32581 + Interview Questions in Mathematics

1.	If A=[12−31] and B=[11−143] Find Matrix X, given that X-5A=3B
Answer» If $A = [\begin{matrix} 1 & 2 - 3 & 1 \end{matrix}] and B = [\begin{matrix} 11 & - 1 4 & 3 \end{matrix}]$ Find Matrix X, given that X-5A=3B

1.

If A=[12−31] and B=[11−143] Find Matrix X, given that X-5A=3B

Answer»

If $A = [\begin{matrix} 1 & 2 - 3 & 1 \end{matrix}] and B = [\begin{matrix} 11 & - 1 4 & 3 \end{matrix}]$

Find Matrix X, given that
X-5A=3B

Discussion

2.	Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for 212 years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.
Answer» Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for $2 \frac{1}{2}$ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

2.

Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for 212 years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

Answer»

Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for $2 \frac{1}{2}$ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

Discussion

3.	Solve the following system of equations in R. 5x−1<24,5x+1>−24
Answer» Solve the following system of equations in R. $5 x - 1 < 24, 5 x + 1 > - 24$

3.

Solve the following system of equations in R. 5x−1<24,5x+1>−24

Answer»

Solve the following system of equations in R.

$5 x - 1 < 24, 5 x + 1 > - 24$

Discussion

4.	The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term.
Answer» The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by $1.$ Find the $15^{t h}$ term.

Discussion

5.	If a line segment AB is divided in the ratio m : n, both m and n should be ___ integers.
Answer» If a line segment AB is divided in the ratio m : n, both m and n should be ___ integers.

Discussion

6.	One family has been chosen out of 200 families having 3 children . What is the probability that there is at least one girl ?
Answer» One family has been chosen out of 200 families having 3 children . What is the probability that there is at least one girl ?

Discussion

7.	Question 170 Three angles of a quadrilateral are equal. The fourth angle is 120∘. What is the measure of equal angles?
Answer» Question 170 Three angles of a quadrilateral are equal. The fourth angle is $120^{\circ}$ . What is the measure of equal angles?

Discussion

8.	Hemakshi reshaped a cone of height h cm and radius of its base r cm is into a sphere. Then, which of the following option is always correct?
Answer» Hemakshi reshaped a cone of height h cm and radius of its base r cm is into a sphere. Then, which of the following option is always correct?

Discussion

9.	If the point (2,a) lies on the line 2x-y=3 then 'a' is equal to
Answer» If the point (2,a) lies on the line 2x-y=3 then 'a' is equal to

Discussion

10.	The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.
Answer» The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.

Discussion

11.	Two different dice are thrown together. Find the probability that the numbers obtained have (i) even sum, and (ii) even product.
Answer» Two different dice are thrown together. Find the probability that the numbers obtained have (i) even sum, and (ii) even product.

Discussion

12.	Question 17 A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h(1+tan α cot β)m.
Answer» Question 17 A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be $α$ and $β$ , respectively. Prove that the height of the other house is $h (1 + t a n α c o t β) m$ .

Discussion

13.	Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. "Is not this interesting? Represent this situation algebracially and graphically.
Answer» Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. "Is not this interesting? Represent this situation algebracially and graphically.

Discussion

14.	A die is thrown once. The probability of getting an odd number greater than 3 is (a) 13 (b) 16 (c) 12 (d) 0
Answer» A die is thrown once. The probability of getting an odd number greater than 3 is (a) $\frac{1}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{2}$ (d) 0

Discussion

15.	A and B each has some money. If A gives Rs 30 to B, then B will have twice the money left with A. But, if B gives Rs 10 to A, then A will have thrice as much as is left with B. How much money does each have?
Answer» A and B each has some money. If A gives Rs 30 to B, then B will have twice the money left with A. But, if B gives Rs 10 to A, then A will have thrice as much as is left with B. How much money does each have?

