frac{2}{x} + \frac{3}{y} = 13$ $\frac{5}{x} - \frac{4}{y} = - 2$

Discussion

4669.	Question 9 If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is: A) 1:3 B) 1:2 C) 3:1 D) 1:4
Answer» Question 9 If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is: A) 1:3 B) 1:2 C) 3:1 D) 1:4

Discussion

4670.	Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=x3-6x2+2x-4, gx=1-32x.
Answer» Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where $p (x) = x^{3} - 6 x^{2} + 2 x - 4, g (x) = 1 - \frac{3}{2} x$ .

Discussion

4671.	Question 75 ___ measurements can determine a quadrilateral uniquely.
Answer» Question 75 ___ measurements can determine a quadrilateral uniquely.

Discussion

4672.	The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm, find its length.
Answer» The surface area of a cuboid is $1300 c m^{2} .$ If its breadth is 10 cm and height is 20 cm, find its length.

Discussion

4673.	For what value of p , x=3 will be a root of the equation px2+2x−3=0
Answer» For what value of $p$ , $x = 3$ will be a root of the equation $p x^{2} + 2 x - 3 = 0$

Discussion

4674.	The zeroes of the polynomial p(x) = 3x2 − 1 are(a) 13 and 3(b) 13 and 3(c) -13 and 3(d) 13and-13
Answer» The zeroes of the polynomial p(x) = 3x² − 1 are (a) $\frac{1}{3}$ and 3 (b) $\frac{1}{\sqrt{3}} and \sqrt{3}$ (c) $\frac{- 1}{\sqrt{3}} and \sqrt{3}$ (d) $\frac{1}{\sqrt{3}} and \frac{- 1}{\sqrt{3}}$

Discussion

4675.	In quadrilateral PQRS, if ∠P=60∘ and ∠Q:∠R:∠S=2:3:7, then find the measure of ∠S.
Answer» In quadrilateral PQRS, if $∠ P = 60^{\circ}$ and $∠ Q : ∠ R : ∠ S = 2 : 3 : 7,$ then find the measure of $∠ S .$

Discussion

4676.	In the adjoining figure, D and E are respectively the midpoints of sides AB and AC of ∆ABC. If PQ \|\| BC and CDP and BEQ are straight lines then prove that ar(∆ABQ) = ar(∆ACP).
Answer» In the adjoining figure, D and E are respectively the midpoints of sides AB and AC of ∆ABC. If PQ \|\| BC and CDP and BEQ are straight lines then prove that ar(∆ABQ) = ar(∆ACP).

Discussion

4677.	Which of the following is correct for the given data :- 1, 0, 2, 3, 5, 5, 6, 8, 10, 11, 12
Answer» Which of the following is correct for the given data :- 1, 0, 2, 3, 5, 5, 6, 8, 10, 11, 12

Discussion

4678.	Factorise: 2(x+y)2−9(x+y)−5
Answer» Factorise: $2 (x + y)^{2} - 9 (x + y) - 5$

Discussion

4679.	(2x−3y)3+(x+3y)3+3(2x−3y)2(x+3y)+3(2x−3y)(x+3y)2=
Answer» $(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =$

Discussion

4680.	If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is (a) 25 (b) 53 (c) 35 (d) 27
Answer» If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is (a) $\frac{2}{5}$ (b) $\frac{5}{3}$ (c) $\frac{3}{5}$ (d) $\frac{2}{7}$

4680.

If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is (a) 25 (b) 53 (c) 35 (d) 27

Answer»

If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is

(a) $\frac{2}{5}$

(b) $\frac{5}{3}$

(c) $\frac{3}{5}$

(d) $\frac{2}{7}$

Discussion

4681.

The following data shows the average age of men in various countries in a certain year: Country India Nepal China Pakistan U.K U.S.A Average age (in years) 55 52 60 50 70 75 Represent the above information by a bar graph.

Answer» The following data shows the average age of men in various countries in a certain year:

Country	India	Nepal	China	Pakistan	U.K	U.S.A
Average age (in years)	55	52	60	50	70	75

Represent the above information by a bar graph.

Discussion

4682.	Question 4 (ii)Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:A fraction becomes 13 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.
Answer» Question 4 (ii) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Discussion

4683.	How many arcs are need to be drawn using the method of Triangle Construction 2?
Answer» How many arcs are need to be drawn using the method of Triangle Construction 2?

Discussion

4684.	The mean of 15 observations is 14. If the means of first 7 observations is 12 and that of last 7 observation is 16. Find the middle term.
Answer» The mean of 15 observations is 14. If the means of first 7 observations is 12 and that of last 7 observation is 16. Find the middle term.

Discussion

4685.	Find the cost of painting a cuboid of dimensions 20 cm ×15 cm ×12 cm at the rate of 5 paise per square centimeter
Answer» Find the cost of painting a cuboid of dimensions $20$ cm $\times 15$ cm $\times 12$ cm at the rate of 5 paise per square centimeter

Discussion

4686.	50. If each diagonal of a quadrilateral divides it into two triangles of equal area , then prove that the quadrilateral is a parallelogram.
Answer» 50. If each diagonal of a quadrilateral divides it into two triangles of equal area , then prove that the quadrilateral is a parallelogram.

