32581 + Interview Questions in Mathematics

1.	If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are(a) (−6, 7) (b) (6, −7) (c) (6, 7) (d) (−6,−7) [CBSE 2012]
Answer» If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are (a) (−6, 7) (b) (6, −7) (c) (6, 7) (d) (−6,−7) [CBSE 2012]

Discussion

2.	Solve the equation 3a^2 x^2 +8abx + 4b^2 =0, by factorization method
Answer» Solve the equation 3a^2 x^2 +8abx + 4b^2 =0, by factorization method

Discussion

3.	If acosθ+bsinθ=4 and asinθ−bcosθ=3, then a2+b2=
Answer» If $a c o s θ + b s i n θ = 4$ and $a s i n θ - b c o s θ = 3$ , then $a^{2} + b^{2} =$

Discussion

4.	Match the following shaded portions of venn diagram representation of two sets A,B.
Answer» Match the following shaded portions of venn diagram representation of two sets $A, B$ .

Discussion

5.	Find the volume and surface area of a pyramid with height 3√2 cm and a square base with sides all 6 cm in length [4 MARKS]
Answer» Find the volume and surface area of a pyramid with height $3 \sqrt{2} c m$ and a square base with sides all 6 cm in length [4 MARKS]

Discussion

6.	Find the smallest positive integer which when divided by 3 ,7, 11 leaves remainder 1, 6, 5 respectively
Answer» Find the smallest positive integer which when divided by 3 ,7, 11 leaves remainder 1, 6, 5 respectively

Discussion

7.	In a right angled ΔABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.
Answer» In a right angled $Δ$ ABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.

7.

In a right angled ΔABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.

Answer»

In a right angled $Δ$ ABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.

Discussion

8.	Find the sumof 2n terms of the series whose every enen term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.
Answer» Find the sumof 2n terms of the series whose every enen term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.

Discussion

9.	ntProve the determinant a b-c c-bn nt a-c b c-a = (a+b-c)(b+c-a)(c+a-b)n nt a-b b-a c n
Answer» ntProve the determinant a b-c c-bn nt a-c b c-a = (a+b-c)(b+c-a)(c+a-b)n nt a-b b-a c n

Discussion

10.	The point P divide the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?
Answer» The point P divide the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?

Discussion

11.	What is D in quadratic polynomial?Why and how D>0,D=0,D
Answer» What is D in quadratic polynomial? Why and how D>0,D=0,D<0?

Discussion

12.	A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many litres of water can the bucket hold ? (Take π = 227) __
Answer» A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many litres of water can the bucket hold ? (Take $π$ = $\frac{22}{7}$ ) __

Discussion

13.	The number of terms from 1 to 1000 divisible by 7 are
Answer» The number of terms from 1 to 1000 divisible by 7 are

Discussion

14.	The probability of picking the letter K if you pick a random letter from the word TREKKING is x4. x is ___.
Answer» The probability of picking the letter K if you pick a random letter from the word TREKKING is $\frac{x}{4}$ . x is ___.

Discussion

15.	Question 1Match the AP’s given in column A with suitable common differences given in column B. Column A Column B(A1)2,−2,−6,−10,. . . .(B1)23(A2)a=−18, n=10, an=0(B2)−5(A3)a=0, a10=6(B3)4(A4)a2=13, a4=3(B4)−4 (B5)2 (B6)12 (B7)5
Answer» Question 1 Match the AP’s given in column A with suitable common differences given in column B. $\begin{matrix} C o l u m n A & C o l u m n B (A_{1}) & 2, - 2, - 6, - 10, . . . . & (B_{1}) & \frac{2}{3} (A_{2}) & a = - 18, n = 10, a_{n} = 0 & (B_{2}) & - 5 (A_{3}) & a = 0, a_{10} = 6 & (B_{3}) & 4 (A_{4}) & a_{2} = 13, a_{4} = 3 & (B_{4}) & - 4 (B_{5}) & 2 (B_{6}) & \frac{1}{2} (B_{7}) & 5 \end{matrix}$

