32581 + Interview Questions in Mathematics Page 158 InterviewSolution

7851.	Find the greatest number that exactly divides 168 and 980.
Answer» Find the greatest number that exactly divides 168 and 980.

Discussion

7852.	Read the following information carefully to answer the given questions: V, U and T are sitting around a circle. A, B and C are sitting around the same circle but two of them are not facing centre (they are facing the direction opposite to centre). V is second to the left of C. U is second to the right of A. B is third to the left of T. C is second to the right of T. A and C are not sitting together. Which of the following statement is correct?
Answer» Read the following information carefully to answer the given questions: V, U and T are sitting around a circle. A, B and C are sitting around the same circle but two of them are not facing centre (they are facing the direction opposite to centre). V is second to the left of C. U is second to the right of A. B is third to the left of T. C is second to the right of T. A and C are not sitting together. Which of the following statement is correct?

Discussion

7853.	If 3 + 8 = 17; 5 – 2 = 23; 6 × 2 = 72, then 8 ÷ 4 = ?
Answer» If 3 + 8 = 17; 5 – 2 = 23; 6 × 2 = 72, then 8 ÷ 4 = ?

Discussion

7854.	Anna Patil (Thane, Maharashtra) supplied vacuum cleaner to a shopkeeper in Vasai (Mumbai) for the taxable value of Rs 14,000, and GST rate of 28%. Shopkeeper sold it to the customer at the same GST rate for Rs 16,800 (taxable value) Find the following – (1) Amount of CGST and SGST shown in the tax invoice issued by Anna Patil.(2) Amount of CGST and SGST charged by the shopkeeper in Vasai. (3) What is the CGST and SGST payable by shopkeeper in Vasai at the time of filing the return.
Answer» Anna Patil (Thane, Maharashtra) supplied vacuum cleaner to a shopkeeper in Vasai (Mumbai) for the taxable value of Rs 14,000, and GST rate of 28%. Shopkeeper sold it to the customer at the same GST rate for Rs 16,800 (taxable value) Find the following – (1) Amount of CGST and SGST shown in the tax invoice issued by Anna Patil. (2) Amount of CGST and SGST charged by the shopkeeper in Vasai. (3) What is the CGST and SGST payable by shopkeeper in Vasai at the time of filing the return.

Discussion

7855.	If tan θ=45, find the value of cos θ-sin θcos θ+sin θ.
Answer» If $\tan θ = \frac{4}{5}$ , find the value of $\frac{\cos θ - \sin θ}{\cos θ + \sin θ}$ .

Discussion

7856.	If a1,a2, a3(a1>0) are three successive terms of a G.P. with common ratio r, then find the value of r for which a3>4a2−3a1.
Answer» If $a_{1}$ , $a_{2}$ , $a_{3}$ ( $a_{1} > 0)$ are three successive terms of a G.P. with common ratio r, then find the value of r for which $a_{3} > 4 a_{2} - 3 a_{1}$ .

Discussion

7857.	If sum of first n numbers is cn square then find the sum of squares of these n terms
Answer» If sum of first n numbers is cn square then find the sum of squares of these n terms

Discussion

7858.	34. How to uderstand the statement and make proper figure from given detail like in A verticle tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane , the angle of elevation of the bottom and the top of the flagstaff are alpha and beta respectively. Prove that the height of tower is {h tan alpha/tan beta-tan alpha}.
Answer» 34. How to uderstand the statement and make proper figure from given detail like in A verticle tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane , the angle of elevation of the bottom and the top of the flagstaff are alpha and beta respectively. Prove that the height of tower is {h tan alpha/tan beta-tan alpha}.

Discussion

7859.	Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers:(i) 26 and 91(ii) 510 and 92(iii) 336 and 54
Answer» Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers: (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Discussion

7860.	The area of a rhombus is 119 cm2 and its perimeter is 56 cm. find its height.
Answer» The area of a rhombus is $119 c m^{2}$ and its perimeter is $56 c m$ . find its height.