Discussion

16.	For every integer a, a×1=1×a=a. This shows
Answer» For every integer $a$ , $a \times 1 = 1 \times a = a$ . This shows

Discussion

17.	A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.
Answer» A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Discussion

18.	Q. If two positive integer a and b are written as a=x3y2 and b=xy3 ; x and y are prime numbers, then find the HCF (a,b).
Answer» Q. If two positive integer a and b are written as a=x³y² and b=xy³ ; x and y are prime numbers, then find the HCF (a,b).

Discussion

19.	Solve each of the following systems of equations by the method of cross-multiplication: (a−b)x+(a+b)y=2a2−2b2 (a+b)(x+y)=4ab
Answer» Solve each of the following systems of equations by the method of cross-multiplication: $(a - b) x + (a + b) y = 2 a^{2} - 2 b^{2}$ $(a + b) (x + y) = 4 a b$

19.

Solve each of the following systems of equations by the method of cross-multiplication: (a−b)x+(a+b)y=2a2−2b2 (a+b)(x+y)=4ab

Answer»

Solve each of the following systems of equations by the method of cross-multiplication:

$(a - b) x + (a + b) y = 2 a^{2} - 2 b^{2}$

$(a + b) (x + y) = 4 a b$

Discussion

20.	If point P lies on the line y = 2, then what is its x-coordinate?
Answer» If point P lies on the line y = 2, then what is its x-coordinate?

20.

If point P lies on the line y = 2, then what is its x-coordinate?

Answer»

If point P lies on the line y = 2, then what is its x-coordinate?

Discussion

21.	secA.cosec2A=tan2A+cot2A+2
Answer» $s e c^{A} . c o s e c^{2} A = t a n^{2} A + c o t^{2} A + 2$

Discussion

22.	Q.2 women and 5 men together finish a work in 4 days.3 women and 6 men can finish it in 3 days .find the time taken by 1 women and men to finish the work. please send different methods to do this solution thank u
Answer» Q.2 women and 5 men together finish a work in 4 days.3 women and 6 men can finish it in 3 days .find the time taken by 1 women and men to finish the work. please send different methods to do this solution thank u

Discussion

23.	Sakshi has a recurring deposit account in a bank for 5 years at 9% per annum simple interest. If she gets ₹51607.50 at the time of maturity, what was her monthly instalment?
Answer» Sakshi has a recurring deposit account in a bank for 5 years at 9% per annum simple interest. If she gets ₹51607.50 at the time of maturity, what was her monthly instalment?

Discussion

24.	Input: the in cot as he mix my Which of the following will be the third step for this input?
Answer» Input: the in cot as he mix my Which of the following will be the third step for this input?

24.

Input: the in cot as he mix my Which of the following will be the third step for this input?

Answer»

Input: the in cot as he mix my

Which of the following will be the third step for this input?

Discussion

25.	✓2 is a polynomial of degree (a)2 (b)0 (c)1 (d)½
Answer» ✓2 is a polynomial of degree (a)2 (b)0 (c)1 (d)½

Discussion

26.	Three different dice are thrown three times. What is the probability that they show different numbers only two times?
Answer» Three different dice are thrown three times. What is the probability that they show different numbers only two times?

Discussion

27.	Let z=−1+√3i2, where i=√−1, and r, s ϵ {1, 2, 3}. Let P=[(−z)rz2sz2szr] and I be the identity matrix of order 2. Then, the total number of ordered pairs (r, s) for which P2 = -I is ___
Answer» Let $z = \frac{- 1 + \sqrt{3} i}{2}$ , where $i = \sqrt{- 1}$ , and r, s $ϵ$ {1, 2, 3}. Let $P = [\begin{matrix} (- z)^{r} & z^{2 s} z^{2 s} & z^{r} \end{matrix}]$ and I be the identity matrix of order 2. Then, the total number of ordered pairs (r, s) for which $P^{2}$ = -I is ___

Discussion

28.	Evaluate ; if possible: (i)[32][20](ii)[1−2][−23−14](iii)[643−1][−13](iv)[643−1][−13] IF not possible Give a reason.
Answer» Evaluate ; if possible: $(i) [\begin{matrix} 3 & 2 \end{matrix}] [\begin{matrix} 20 \end{matrix}] (i i) [\begin{matrix} 1 & - 2 \end{matrix}] [\begin{matrix} - 2 & 3 - 1 & 4 \end{matrix}] (i i i) [\begin{matrix} 6 & 4 3 & - 1 \end{matrix}] [\begin{matrix} - 1 3 \end{matrix}] (i v) [\begin{matrix} 6 & 4 3 & - 1 \end{matrix}] [\begin{matrix} - 1 & 3 \end{matrix}]$ IF not possible Give a reason.