Discussion

16.	Which of the following has to pay the Sales tax?
Answer» Which of the following has to pay the Sales tax?

Discussion

17.	Question 1ΔABC with vertices A(- 2,0), B(2,0) and C(0,2) is similar to ΔDEF with vertices D(-4, 0), E(4,0) and F(0,4). State true or false and justify your answer.
Answer» Question 1 $Δ$ ABC with vertices A(- 2,0), B(2,0) and C(0,2) is similar to $Δ$ DEF with vertices D(-4, 0), E(4,0) and F(0,4). State true or false and justify your answer.

Discussion

18.	1+tan2A1+cot2A=[1 mark]
Answer» $\frac{1 + {tan}^{2} A}{1 + {cot}^{2} A} =$ [1 mark]

Discussion

19.	The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is
Answer» The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

Discussion

20.	The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x+y=1 are(a) y+2=0, 3x–y–2–33=0(b) x–2=0, 3x–y+2+33=0(c) 3x–y–2±33=0(d) none of these
Answer» The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line $\sqrt{3} x + y = 1$ are (a) $y + 2 = 0, \sqrt{3} x - y - 2 - 3 \sqrt{3} = 0$ (b) $x - 2 = 0, \sqrt{3} x - y + 2 + 3 \sqrt{3} = 0$ (c) $\sqrt{3} x - y - 2 \pm 3 \sqrt{3} = 0$ (d) none of these

Discussion

21.	A plumbline (sahul) is the combination of (a) a hemisphere and a cone (b) a cylinder and a cone (c) a cylinder and frustum of a cone (d) a cylinder and a sphere
Answer» A plumbline (sahul) is the combination of (a) a hemisphere and a cone (b) a cylinder and a cone (c) a cylinder and frustum of a cone (d) a cylinder and a sphere

21.

A plumbline (sahul) is the combination of (a) a hemisphere and a cone (b) a cylinder and a cone (c) a cylinder and frustum of a cone (d) a cylinder and a sphere

Answer»

A plumbline (sahul) is the combination of

(a) a hemisphere and a cone

(b) a cylinder and a cone

(c) a cylinder and frustum of a cone

(d) a cylinder and a sphere

Discussion

22.	Pramod deposits Rs 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.
Answer» Pramod deposits Rs 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.

Discussion

23.	Correct the spellings.1. Itaaly2. Arabee Saoudit3. Américue4. Angletaire5. Shine
Answer» Correct the spellings. 1. Itaaly 2. Arabee Saoudit 3. Américue 4. Angletaire 5. Shine

Discussion

24.	If A={5,6,9,11},B={9,10} let a R b means a<b.a belongs to A(a,b ) belongs to R, b belongs to B then the domain of the sets is {5,6,9,11}am I correct?
Answer» If A={5,6,9,11},B={9,10} let a R b means a<b.a belongs to A(a,b ) belongs to R, b belongs to B then the domain of the sets is {5,6,9,11}am I correct?

Discussion

25.	In △OAB, E is the mid point of −−→AB and F is point on −−→OA such that −−→OF=2−−→FA. If C is the point of intersection of −−→OE and −−→BF, then which of the following is/are correct ?
Answer» In $△ O A B,$ $E$ is the mid point of $- - \to A B$ and $F$ is point on $- - \to O A$ such that $- - \to O F = 2 - - \to F A .$ If $C$ is the point of intersection of $- - \to O E$ and $- - \to B F,$ then which of the following is/are correct ?

Discussion

26.	Question 3ABCD is a rhombus such that ∠ACB=40∘, then ∠ADB is(a) 40∘ (b) 45∘(c) 50∘(d) 60∘
Answer» Question 3 ABCD is a rhombus such that $∠ A C B = 40^{\circ}$ , then $∠ A D B$ is (a) $40^{\circ}$ (b) $45^{\circ}$ (c) $50^{\circ}$ (d) $60^{\circ}$

Discussion

27.	If }α and }β are the roots of the equation }x^2+6x+λ=0 and }3α+2β=-20, then }λ=
Answer» If }α and }β are the roots of the equation }x^2+6x+λ=0 and }3α+2β=-20, then }λ=

Discussion

28.	ntThree concentric spherical shells have radii a,b,c respectively (a
Answer» ntThree concentric spherical shells have radii a,b,c respectively (a

Discussion

29.	In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.
Answer» In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

29.