Discussion

7861.	Let the probability that February of a leap year will have 5 Saturdays be ab, where a and b are co-prime. Then the value of a+b is
Answer» Let the probability that February of a leap year will have $5$ Saturdays be $\frac{a}{b},$ where $a$ and $b$ are co-prime. Then the value of $a + b$ is

Discussion

7862.	Question 6In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.
Answer» Question 6 In a right angle $∠$ ABC is which $∠ B = 90^{\circ}$ , a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

Discussion

7863.	The value of p for which the polynomial x3 + 4x2 − px + 8 is exactly divisible by (x−2) is(a) 0(b) 3(c) 5(d) 16
Answer» The value of p for which the polynomial x³ + 4x² − px + 8 is exactly divisible by (x−2) is (a) 0 (b) 3 (c) 5 (d) 16

Discussion

7864.

Prepare Bank Reconciliation Statement as on 31st March, 2018 from the following particulars: ₹ (i) Bank balancle as per Pass Book. 10,000 (ii) Cheque depisited into the Bank, but no entry was passed in the Cash Book. 500 (iii) Cheque redceived and entered in the Cash Book but not sent to bank. 1,200 (iv) Credit side of the Cash Book bank column cast short. 200 (v) Insurance premium paid directly by the bank under the standing advice. 600 (vi) Bank charges entered twice in the Cash Book. 20 (vii) Cheque issued but not presented to the bank for payment. 500 (viii) Cheque received entered twice in the Cash Book. 1,000 (ix) Bill discounted dishonoured not recorded in the Cash Book. 5,000 (x) Bank had wrongly allowed interest of ₹ 5,000, which was reveresed by it on 5th April, 208.

Answer» Prepare Bank Reconciliation Statement as on 31st March, 2018 from the following particulars:

		₹
(i)	Bank balancle as per Pass Book.	10,000
(ii)	Cheque depisited into the Bank, but no entry was passed in the Cash Book.	500
(iii)	Cheque redceived and entered in the Cash Book but not sent to bank.	1,200
(iv)	Credit side of the Cash Book bank column cast short.	200
(v)	Insurance premium paid directly by the bank under the standing advice.	600
(vi)	Bank charges entered twice in the Cash Book.	20
(vii)	Cheque issued but not presented to the bank for payment.	500
(viii)	Cheque received entered twice in the Cash Book.	1,000
(ix)	Bill discounted dishonoured not recorded in the Cash Book.	5,000
(x)	Bank had wrongly allowed interest of ₹ 5,000, which was reveresed by it on 5th April, 208.

Discussion

7865.	If \|x−2\|+\|x−6\|=3, then find the value(s) of x.
Answer» If $\| x - 2 \| + \| x - 6 \| = 3$ , then find the value(s) of $x$ .

Discussion

7866.	If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =(a) b2-aca2(b) b2-2aca(c) b2+2acb2(d) b2-2aca2
Answer» If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx²+ cx + d, then α² + β² + γ² = (a) $\frac{b^{2} - a c}{a^{2}}$ (b) $\frac{b^{2} - 2 a c}{a}$ (c) $\frac{b^{2} + 2 a c}{b^{2}}$ (d) $\frac{b^{2} - 2 a c}{a^{2}}$

Discussion

7867.	There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4 m. Find the cost of cleaning them at ₹ 14 per m2.
Answer» There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4 m. Find the cost of cleaning them at ₹ 14 per m².

Discussion

7868.	A passenger is travelling in an airplane. An airplane isflying at a height of 3000 m above the level ground. He observes that the angle of depressionfrom the plane to the foot of a tree is a, such that cos3a = sin(120° - 4a). Find the distance thatthe airplane must fly to be directly above the tree.
Answer» A passenger is travelling in an airplane. An airplane is flying at a height of 3000 m above the level ground. He observes that the angle of depression from the plane to the foot of a tree is a, such that cos3a = sin(120° - 4a). Find the distance that the airplane must fly to be directly above the tree.

