32581 + Interview Questions in Mathematics

1.	How to factorise 3x2 - 3√2x + 1.
Answer» How to factorise 3x² - 3√2x + 1.

1.

How to factorise 3x2 - 3√2x + 1.

Answer»

How to factorise

3x² - 3√2x + 1.

2.	Find the smallest number which when divided by 23, 45, 5, 27 and 48 leaves a remainder 7.
Answer» Find the smallest number which when divided by 23, 45, 5, 27 and 48 leaves a remainder 7.

Discussion

3.	Which of the following are Pair of Linear Equation in two variables?
Answer» Which of the following are Pair of Linear Equation in two variables?

Discussion

4.	If cos 3θ=√32, 0° < 3θ < 90°, then find the value of θ.
Answer» $If c o s 3 θ = \frac{\sqrt{3}}{2}$ , 0° < $3 θ$ < 90°, then find the value of $θ$ .

Discussion

5.	Question 4 Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
Answer» Question 4 Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

Discussion

6.	Which of the following has a terminating decimal ?
Answer» Which of the following has a terminating decimal ?

Discussion

7.	Which of following is not a quadratic equation:
Answer» Which of following is not a quadratic equation:

Discussion

8.	Find the two consecutive positive integers, such that the sum of their squares is 365.
Answer» Find the two consecutive positive integers, such that the sum of their squares is 365.

Discussion

9.	Question 10 (ii) Show that a1,a2……,an,…… form an AP where an is defined as below. (ii) an=9−5n Also find the sum of the first 15 terms in each case.
Answer» Question 10 (ii) Show that $a_{1}, a_{2} \dots \dots, a_{n}, \dots \dots$ form an AP where $a_{n}$ is defined as below. (ii) $a_{n} = 9 - 5 n$ Also find the sum of the first 15 terms in each case.

Discussion

10.	A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.
Answer» A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

Discussion

11.	The sum of first 10 terms of the G.P 3, 6, 12, 24 .......... is __.
Answer» The sum of first 10 terms of the G.P 3, 6, 12, 24 .......... is __.

Discussion

12.	Simplify the expression: cosecθcotθ
Answer» Simplify the expression: $\frac{c o s e c θ}{c o t θ}$

Discussion

13.	Factories: 1/3x2-2x-9
Answer» Factories: 1/3x²-2x-9

Discussion

14.	The trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle is .
Answer» The trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle is .

Discussion

15.	In given figure △ ABC and △ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54cm2. The area of △ DEF is ___ cm2.
Answer» In given figure $△$ ABC and $△$ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54 $c m^{2}$ . The area of $△$ DEF is ___ ${c m}^{2}$ .

15.

In given figure △ ABC and △ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54cm2. The area of △ DEF is ___ cm2.

Answer»

In given figure $△$ ABC and $△$ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54 $c m^{2}$ . The area of $△$ DEF is ___ ${c m}^{2}$ .

Discussion

16.	The number of proper subsets of the set {1, 2, 3} is
Answer» The number of proper subsets of the set {1, 2, 3} is

Discussion

17.	If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
Answer» If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?

17.

If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?

Answer»

If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?

Discussion

18.	Question 3 (iv) In an AP: (iv) Given a3=15,S10=125, find d and a10.
Answer» Question 3 (iv) In an AP: (iv) Given $a_{3} = 15, S_{10} = 125$ , find d and $a_{10}$ .

Discussion

19.	Question 1 (iii) Find the distance between the following pairs of points: (iii) (a, b), (− a, − b)
Answer» Question 1 (iii) Find the distance between the following pairs of points: (iii) (a, b), (− a, − b)

Discussion

20.	Question 3 The distance of the point P( - 6, 8) from the origin is: (A) 8 (B) 2√7 (C) 10 (D) 6
Answer» Question 3 The distance of the point P( - 6, 8) from the origin is: (A) 8 (B) $2 \sqrt{7}$ (C) 10 (D) 6

Discussion

21.	Find the discriminant of the quadratic equation 3x2–5x+2=0 and find the nature of their roots.
Answer» Find the discriminant of the quadratic equation $3 x^{2} - 5 x + 2 = 0$ and find the nature of their roots.