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

Answer»

In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

Discussion

30.	A cylindrical jar of radius 12 cm contains oil. Iron spheres each of radius 3 cm are immersed in the oil. How many such spheres are needed to raise the oil by 4 cm?
Answer» A cylindrical jar of radius $12 c m$ contains oil. Iron spheres each of radius $3 c m$ are immersed in the oil. How many such spheres are needed to raise the oil by $4 c m$ ?

Discussion

31.	In the given figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. AE intersects BC in F. Prove that(i) ar (Δ BDE) = 14 ar (Δ ABC)(ii) ar (Δ BDE) = 12 ar (Δ BAE)(iii) ar (Δ BFE) =ar (Δ AFD)(iv) ar (ΔABC) = 2 ar (Δ BEC)(v) ar (Δ FED) = 18 ar (Δ AFC)(vi) ar (Δ BFE) = 2 ar (EFD)
Answer» In the given figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. AE intersects BC in F. Prove that (i) ar (Δ BDE) = $\frac{1}{4}$ ar (Δ ABC) (ii) ar (Δ BDE) = $\frac{1}{2}$ ar (Δ BAE) (iii) ar (Δ BFE) =ar (Δ AFD) (iv) ar (ΔABC) = 2 ar (Δ BEC) (v) ar (Δ FED) = $\frac{1}{8}$ ar (Δ AFC) (vi) ar (Δ BFE) = 2 ar (EFD)

Discussion

32.	If PA and PB are two tangents drawn from an external point P to a circle such that PA = 5 cm and ∠APB = 60°, then the length of chord AB is ________.
Answer» If PA and PB are two tangents drawn from an external point P to a circle such that PA = 5 cm and ∠APB = 60°, then the length of chord AB is ________.

Discussion

33.	If tan−1(√1+x2−1x)=4, then x is equal to
Answer» If ${tan}^{- 1} (\frac{\sqrt{1 + x^{2}} - 1}{x}) = 4,$ then $x$ is equal to

Discussion

34.	Question 3For what values of a and b will the following pair of linear equations have infinitely many solutions?x + 2y = 1(a - b)x + (a + b)y = a + b - 2
Answer» Question 3 For what values of a and b will the following pair of linear equations have infinitely many solutions? x + 2y = 1 (a - b)x + (a + b)y = a + b - 2

Discussion

35.	In the adjacent figure, If AB = 12 cm, BC = 8 cm and AC = 10 cm, then AD =(a) 5 cm(b) 4 cm(c) 6 cm(d) 7 cm
Answer» In the adjacent figure, If AB = 12 cm, BC = 8 cm and AC = 10 cm, then AD = (a) 5 cm (b) 4 cm (c) 6 cm (d) 7 cm

Discussion

36.	evaluate lim x-->1 sin -1(x^3-1)/tan_1(x^2-1)
Answer» evaluate lim x-->1 sin -1(x^3-1)/tan_1(x^2-1)

Discussion

37.	Question 12 To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80∘ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π=3.14)
Answer» Question 12 To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. $(U s e π = 3.14)$

Discussion

38.	The line ax+by+c=0, is parallel to x axis when a = .
Answer» The line $a x + b y + c = 0,$ is parallel to $x$ axis when $a$ = .

Discussion

39.	Find the value of tan 60 geometrically please
Answer» Find the value of tan 60 geometrically please

Discussion

40.	If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=(a) −2, 4(b) −2, −4(c) 2, −4(d) 2, 4
Answer» If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y= (a) −2, 4 (b) −2, −4 (c) 2, −4 (d) 2, 4

Discussion

41.	Question 2Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.
Answer» Question 2 Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.