Discussion

7869.	A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance the two cars and how far is each car from the tower?
Answer» A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance the two cars and how far is each car from the tower?

Discussion

7870.	A metal cylinder of base-radius 4 centimetres and height 10 centimetres is melted and recast into spheres of radius 2 centimetres. How many such spheres are got?
Answer» A metal cylinder of base-radius 4 centimetres and height 10 centimetres is melted and recast into spheres of radius 2 centimetres. How many such spheres are got?

Discussion

7871.	The value of polynomial f(x) = 6xcube + 4xsquare - x/3 where x=1/31)5/9 2)13)4/3 4)3/2
Answer» The value of polynomial f(x) = 6xcube + 4xsquare - x/3 where x=1/3 1)5/9 2)1 3)4/3 4)3/2

Discussion

7872.	The circumference of the base of a cylinder is 88 cm and height is 10 cm. Calculate the volume of the cylinder.
Answer» The circumference of the base of a cylinder is 88 cm and height is 10 cm. Calculate the volume of the cylinder.

Discussion

7873.	6 Mean of twenty observations is 15 if two observation 17 and 20 replaced by 8and9 respectively,then the new mean will be
Answer» 6 Mean of twenty observations is 15 if two observation 17 and 20 replaced by 8and9 respectively,then the new mean will be

Discussion

7874.	A sphere S passes through the origin and the image of its centre in the plane x+y+z=3 is (0,0,0). Radius of the sphere is
Answer» A sphere $S$ passes through the origin and the image of its centre in the plane $x + y + z = 3$ is $(0, 0, 0) .$ Radius of the sphere is

Discussion

7875.	Solve the following pair of equations 5x−1+1y−2=2 6x−1−3y−2=1
Answer» Solve the following pair of equations $\frac{5}{x - 1} + \frac{1}{y - 2} = 2$ $\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

7875.

Solve the following pair of equations 5x−1+1y−2=2 6x−1−3y−2=1

Answer»

Solve the following pair of equations

$\frac{5}{x - 1} + \frac{1}{y - 2} = 2$

$\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

Discussion

7876.	cos (90-θ) =
Answer» $cos$ (90- $θ$ ) =

Discussion

7877.	In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm.25
Answer» In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm. 25

Discussion

7878.	28. Show that the function given by f(x)= logx/x has minimum at x=e
Answer» 28. Show that the function given by f(x)= logx/x has minimum at x=e

Discussion

7879.	Solve each of the following equations by using the method of completing the square: 4x2+4bx−(a2−b2)=0
Answer» Solve each of the following equations by using the method of completing the square: $4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$

Discussion

7880.	Question 2 (ii)Fill in the blanks:(ii) A line intersecting a circle at two points is called a___.
Answer» Question 2 (ii) Fill in the blanks: (ii) A line intersecting a circle at two points is called a___.

Discussion

7881.

The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method. Time (hrs.) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 No. of students 7 18 12 10 3

Answer» The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.

Time (hrs.)	0 - 2	2 - 4	4 - 6	6 - 8	8 - 10
No. of students	7	18	12	10	3

Discussion

7882.	Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
Answer» Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Discussion

7883.	If x,y,z are in A.P. then find the value of (x+y-z)(y+z-x)
Answer» If x,y,z are in A.P. then find the value of (x+y-z)(y+z-x)

Discussion

7884.	Question 32(i)Cardswith numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number?
Answer» Question 32(i) Cardswith numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number?

Discussion

7885.	The lengths of two tangents drawn from an external point to a circle are _________.
Answer» The lengths of two tangents drawn from an external point to a circle are _________.

Discussion

7886.	Q. Show that any positive integer is of the form 3q or 3q+1 or 3q+2 for some integer q.
Answer» Q. Show that any positive integer is of the form 3q or 3q+1 or 3q+2 for some integer q.

