32581 + Interview Questions in Mathematics

1.	The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
Answer» The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m², what are the length and breadth of the hall?

Discussion

2.	In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27∘ then ∠QAR equals [CBSE 2012](a) 63∘(b) 117∘(c) 126∘(d) 153∘
Answer» In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27^∘ then ∠QAR equals [CBSE 2012] (a) 63^∘ (b) 117^∘ (c) 126^∘ (d) 153^∘

Discussion

3.	The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is __________.
Answer» The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is __________.

Discussion

4.

Choose the correct alternative answer for each of the following sub questions.(1) The sequence –10, –6, –2, 2,... (A) is an A.P., Reason d= –16 (B) is an A.P., Reason d= 4 (C) is an A.P., Reason d= –4 (D) is not an A.P. (2) First four terms of an A.P. are ....., whose first term is –2 and common difference is –2. (A) –2, 0, 2, 4 (B) –2, 4, –8, 16 (C) –2, –4, –6, –8 (D) –2, –4, –8, –16 (3) What is the sum of the first 30 natural numbers ? (A) 464 (B) 465 (C) 462 (D) 461 (4) For an given A.P. t7 = 4, d = –4, n = 101, then a = .... (A) 6 (B) 7 (C) 20 (D) 28 (5) For an given A.P. a = 3.5, d = 0, n = 101, then tn = .... (A) 0 (B) 3.5 (C) 103.5 (D) 14.5 (6) In an A.P. first two terms are –3, 4 then 21st term is ... (A) –143 (B) 143 (C) 137 (D) 17 (7) If for any A.P. d = 5 then t18 – t13 = .... (A) 5 (B) 20 (C) 25 (D) 30 (8) Sum of first five multuiples of 3 is... (A) 45 (B) 55 (C) 15 (D) 75 (9) 15, 10, 5,... In this A.P sum of first 10 terms is... (A) –75 (B) –125 (C) 75 (D) 125 (10) In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = .... (A) 42 (B) 38 (C) 21 (D) 19

Answer» Choose the correct alternative answer for each of the following sub questions.

(1) The sequence –10, –6, –2, 2,...

(A) is an A.P., Reason d= –16	(B) is an A.P., Reason d= 4
(C) is an A.P., Reason d= –4	(D) is not an A.P.

(2) First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.

(A) –2, 0, 2, 4	(B) –2, 4, –8, 16
(C) –2, –4, –6, –8	(D) –2, –4, –8, –16

(3) What is the sum of the first 30 natural numbers ?

(A) 464

(B) 465

(C) 462

(D) 461

(4) For an given A.P. t₇ = 4, d = –4, n = 101, then a = ....

(A) 6

(B) 7

(C) 20

(D) 28

(5) For an given A.P. a = 3.5, d = 0, n = 101, then t_n = ....

(A) 0

(B) 3.5

(C) 103.5

(D) 14.5

(6) In an A.P. first two terms are –3, 4 then 21^st term is ...

(A) –143

(B) 143

(C) 137

(D) 17

(7) If for any A.P. d = 5 then t₁₈ – t₁₃ = ....

(A) 5

(B) 20

(C) 25

(D) 30

(8) Sum of first five multuiples of 3 is...

(A) 45

(B) 55

(C) 15

(D) 75

(9) 15, 10, 5,... In this A.P sum of first 10 terms is...

(A) –75

(B) –125

(C) 75

(D) 125

(10) In an A.P. 1^st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

(A) 42

(B) 38

(C) 21

(D) 19

Discussion

5.	If the angles A B and C are in AP then find the value of cosB
Answer» If the angles A B and C are in AP then find the value of cosB

Discussion

6.	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

7.	An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°.Find the height of the chimney. [CBSE 2013C]
Answer» An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney. [CBSE 2013C]

Discussion

8.	If y=12(3x+7) is rewritten in the form ax + by + c = 0, which of the following is/are true regarding the values of a, b and c?
Answer» If $y = \frac{1}{2} (3 x + 7)$ is rewritten in the form ax + by + c = 0, which of the following is/are true regarding the values of a, b and c?