Discussion

42.	The 5th term of an arithmetic sequence is 11 and its 12th term is 32. What are its first three terms?
Answer» The 5^th term of an arithmetic sequence is 11 and its 12^th term is 32. What are its first three terms?

Discussion

43.	In a similar triangle,I. The corresponding angles are equal.II. The corresponding sides are always equal.III. The corresponding sides are always proportional.
Answer» In a similar triangle, I. The corresponding angles are equal. II. The corresponding sides are always equal. III. The corresponding sides are always proportional.

43.

In a similar triangle,I. The corresponding angles are equal.II. The corresponding sides are always equal.III. The corresponding sides are always proportional.

Answer»

In a similar triangle,

I. The corresponding angles are equal.

II. The corresponding sides are always equal.

III. The corresponding sides are always proportional.

Discussion

44.	One angle of a right angled triangle is 30° and its hypotenuse is 4 centimetres. What is its area?
Answer» One angle of a right angled triangle is 30° and its hypotenuse is 4 centimetres. What is its area?

Discussion

45.	If two circles touches each other internally then they have ____ common tangent/tangents.
Answer» If two circles touches each other internally then they have ____ common tangent/tangents.

Discussion

46.	Which of the following is a linear equation ?
Answer» Which of the following is a linear equation ?

Discussion

47.	A journey of 192 km between two cities takes 2 hours less by a fast train than by a slow train .If the average speed of the slow train is 16km/h less than that of a fast train .Find the average speed of each train
Answer» A journey of 192 km between two cities takes 2 hours less by a fast train than by a slow train .If the average speed of the slow train is 16km/h less than that of a fast train .Find the average speed of each train

Discussion

48.	An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.
Answer» An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.

Discussion

49.	Solve the following pair of linear equations by the substitution method.
Answer» Solve the following pair of linear equations by the substitution method.

49.

Solve the following pair of linear equations by the substitution method.

Answer»

Solve the following pair of linear equations by the substitution method.

Discussion

50.	{ †ext { If } \operatorname { cos } ^ { 2 } θ + 2 \operatorname { sin } ^ { 2 } θ + 3 \operatorname { cos } ^ { 2 } θ + 4 \operatorname { sin } ^ { 2 } θ + } { ( 200 †ext { terms } ) = 10025 †ext { , where } θ †ext { is acute, then } } { †ext { ealue of } \operatorname { sin } θ - \operatorname { cos } θ †ext { is }
Answer» { †ext { If } \operatorname { cos } ^ { 2 } θ + 2 \operatorname { sin } ^ { 2 } θ + 3 \operatorname { cos } ^ { 2 } θ + 4 \operatorname { sin } ^ { 2 } θ + } { ( 200 †ext { terms } ) = 10025 †ext { , where } θ †ext { is acute, then } } { †ext { ealue of } \operatorname { sin } θ - \operatorname { cos } θ †ext { is }

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are(a) (−6, 7) (b) (6, −7) (c) (6, 7) (d) (−6,−7) [CBSE 2012]

Solve the equation 3a^2 x^2 +8abx + 4b^2 =0, by factorization method

If acosθ+bsinθ=4 and asinθ−bcosθ=3, then a2+b2=

Match the following shaded portions of venn diagram representation of two sets A,B.

Find the volume and surface area of a pyramid with height 3√2 cm and a square base with sides all 6 cm in length [4 MARKS]

Find the smallest positive integer which when divided by 3 ,7, 11 leaves remainder 1, 6, 5 respectively

In a right angled ΔABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.

Find the sumof 2n terms of the series whose every enen term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.

ntProve the determinant a b-c c-bn nt a-c b c-a = (a+b-c)(b+c-a)(c+a-b)n nt a-b b-a c n

The point P divide the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?