Discussion

7887.	Anna deposited Rs 200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum , what is the amount she gets on maturity (i.e. at the end of 36 months)?
Answer» Anna deposited Rs 200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum , what is the amount she gets on maturity (i.e. at the end of 36 months)?

Discussion

7888.	The angle of elevation from the foot of a building to the top of a tower is 60°. The angle of depression from the top of the same building to the foot of the tower is 30°. What is the ratio of their heights?
Answer» The angle of elevation from the foot of a building to the top of a tower is 60°. The angle of depression from the top of the same building to the foot of the tower is 30°. What is the ratio of their heights?

Discussion

7889.	The vertex points of a parabola is given by
Answer» The vertex points of a parabola is given by

Discussion

7890.	Two dice are thrown together. The probability of getting a doublet is(a) 13(b) 16(c) 14(d) 23
Answer» Two dice are thrown together. The probability of getting a doublet is (a) $\frac{1}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{4}$ (d) $\frac{2}{3}$

Discussion

7891.	In the given figure, AB \|\| DC and ∠ADC = 90º. If AD = 3 cm and AB = 4 cm, then the length of AC is
Answer» In the given figure, AB \|\| DC and ∠ADC = 90º. If AD = 3 cm and AB = 4 cm, then the length of AC is

Discussion

7892.	Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2? If so, find its length and breadth.
Answer» Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m²? If so, find its length and breadth.

Discussion

7893.	Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are(a) y = x, y = x + 1(b) y = x, x + y = 2(c) 2y=x, x+y=13(d) y = 2x, y = 2x + 1
Answer» Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are (a) y = x, y = x + 1 (b) y = x, x + y = 2 (c) $2 y = x, x + y = \frac{1}{3}$ (d) y = 2x, y = 2x + 1

Discussion

7894.	If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
Answer» If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.

Discussion

7895.	A and B are partners in a firm sharing profits in the ratio of 2 : 1. They decided with effect from 1st April, 2018, that they would share profits in the ratio of 3 : 2. But, this decision was taken after the profit for the year ended 31st March, 2019 of ₹ 90,000 was distributed in the old ratio.The profits for the year ended 31st March, 2017 and 2018 were ₹ 60,000 and ₹ 75,000 respectively. It was decided that Goodwill Account will not be opened in the books of the firm and necessary adjustment be made through Capital Accounts which on 31st March, 2019 stood at ₹ 1,50,000 for A and ₹ 90,000 for B.Pass necessary Journal entries and prepare Capital Accounts.
Answer» A and B are partners in a firm sharing profits in the ratio of 2 : 1. They decided with effect from 1st April, 2018, that they would share profits in the ratio of 3 : 2. But, this decision was taken after the profit for the year ended 31st March, 2019 of ₹ 90,000 was distributed in the old ratio. The profits for the year ended 31st March, 2017 and 2018 were ₹ 60,000 and ₹ 75,000 respectively. It was decided that Goodwill Account will not be opened in the books of the firm and necessary adjustment be made through Capital Accounts which on 31st March, 2019 stood at ₹ 1,50,000 for A and ₹ 90,000 for B. Pass necessary Journal entries and prepare Capital Accounts.

Discussion

7896.	∆ABC is an isosceles triangle in which ∠C = 90. If AC = 6 cm, then AB =(a) 62 cm(b) 6 cm(c) 26 cm(d) 42 cm
Answer» ∆ABC is an isosceles triangle in which ∠C = 90. If AC = 6 cm, then AB = (a) $6 \sqrt{2} cm$ (b) 6 cm (c) $2 \sqrt{6} cm$ (d) $4 \sqrt{2} cm$

Discussion

7897.	24. A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the first instalment.
Answer» 24. A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the first instalment.