Discussion

22.	In the given figure, find area of the unshaded portion within the rectangle (Take π = 3.14)
Answer» In the given figure, find area of the unshaded portion within the rectangle (Take π = 3.14)

22.

In the given figure, find area of the unshaded portion within the rectangle (Take π = 3.14)

Answer»

In the given figure, find area of the unshaded portion within the rectangle (Take π = 3.14)

Discussion

23.	Question 1 (ii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (ii) 3x2−4√3x+4=0
Answer» Question 1 (ii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (ii) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Discussion

24.	Question 2 In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Answer» Question 2 In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Discussion

25.	In a school, students decided to plant trees in and around the school to reduce air polution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the studetns.
Answer» In a school, students decided to plant trees in and around the school to reduce air polution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the studetns.

Discussion

26.	If p=ax.by.cz and q=3x.b4.5z where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?
Answer» If $p = a^{x} . b^{y} . c^{z}$ and $q = 3^{x} . b^{4} {.5}^{z}$ where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

Discussion

27.	Find the value of α for which the equation (α−12)x2+2(α−12)x+2=0 has equal roots.
Answer» Find the value of $α$ for which the equation $(α - 12) x^{2} + 2 (α - 12) x + 2 = 0$ has equal roots.

Discussion

28.	Construct any two similar triangles with the ratio of corresponding sides 7:3 and prove that the triangles are similar.
Answer» Construct any two similar triangles with the ratio of corresponding sides 7:3 and prove that the triangles are similar.

Discussion

29.	Find the lengths of the medians AD and BE of △ ABC whose vertices are A(7, -3), B(5, 3)and C(3, -1).
Answer» Find the lengths of the medians AD and BE of $△$ ABC whose vertices are A(7, -3), B(5, 3)and C(3, -1).

Discussion

30.	Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 178
Answer» Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{17}{8}$

Discussion

31.	In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2). ___
Answer» In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c m^{2}$ ). ___

31.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2). ___

Answer»

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c m^{2}$ ).

___

Discussion

32.	If A=45∘ Then, secA cotA –cosecA tanA =__
Answer» If A= $45^{\circ}$ Then, secA cotA –cosecA tanA =__

32.

If A=45∘ Then, secA cotA –cosecA tanA =__

Answer»

If A= $45^{\circ}$

Then, secA cotA –cosecA tanA =__

Discussion

33.	In the figure given below, if AB∥PQ, then, ∠ACX ___ ∠PRC.
Answer» In the figure given below, if $A B ∥ P Q$ , then, $∠ A C X$ ___ $∠ P R C$ .

33.

In the figure given below, if AB∥PQ, then, ∠ACX ___ ∠PRC.

Answer»

In the figure given below, if $A B ∥ P Q$ , then, $∠ A C X$ ___ $∠ P R C$ .

Discussion

34.	Find the zeroes of 4x2−4x−3 via factorization.
Answer» Find the zeroes of $4 x^{2} - 4 x - 3$ via factorization.

Discussion

35.	Verify whether x =1, y = 3 is a solution of 4x + 3y = 13
Answer» Verify whether x =1, y = 3 is a solution of 4x + 3y = 13

Discussion

36.	The are of △ABC with vertices A(3, 0), B(7, 0) and C(8, 4) is (a) 14 sq units (b) 28 sq units (c) 8 sq units (d) 6 sq units
Answer» The are of $△ A B C$ with vertices A(3, 0), B(7, 0) and C(8, 4) is (a) 14 sq units (b) 28 sq units (c) 8 sq units (d) 6 sq units

36.

The are of △ABC with vertices A(3, 0), B(7, 0) and C(8, 4) is (a) 14 sq units (b) 28 sq units (c) 8 sq units (d) 6 sq units

Answer»

The are of $△ A B C$ with vertices A(3, 0), B(7, 0) and C(8, 4) is

(a) 14 sq units (b) 28 sq units (c) 8 sq units (d) 6 sq units

Discussion

37.	The area enclosed between between the circumferences of two concentric circles is 2464 sq cm. If their radii are in the ratio 5:3 calculate: A) the area of outer circle B) the circumference of the inner circle. If a third circle is drawn, outside the larger circle, so that the area enclosed between this circle is twice the area enclosd between the given circles, claculate the area of the circles.
Answer» The area enclosed between between the circumferences of two concentric circles is 2464 sq cm. If their radii are in the ratio 5:3 calculate: A) the area of outer circle B) the circumference of the inner circle. If a third circle is drawn, outside the larger circle, so that the area enclosed between this circle is twice the area enclosd between the given circles, claculate the area of the circles.