What is D in quadratic polynomial?Why and how D>0,D=0,D

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many litres of water can the bucket hold ? (Take π = 227) __

The number of terms from 1 to 1000 divisible by 7 are

The probability of picking the letter K if you pick a random letter from the word TREKKING is x4. x is ___.

Question 1Match the AP’s given in column A with suitable common differences given in column B. Column A Column B(A1)2,−2,−6,−10,. . . .(B1)23(A2)a=−18, n=10, an=0(B2)−5(A3)a=0, a10=6(B3)4(A4)a2=13, a4=3(B4)−4 (B5)2 (B6)12 (B7)5

Which of the following has to pay the Sales tax?

Question 1ΔABC with vertices A(- 2,0), B(2,0) and C(0,2) is similar to ΔDEF with vertices D(-4, 0), E(4,0) and F(0,4). State true or false and justify your answer.

1+tan2A1+cot2A=[1 mark]

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x+y=1 are(a) y+2=0, 3x–y–2–33=0(b) x–2=0, 3x–y+2+33=0(c) 3x–y–2±33=0(d) none of these

A plumbline (sahul) is the combination of (a) a hemisphere and a cone (b) a cylinder and a cone (c) a cylinder and frustum of a cone (d) a cylinder and a sphere

Pramod deposits Rs 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.

Correct the spellings.1. Itaaly2. Arabee Saoudit3. Américue4. Angletaire5. Shine

If A={5,6,9,11},B={9,10} let a R b means a&lt;b.a belongs to A(a,b ) belongs to R, b belongs to B then the domain of the sets is {5,6,9,11}am I correct?

In △OAB, E is the mid point of −−→AB and F is point on −−→OA such that −−→OF=2−−→FA. If C is the point of intersection of −−→OE and −−→BF, then which of the following is/are correct ?

Question 3ABCD is a rhombus such that ∠ACB=40∘, then ∠ADB is(a) 40∘ (b) 45∘(c) 50∘(d) 60∘

If }α and }β are the roots of the equation }x^2+6x+λ=0 and }3α+2β=-20, then }λ=

ntThree concentric spherical shells have radii a,b,c respectively (a

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

A cylindrical jar of radius 12 cm contains oil. Iron spheres each of radius 3 cm are immersed in the oil. How many such spheres are needed to raise the oil by 4 cm?

If PA and PB are two tangents drawn from an external point P to a circle such that PA = 5 cm and ∠APB = 60°, then the length of chord AB is ________.

If tan−1(√1+x2−1x)=4, then x is equal to

Question 3For what values of a and b will the following pair of linear equations have infinitely many solutions?x + 2y = 1(a - b)x + (a + b)y = a + b - 2

In the adjacent figure, If AB = 12 cm, BC = 8 cm and AC = 10 cm, then AD =(a) 5 cm(b) 4 cm(c) 6 cm(d) 7 cm

evaluate lim x-->1 sin -1(x^3-1)/tan_1(x^2-1)

Question 12 To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80∘ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π=3.14)

The line ax+by+c=0, is parallel to x axis when a = .

Find the value of tan 60 geometrically please ​​​​​​

If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=(a) −2, 4(b) −2, −4(c) 2, −4(d) 2, 4

Question 2Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.

The 5th term of an arithmetic sequence is 11 and its 12th term is 32. What are its first three terms?

In a similar triangle,I. The corresponding angles are equal.II. The corresponding sides are always equal.III. The corresponding sides are always proportional.

One angle of a right angled triangle is 30° and its hypotenuse is 4 centimetres. What is its area?

If two circles touches each other internally then they have ____ common tangent/tangents.

Which of the following is a linear equation ?

A journey of 192 km between two cities takes 2 hours less by a fast train than by a slow train .If the average speed of the slow train is 16km/h less than that of a fast train .Find the average speed of each train

An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.

Solve the following pair of linear equations by the substitution method.

If A={5,6,9,11},B={9,10} let a R b means a<b.a belongs to A(a,b ) belongs to R, b belongs to B then the domain of the sets is {5,6,9,11}am I correct?

Find the value of tan 60 geometrically please