Discussion

7898.	The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.
Answer» The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

Discussion

7899.	What are the coordinates of the origin?
Answer» What are the coordinates of the origin?

Discussion

7900.	If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?
Answer» If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Discussion

Explore topic-wise InterviewSolutions in .

Find the greatest number that exactly divides 168 and 980.

If 3 + 8 = 17; 5 – 2 = 23; 6 × 2 = 72, then 8 ÷ 4 = ?

If tan θ=45, find the value of cos θ-sin θcos θ+sin θ.

If a1,a2, a3(a1&gt;0) are three successive terms of a G.P. with common ratio r, then find the value of r for which a3&gt;4a2−3a1.

If sum of first n numbers is cn square then find the sum of squares of these n terms

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers:(i) 26 and 91(ii) 510 and 92(iii) 336 and 54

The area of a rhombus is 119 cm2 and its perimeter is 56 cm. find its height.

Let the probability that February of a leap year will have 5 Saturdays be ab, where a and b are co-prime. Then the value of a+b is

Question 6In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

The value of p for which the polynomial x3 + 4x2 − px + 8 is exactly divisible by (x−2) is(a) 0(b) 3(c) 5(d) 16

If |x−2|+|x−6|=3, then find the value(s) of x.

If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =(a) b2-aca2(b) b2-2aca(c) b2+2acb2(d) b2-2aca2

There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4 m. Find the cost of cleaning them at ₹ 14 per m2.

A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance the two cars and how far is each car from the tower?

A metal cylinder of base-radius 4 centimetres and height 10 centimetres is melted and recast into spheres of radius 2 centimetres. How many such spheres are got?

The value of polynomial f(x) = 6xcube + 4xsquare - x/3 where x=1/31)5/9 2)13)4/3 4)3/2

The circumference of the base of a cylinder is 88 cm and height is 10 cm. Calculate the volume of the cylinder.

6 Mean of twenty observations is 15 if two observation 17 and 20 replaced by 8and9 respectively,then the new mean will be

A sphere S passes through the origin and the image of its centre in the plane x+y+z=3 is (0,0,0). Radius of the sphere is

Solve the following pair of equations 5x−1+1y−2=2 6x−1−3y−2=1

cos (90-θ) =

In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm.25

28. Show that the function given by f(x)= logx/x has minimum at x=e

Solve each of the following equations by using the method of completing the square: 4x2+4bx−(a2−b2)=0

Question 2 (ii)Fill in the blanks:(ii) A line intersecting a circle at two points is called a___.

The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method. Time (hrs.) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 No. of students 7 18 12 10 3

Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

If x,y,z are in A.P. then find the value of (x+y-z)(y+z-x)

Question 32(i)Cardswith numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number?

The lengths of two tangents drawn from an external point to a circle are _________.

Q. Show that any positive integer is of the form 3q or 3q+1 or 3q+2 for some integer q.

Anna deposited Rs 200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum , what is the amount she gets on maturity (i.e. at the end of 36 months)?

The angle of elevation from the foot of a building to the top of a tower is 60°. The angle of depression from the top of the same building to the foot of the tower is 30°. What is the ratio of their heights?

The vertex points of a parabola is given by

Two dice are thrown together. The probability of getting a doublet is(a) 13(b) 16(c) 14(d) 23

In the given figure, AB || DC and ∠ADC = 90º. If AD = 3 cm and AB = 4 cm, then the length of AC is

Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2? If so, find its length and breadth.

Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are(a) y = x, y = x + 1(b) y = x, x + y = 2(c) 2y=x, x+y=13(d) y = 2x, y = 2x + 1

If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.

∆ABC is an isosceles triangle in which ∠C = 90. If AC = 6 cm, then AB =(a) 62 cm(b) 6 cm(c) 26 cm(d) 42 cm

24. A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the first instalment.

The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

What are the coordinates of the origin?

If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

If a1,a2, a3(a1>0) are three successive terms of a G.P. with common ratio r, then find the value of r for which a3>4a2−3a1.