Discussion

29.	ABC is the right angled triangle with ∠ABC =90∘, The centre of the circle passing through ABC lies on _______.
Answer» ABC is the right angled triangle with $∠$ ABC $= 90^{\circ}$ , The centre of the circle passing through ABC lies on _______.

Discussion

30.	Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3.
Answer» Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3.

Discussion

31.	Draw a triangle with sides 6cm, 8cm and 10cm. Using a common vertex and with the 10cm side, construct a similar triangle with the ratio of corresponding sides 2:1.
Answer» Draw a triangle with sides 6cm, 8cm and 10cm. Using a common vertex and with the 10cm side, construct a similar triangle with the ratio of corresponding sides 2:1.

Discussion

32.	In the figure, PQ \|\| AB, CQ = 4.8 cm, QB = 3.6 cm and AB = 6.3 cm. If AP = x, length of AC in terms of x is .
Answer» In the figure, PQ \|\| AB, CQ = 4.8 cm, QB = 3.6 cm and AB = 6.3 cm. If AP = x, length of AC in terms of x is .

Discussion

33.	Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).
Answer» Find the least number that is divisible by all the numbers between $1$ and $10$ (both inclusive).

Discussion

34.	If the sides of a triangle are in the ratio 5:6:7 and its perimeter is 180 m, then find the sides of the triangle. [2 MARKS]
Answer» If the sides of a triangle are in the ratio 5:6:7 and its perimeter is 180 m, then find the sides of the triangle. [2 MARKS]

Discussion

35.	Show that the following points are the vertices of a square: (i) A(3, 2), B (0, 5), C(-3, 2) and D(0, -1) (ii) A(6, 2), B(2, 1), C(1, 5) and D(5, 6) (iii) A(0, -2), B(3, 1), C(0, 4) and D(-3, 1)
Answer» Show that the following points are the vertices of a square: (i) A(3, 2), B (0, 5), C(-3, 2) and D(0, -1) (ii) A(6, 2), B(2, 1), C(1, 5) and D(5, 6) (iii) A(0, -2), B(3, 1), C(0, 4) and D(-3, 1)

35.

Show that the following points are the vertices of a square: (i) A(3, 2), B (0, 5), C(-3, 2) and D(0, -1) (ii) A(6, 2), B(2, 1), C(1, 5) and D(5, 6) (iii) A(0, -2), B(3, 1), C(0, 4) and D(-3, 1)

Answer»

Show that the following points are the vertices of a square:

(i) A(3, 2), B (0, 5), C(-3, 2) and D(0, -1)
(ii) A(6, 2), B(2, 1), C(1, 5) and D(5, 6)
(iii) A(0, -2), B(3, 1), C(0, 4) and D(-3, 1)

Discussion

36.	When a coin tossed 10 times, the following outcomes are noted H, H, H, T, H, T, T, T, H, H The empirical probability of getting a head is (in decimal form) __
Answer» When a coin tossed 10 times, the following outcomes are noted H, H, H, T, H, T, T, T, H, H The empirical probability of getting a head is (in decimal form) __

36.

When a coin tossed 10 times, the following outcomes are noted H, H, H, T, H, T, T, T, H, H The empirical probability of getting a head is (in decimal form) __

Answer»

When a coin tossed 10 times, the following outcomes are noted

H, H, H, T, H, T, T, T, H, H

The empirical probability of getting a head is (in decimal form)

__

Discussion

37.	In the given figure, ST is parallel to QR. PS=3cm, PQ=8cm TR=10cm PT=?
Answer» In the given figure, ST is parallel to QR. PS=3cm, PQ=8cm TR=10cm PT=?

37.