Discussion

38.	What is the square root of 121(x−a)4(x−b)6(x−c)12?
Answer» What is the square root of $121 (x - a)^{4} (x - b)^{6} (x - c)^{12}$ ?

Discussion

39.	Solve each of the following systems of eqautions by the method of cross-multiplication: xa+yb=2 ax−by=a2−b2
Answer» Solve each of the following systems of eqautions by the method of cross-multiplication: $\frac{x}{a} + \frac{y}{b} = 2$ $a x - b y = a^{2} - b^{2}$

39.

Solve each of the following systems of eqautions by the method of cross-multiplication: xa+yb=2 ax−by=a2−b2

Answer»

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

$\frac{x}{a} + \frac{y}{b} = 2$

$a x - b y = a^{2} - b^{2}$

Discussion

40.	Sum of the roots of the equation is 4x−3(2x+3)+128=0
Answer» Sum of the roots of the equation is $4^{x} - 3 (2^{x + 3}) + 128 = 0$

Discussion

41.	The volume of the largest right circular cone that can be cut out from a cube of edge 7 cm is:
Answer» The volume of the largest right circular cone that can be cut out from a cube of edge 7 cm is:

Discussion

42.	The value of the variable for which the value of the polynomial in that variable is 0 is called __ of the polynomial.
Answer» The value of the variable for which the value of the polynomial in that variable is 0 is called __ of the polynomial.

Discussion

43.	If √3 is an irrational number, then which of the following is an irrational number?
Answer» If $\sqrt{3}$ is an irrational number, then which of the following is an irrational number?

Discussion

44.	In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠ QPT = 60o, find ∠ PRQ.
Answer» In the following figure, $P Q$ is a chord of a circle with centre $O$ and $P T$ is a tangent. If $∠$ $Q P T$ = $60^{o}$ , find $∠$ $P R Q$ .

44.

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠ QPT = 60o, find ∠ PRQ.

Answer»

In the following figure, $P Q$ is a chord of a circle with centre $O$ and $P T$ is a tangent. If $∠$ $Q P T$ = $60^{o}$ , find $∠$ $P R Q$ .

Discussion

45.	Solve each of the following systems of equations by the method of cross-multiplication: bx+cy=a+b ax(1a−b−1a+b)+cy(1b−a−1b+a)=2aa+b
Answer» Solve each of the following systems of equations by the method of cross-multiplication: $b x + c y = a + b$ $a x (\frac{1}{a - b} - \frac{1}{a + b}) + c y (\frac{1}{b - a} - \frac{1}{b + a}) = \frac{2 a}{a + b}$

45.

Solve each of the following systems of equations by the method of cross-multiplication: bx+cy=a+b ax(1a−b−1a+b)+cy(1b−a−1b+a)=2aa+b

Answer»

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

$b x + c y = a + b$

$a x (\frac{1}{a - b} - \frac{1}{a + b}) + c y (\frac{1}{b - a} - \frac{1}{b + a}) = \frac{2 a}{a + b}$

Discussion

46.	Find the value k for which each of the following systems of equations has a unique solution: 4x−5y=k,2x−3y=12.
Answer» Find the value $k$ for which each of the following systems of equations has a unique solution: $4 x - 5 y = k, 2 x - 3 y = 12.$

46.

Find the value k for which each of the following systems of equations has a unique solution: 4x−5y=k,2x−3y=12.

Answer»

Find the value $k$ for which each of the following systems of equations has a unique solution:

$4 x - 5 y = k, 2 x - 3 y = 12.$

Discussion

47.	A two-digit number is such that the product of its digits is 18.If 63 is subtracted from the number,the digits interchange their places.Find the number.
Answer» A two-digit number is such that the product of its digits is 18.If 63 is subtracted from the number,the digits interchange their places.Find the number.

Discussion

48.	Question 136 PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2 :3. Find ∠TPQ.
Answer» Question 136 PQRS is a rectangle. The perpendicular ST from S on PR divides $∠ S$ in the ratio 2 :3. Find $∠ T P Q$ .