Discussion

4687.	Factorise the quadratic polynomial by splitting the middle term: x2 + 14x + 45
Answer» Factorise the quadratic polynomial by splitting the middle term: x² + 14x + 45

4687.

Factorise the quadratic polynomial by splitting the middle term: x2 + 14x + 45

Answer»

Factorise the quadratic polynomial by splitting the middle term:

x² + 14x + 45

Discussion

4688.	Find the value of x, where AB \|\| CD
Answer» Find the value of $x$ , where AB \|\| CD

Discussion

4689.	ABCD is a trapezium in which AB \|\| CD, AB = 16 cm and DC = 24 cm. If E and F are respectively the midpoints of AD and BC, prove that ar(ABFE) = 911 ar(EFCD).
Answer» ABCD is a trapezium in which AB \|\| CD, AB = 16 cm and DC = 24 cm. If E and F are respectively the midpoints of AD and BC, prove that ar(ABFE) = $\frac{9}{11}$ ar(EFCD).

Discussion

4690.	If the diameter of the base of a right circular cylinder is 20% greater than its height h, then its volume is equal to (in cubic units)
Answer» If the diameter of the base of a right circular cylinder is 20% greater than its height h, then its volume is equal to (in cubic units)

Discussion

4691.	Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is ₹360 per dozen.
Answer» Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is ₹360 per dozen.

Discussion

4692.	If O is a point within a quadrilateral ABCD, show that OA + OB + OC + OD > AC + BD
Answer» If O is a point within a quadrilateral ABCD, show that OA + OB + OC + OD > AC + BD

Discussion

4693.	If one side of the triangle is the longest line that can be drawn inside the circle, what will be the ratio of maximum area covered by green to blue region?
Answer» If one side of the triangle is the longest line that can be drawn inside the circle, what will be the ratio of maximum area covered by green to blue region?

Discussion

4694.	Question 3 (ii)Express 0.4¯7 in the form pq, where p and q are integers and q≠0.
Answer» Question 3 (ii) Express $0.4 ¯ 7$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Discussion

4695.	If ab = 57 then find the ratio 5a−bb.
Answer» If $\frac{a}{b}$ = $\frac{5}{7}$ then find the ratio $\frac{5 a - b}{b}$ .

Discussion

4696.	Solve for θ if 4cos2θ + 2sinθ – 4 = 0, where 0∘ ≤ θ ≤ 90∘.
Answer» Solve for $θ$ if $4 {cos}^{2} θ$ + 2 $sin θ$ – 4 = 0, where $0^{\circ}$ $\leq$ $θ$ $\leq$ $90^{\circ}$ .

Discussion

4697.	Read the bar graph given in Fig. 23.22 and answer the following questions:(i) What information is given by the bar graph?(ii) Which Doordarshan centre covers maximum area? Also tell the covered area.(iii) What is the difference between the areas covered by the centres at Delhi and Bombay?(iv) Which Doordarshan centres are in U.P. State? What are the areas covered by them?
Answer» Read the bar graph given in Fig. 23.22 and answer the following questions: (i) What information is given by the bar graph? (ii) Which Doordarshan centre covers maximum area? Also tell the covered area. (iii) What is the difference between the areas covered by the centres at Delhi and Bombay? (iv) Which Doordarshan centres are in U.P. State? What are the areas covered by them?

Discussion

4698.	Which one of the following is an equation of a line perpendicular to X-Axis?
Answer» Which one of the following is an equation of a line perpendicular to X-Axis?

Discussion

4699.	A pipe is connected to a tank. The water flows out from the tank through pipe at the rate of 64 m3/min. Find the time taken by the pipe to empty the volume of 1024 m3 (in mins).
Answer» A pipe is connected to a tank. The water flows out from the tank through pipe at the rate of 64 $m^{3}$ /min. Find the time taken by the pipe to empty the volume of 1024 $m^{3}$ (in mins).

Discussion

4700.	The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is Rs. 8800. If painter takes Rs. 40 per metre square to paint the cylindrical container, then find radius of the cylindrical vessel.Take π=227
Answer» The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is Rs. 8800. If painter takes Rs. 40 per metre square to paint the cylindrical container, then find radius of the cylindrical vessel. Take $π = \frac{22}{7}$

Discussion

Explore topic-wise InterviewSolutions in .

Question 5A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall then find the distance by which the top of the ladder would slide upwards on the wall.

The distances measured along the X-axis from the origin to its right, are considered _____ and the distances measured along the X-axis from the origin to its left are considered _____ by convention.