In the given figure, ST is parallel to QR. PS=3cm, PQ=8cm TR=10cm PT=?

Answer»

In the given figure, ST is parallel to QR. PS=3cm, PQ=8cm TR=10cm PT=?

Discussion

38.	What is the LCM of (x2+5x+6) and (x2+7x+10)
Answer» What is the LCM of $(x^{2} + 5 x + 6)$ and $(x^{2} + 7 x + 10)$

Discussion

39.	Find the value of 'a', if (x-a) is a factor of x3−ax2+x+2.
Answer» Find the value of 'a', if (x-a) is a factor of $x^{3} - a x^{2} + x + 2.$

Discussion

40.	Find the sum to n terms of the AP: 5, 2, -1, -4, -7, ...
Answer» Find the sum to n terms of the AP: 5, 2, -1, -4, -7, ...

Discussion

41.	The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.
Answer» The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

Discussion

42.	How many of them are sitting between γ and β?
Answer» How many of them are sitting between $γ$ and $β$ ?

Discussion

43.	Find the solution set in log2(x−1)+log2(x−2)>1
Answer» Find the solution set in ${log}_{2} (x - 1) + {log}_{2} (x - 2) > 1$

Discussion

44.	A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115∘. Find the total area cleaned at each sweep of the blades.
Answer» A car has two wipers which do not overlap. Each wiper has a blade of length $25 c m$ sweeping through an angle of $115^{\circ}$ . Find the total area cleaned at each sweep of the blades.

Discussion

45.	Question 4 (i) The heights of 50 students, measured to the nearest centimeters, have been found to be as follows: 161150154165168161154162150151162164171165158154156172160170153159161170162165166168165164154152153156158162160161173166161159162167168159158153154159 (i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.
Answer» Question 4 (i) The heights of 50 students, measured to the nearest centimeters, have been found to be as follows: $\begin{matrix} 161 & 150 & 154 & 165 & 168 & 161 & 154 & 162 & 150 & 151 162 & 164 & 171 & 165 & 158 & 154 & 156 & 172 & 160 & 170 153 & 159 & 161 & 170 & 162 & 165 & 166 & 168 & 165 & 164 154 & 152 & 153 & 156 & 158 & 162 & 160 & 161 & 173 & 166 161 & 159 & 162 & 167 & 168 & 159 & 158 & 153 & 154 & 159 \end{matrix}$ (i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.

Discussion

46.	1−sinA1+sinA=(secA−tanA)2
Answer» $\frac{1 - s i n A}{1 + s i n A} = (s e c A - t a n A)^{2}$

Discussion

47.	The value of tan 60∘ is
Answer» The value of $tan$ $60^{\circ}$ is

Discussion

48.	Question 13 In a triangle ABC, D is the mid-point of side AC such that BD = 12 AC. Show that ∠ABC=90∘.
Answer» Question 13 In a triangle ABC, D is the mid-point of side AC such that BD = $\frac{1}{2}$ AC. Show that $∠ A B C = 90^{\circ}$ .

Discussion

49.	Question 84 Solve the following: The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.
Answer» Question 84 Solve the following: The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

49.

Question 84 Solve the following: The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Answer»

Question 84

Solve the following:

The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Discussion

50.	Question 1 (i) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) 2x2−3x+5=0
Answer» Question 1 (i) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) $2 x^{2} - 3 x + 5 = 0$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If A=[12−31] and B=[11−143] Find Matrix X, given that X-5A=3B

Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for 212 years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

Solve the following system of equations in R. 5x−1&lt;24,5x+1&gt;−24

The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term.

If a line segment AB is divided in the ratio m : n, both m and n should be ___ integers.

One family has been chosen out of 200 families having 3 children . What is the probability that there is at least one girl ?

Question 170 Three angles of a quadrilateral are equal. The fourth angle is 120∘. What is the measure of equal angles?

Hemakshi reshaped a cone of height h cm and radius of its base r cm is into a sphere. Then, which of the following option is always correct?

If the point (2,a) lies on the line 2x-y=3 then 'a' is equal to

The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.