Discussion

49.	If d,a and l denote the common difference, first and last terms respectively, then nth term from the end is ___________ .
Answer» If $d, a$ and $l$ denote the common difference, first and last terms respectively, then $n^{t h}$ term from the end is ___________ .

Discussion

50.	Question 6 Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 (Take π=3.14)
Answer» Question 6 Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 $(T a k e π = 3.14)$

50.

Question 6 Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 (Take π=3.14)

Answer»

Question 6

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 $(T a k e π = 3.14)$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How to factorise 3x2 - 3√2x + 1.

Find the smallest number which when divided by 23, 45, 5, 27 and 48 leaves a remainder 7.

Which of the following are Pair of Linear Equation in two variables?

If cos 3θ=√32, 0° &lt; 3θ &lt; 90°, then find the value of θ.

Question 4 Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

Which of the following has a terminating decimal ?

Which of following is not a quadratic equation:

Find the two consecutive positive integers, such that the sum of their squares is 365.

Question 10 (ii) Show that a1,a2……,an,…… form an AP where an is defined as below. (ii) an=9−5n Also find the sum of the first 15 terms in each case.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

The sum of first 10 terms of the G.P 3, 6, 12, 24 .......... is __.

Simplify the expression: cosecθcotθ

Factories: 1/3x2-2x-9

The trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle is .

In given figure △ ABC and △ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54cm2. The area of △ DEF is ___ cm2.

The number of proper subsets of the set {1, 2, 3} is

If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?

Question 3 (iv) In an AP: (iv) Given a3=15,S10=125, find d and a10.

Question 1 (iii) Find the distance between the following pairs of points: (iii) (a, b), (− a, − b)

Question 3 The distance of the point P( - 6, 8) from the origin is: (A) 8 (B) 2√7 (C) 10 (D) 6

Find the discriminant of the quadratic equation 3x2–5x+2=0 and find the nature of their roots.

In the given figure, find area of the unshaded portion within the rectangle (Take π = 3.14)

Question 1 (ii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (ii) 3x2−4√3x+4=0

Question 2 In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

If p=ax.by.cz and q=3x.b4.5z where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

Find the value of α for which the equation (α−12)x2+2(α−12)x+2=0 has equal roots.

Construct any two similar triangles with the ratio of corresponding sides 7:3 and prove that the triangles are similar.

Find the lengths of the medians AD and BE of △ ABC whose vertices are A(7, -3), B(5, 3)and C(3, -1).

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 178

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2). ___

If A=45∘ Then, secA cotA –cosecA tanA =__

In the figure given below, if AB∥PQ, then, ∠ACX ___ ∠PRC.

Find the zeroes of 4x2−4x−3 via factorization.

Verify whether x =1, y = 3 is a solution of 4x + 3y = 13

The are of △ABC with vertices A(3, 0), B(7, 0) and C(8, 4) is (a) 14 sq units (b) 28 sq units (c) 8 sq units (d) 6 sq units

What is the square root of 121(x−a)4(x−b)6(x−c)12?

Solve each of the following systems of eqautions by the method of cross-multiplication: xa+yb=2 ax−by=a2−b2

Sum of the roots of the equation is 4x−3(2x+3)+128=0

The volume of the largest right circular cone that can be cut out from a cube of edge 7 cm is:

The value of the variable for which the value of the polynomial in that variable is 0 is called __ of the polynomial.

If √3 is an irrational number, then which of the following is an irrational number?

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠ QPT = 60o, find ∠ PRQ.

Solve each of the following systems of equations by the method of cross-multiplication: bx+cy=a+b ax(1a−b−1a+b)+cy(1b−a−1b+a)=2aa+b

Find the value k for which each of the following systems of equations has a unique solution: 4x−5y=k,2x−3y=12.

A two-digit number is such that the product of its digits is 18.If 63 is subtracted from the number,the digits interchange their places.Find the number.

Question 136 PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2 :3. Find ∠TPQ.

If d,a and l denote the common difference, first and last terms respectively, then nth term from the end is ___________ .

Question 6 Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 (Take π=3.14)

If cos 3θ=√32, 0° < 3θ < 90°, then find the value of θ.