Find the value of a+b+c, if √5−√3√5+√3=a−b√c20

Factorise :(i)7(2x+5)+3(2x+5) (ii)5a(2x+3y)–2b(2x+3y)

Choose the correct answer in each of the following: If AB = QR, BC = RP and CA = PQ then which of the following holds?(a) ΔABC≅ ΔPQR (b) ΔCBA≅ ΔPQR(c) ΔCAB≅ ΔPQR (d) ΔBCA≅ ΔPQR

Find the vale of p for the following frequency distribution whose mean is 16.6x81215p202530f121620241684

Area of rectangle is 24 sq. cm, if the length of rectangle is 8 cm, what is its width?

In □ABCD , side BC || side AD, side AB ≅ side DC If ∠A = 72° then find the measure of ∠B, and ∠D.

When p(x) = x3 – ax2 + x is divided by (x – a), the remainder is(a) 0(b) a(c) 2a(d) 3a

Represent 12,52,72,92 on the number line.

Find x if log10(x+1)+log10(x−1)=log1011+2log103

The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the parallel sides are 36 m and 20 m, then find the length of the non-parallel sides.

What is the solution of the equation 3x+7y=30 if x=y?

In a quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS.

The probability for a randomly selected number out of 1, 2, 3, 4,...,1500 to be a perfect cube number is

In an triangle ABC with usual notations r1/bc+r2/ca+r3/ab is

In a parallelogram ABCD, if AB=2x+5,CD=y+1,AD=y+5 and BC=3x−4, then the ratio of AB:BC is equal to

Find the values of x and y that satisfy the below given pair of equations, where x≠0 &amp; y≠0. 2x+3y=13 5x−4y=−2

Question 9 If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is: A) 1:3 B) 1:2 C) 3:1 D) 1:4

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=x3-6x2+2x-4, gx=1-32x.

Question 75 ___ measurements can determine a quadrilateral uniquely.

The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm, find its length.

For what value of p , x=3 will be a root of the equation px2+2x−3=0

The zeroes of the polynomial p(x) = 3x2 − 1 are(a) 13 and 3(b) 13 and 3(c) -13 and 3(d) 13and-13

In quadrilateral PQRS, if ∠P=60∘ and ∠Q:∠R:∠S=2:3:7, then find the measure of ∠S.

In the adjoining figure, D and E are respectively the midpoints of sides AB and AC of ∆ABC. If PQ || BC and CDP and BEQ are straight lines then prove that ar(∆ABQ) = ar(∆ACP).

Which of the following is correct for the given data :- 1, 0, 2, 3, 5, 5, 6, 8, 10, 11, 12

Factorise: 2(x+y)2−9(x+y)−5

(2x−3y)3+(x+3y)3+3(2x−3y)2(x+3y)+3(2x−3y)(x+3y)2=

If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is (a) 25 (b) 53 (c) 35 (d) 27

The following data shows the average age of men in various countries in a certain year: Country India Nepal China Pakistan U.K U.S.A Average age (in years) 55 52 60 50 70 75 Represent the above information by a bar graph.

Question 4 (ii)Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:A fraction becomes 13 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

How many arcs are need to be drawn using the method of Triangle Construction 2?

The mean of 15 observations is 14. If the means of first 7 observations is 12 and that of last 7 observation is 16. Find the middle term.

Find the cost of painting a cuboid of dimensions 20 cm ×15 cm ×12 cm at the rate of 5 paise per square centimeter

50. If each diagonal of a quadrilateral divides it into two triangles of equal area , then prove that the quadrilateral is a parallelogram.

Factorise the quadratic polynomial by splitting the middle term: x2 + 14x + 45

Find the value of x, where AB || CD

ABCD is a trapezium in which AB || CD, AB = 16 cm and DC = 24 cm. If E and F are respectively the midpoints of AD and BC, prove that ar(ABFE) = 911 ar(EFCD).

If the diameter of the base of a right circular cylinder is 20% greater than its height h, then its volume is equal to (in cubic units)

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is ₹360 per dozen.

If O is a point within a quadrilateral ABCD, show that OA + OB + OC + OD &gt; AC + BD

If one side of the triangle is the longest line that can be drawn inside the circle, what will be the ratio of maximum area covered by green to blue region?

Question 3 (ii)Express 0.4¯7 in the form pq, where p and q are integers and q≠0.

If ab = 57 then find the ratio 5a−bb.

Solve for θ if 4cos2θ + 2sinθ – 4 = 0, where 0∘ ≤ θ ≤ 90∘.

Which one of the following is an equation of a line perpendicular to X-Axis?

A pipe is connected to a tank. The water flows out from the tank through pipe at the rate of 64 m3/min. Find the time taken by the pipe to empty the volume of 1024 m3 (in mins).

The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is Rs. 8800. If painter takes Rs. 40 per metre square to paint the cylindrical container, then find radius of the cylindrical vessel.Take π=227

The distances measured along the X-axis from the origin to its right, are considered _ and the distances measured along the X-axis from the origin to its left are considered _ by convention.

Find the values of x and y that satisfy the below given pair of equations, where x≠0 & y≠0. 2x+3y=13 5x−4y=−2

If O is a point within a quadrilateral ABCD, show that OA + OB + OC + OD > AC + BD