Two different dice are thrown together. Find the probability that the numbers obtained have (i) even sum, and (ii) even product.

Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. "Is not this interesting? Represent this situation algebracially and graphically.

A die is thrown once. The probability of getting an odd number greater than 3 is (a) 13 (b) 16 (c) 12 (d) 0

A and B each has some money. If A gives Rs 30 to B, then B will have twice the money left with A. But, if B gives Rs 10 to A, then A will have thrice as much as is left with B. How much money does each have?

For every integer a, a×1=1×a=a. This shows

A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Q. If two positive integer a and b are written as a=x​​​​​​3​​y​​​​​​2 and b=xy​​​​​3 ; x and y are prime numbers, then find the HCF (a,b).

Solve each of the following systems of equations by the method of cross-multiplication: (a−b)x+(a+b)y=2a2−2b2 (a+b)(x+y)=4ab

If point P lies on the line y = 2, then what is its x-coordinate?

secA.cosec2A=tan2A+cot2A+2

Q.2 women and 5 men together finish a work in 4 days.3 women and 6 men can finish it in 3 days .find the time taken by 1 women and men to finish the work. please send different methods to do this solution thank u

Sakshi has a recurring deposit account in a bank for 5 years at 9% per annum simple interest. If she gets ₹51607.50 at the time of maturity, what was her monthly instalment?

Input: the in cot as he mix my Which of the following will be the third step for this input?

✓2 is a polynomial of degree (a)2 (b)0 (c)1 (d)½

Three different dice are thrown three times. What is the probability that they show different numbers only two times?

Let z=−1+√3i2, where i=√−1, and r, s ϵ {1, 2, 3}. Let P=[(−z)rz2sz2szr] and I be the identity matrix of order 2. Then, the total number of ordered pairs (r, s) for which P2 = -I is ___

Evaluate ; if possible: (i)[32][20](ii)[1−2][−23−14](iii)[643−1][−13](iv)[643−1][−13] IF not possible Give a reason.

ABC is the right angled triangle with ∠ABC =90∘, The centre of the circle passing through ABC lies on _______.

Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3.

Draw a triangle with sides 6cm, 8cm and 10cm. Using a common vertex and with the 10cm side, construct a similar triangle with the ratio of corresponding sides 2:1.

In the figure, PQ || AB, CQ = 4.8 cm, QB = 3.6 cm and AB = 6.3 cm. If AP = x, length of AC in terms of x is .

Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

If the sides of a triangle are in the ratio 5:6:7 and its perimeter is 180 m, then find the sides of the triangle. [2 MARKS]

Show that the following points are the vertices of a square: (i) A(3, 2), B (0, 5), C(-3, 2) and D(0, -1) (ii) A(6, 2), B(2, 1), C(1, 5) and D(5, 6) (iii) A(0, -2), B(3, 1), C(0, 4) and D(-3, 1)

When a coin tossed 10 times, the following outcomes are noted H, H, H, T, H, T, T, T, H, H The empirical probability of getting a head is (in decimal form) __

In the given figure, ST is parallel to QR. PS=3cm, PQ=8cm TR=10cm PT=?

What is the LCM of (x2+5x+6) and (x2+7x+10)

Find the value of 'a', if (x-a) is a factor of x3−ax2+x+2.

Find the sum to n terms of the AP: 5, 2, -1, -4, -7, ...

The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

How many of them are sitting between γ and β?

Find the solution set in log2(x−1)+log2(x−2)&gt;1

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115∘. Find the total area cleaned at each sweep of the blades.

1−sinA1+sinA=(secA−tanA)2

The value of tan 60∘ is

Question 13 In a triangle ABC, D is the mid-point of side AC such that BD = 12 AC. Show that ∠ABC=90∘.

Question 84 Solve the following: The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Question 1 (i) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) 2x2−3x+5=0

Solve the following system of equations in R. 5x−1<24,5x+1>−24

Q. If two positive integer a and b are written as a=x3y2 and b=xy3 ; x and y are prime numbers, then find the HCF (a,b).

Find the solution set in log2(x−1)+log2(x−2)>1