Discussion

9.	3I DHTV1I1Aright triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm.Find the volume of the solid so obtained.
Answer» 3I DHTV 1I1 Aright triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Discussion

10.	If 3cotθ=4, show that 1-tan2θ1+tan2θ=cos2θ-sin2θ.
Answer» If $3 \cot θ = 4$ , show that $\frac{(1 - \tan^{2} θ)}{(1 + \tan^{2} θ)} = (\cos^{2} θ - \sin^{2} θ)$ .

Discussion

11.	The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharma is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Answer» The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharma is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Discussion

12.	Find the number of terms of the AP 18,1512,13,....,−4912 and find the sum of all its terms.
Answer» Find the number of terms of the AP $18, 15 \frac{1}{2}, 13, . . . ., - 49 \frac{1}{2}$ and find the sum of all its terms.

Discussion

13.	Which among the following can be called as identity matrix/matrices.
Answer» Which among the following can be called as identity matrix/matrices.

Discussion

14.	Prove that the ratio of the perimeters of two similar triangles in the same as the ratio of their corresponding sides.
Answer» Prove that the ratio of the perimeters of two similar triangles in the same as the ratio of their corresponding sides.

Discussion

15.	The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z=0 and parallel to x axis isA) y-3z+6=0 B)3y-z+6=0C)y+3z+6=0 D) 3y-2z+6=0
Answer» The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z=0 and parallel to x axis is A) y-3z+6=0 B)3y-z+6=0 C)y+3z+6=0 D) 3y-2z+6=0

Discussion

16.	If α, β are the zeros of a polynomial such that α + β = 6 and αβ = 4 the write the polynomial. [CBSE 2010]
Answer» If α, β are the zeros of a polynomial such that α + β = 6 and αβ = 4 the write the polynomial. [CBSE 2010]

Discussion

17.	13.In an AP, a and b are first and last term resp.if AP has n+2 term, find the common difference af the AP.
Answer» 13.In an AP, a and b are first and last term resp.if AP has n+2 term, find the common difference af the AP.

Discussion

18.	From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h meters and the line joining the ships passes through the foot of the light house, show that the distance between the ship is h(tan α+tan β)tan α tan β metres.
Answer» From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be $α$ and $β$ . If the height of the light house be h meters and the line joining the ships passes through the foot of the light house, show that the distance between the ship is $\frac{h (t a n α + t a n β)}{t a n α t a n β}$ metres.

Discussion

19.	(i) A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number. [CBSE 2011](ii) A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears(a) a two-digit number(b) a number divisible by 5 [CBSE 2017]
Answer» (i) A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number. [CBSE 2011] (ii) A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (a) a two-digit number (b) a number divisible by 5 [CBSE 2017]

Discussion

20.	[[{{x}}]] is equal to (x€R)
Answer» [[{{x}}]] is equal to (x€R)

Discussion

21.	The area of a circle is 49 π cm2. Its circumference is (a) 7 πcm (b) 14 πcm (c) 21 πcm (d) 28 πcm
Answer» The area of a circle is 49 $π$ $c m^{2}$ . Its circumference is (a) 7 $π$ cm (b) 14 $π$ cm (c) 21 $π$ cm (d) 28 $π$ cm

21.

The area of a circle is 49 π cm2. Its circumference is (a) 7 πcm (b) 14 πcm (c) 21 πcm (d) 28 πcm

Answer»

The area of a circle is 49 $π$ $c m^{2}$ . Its circumference is

(a) 7 $π$ cm (b) 14 $π$ cm (c) 21 $π$ cm (d) 28 $π$ cm

Discussion

22.	D and E are points on equal sides AB and AC of isosceles triangle respectively and B,C,E and D are concyclic points. If O is point of intersection of CD and BE,then prove that AO bisects the line segment DE
Answer» D and E are points on equal sides AB and AC of isosceles triangle respectively and B,C,E and D are concyclic points. If O is point of intersection of CD and BE,then prove that AO bisects the line segment DE

Discussion

23.

With Goods and Services Tax (GST)Journalise the following transactions of Singh Enterprises, Delhi: 2017 June 1 June 2 June 3 June 4 June 11 June 13 June 17 June 20 June 27 June 30 Started business with cash Deposited cheque from Savings Account in firm's account Received cash from Ram Purchased goods for cash Sold goods to M/s. Hari Sales, Delhi Paid to Ramavtar Received from M/s. Hari Sales Bought furniture from S.R. Furnishers against Cash (including CGST and SGST) Paid rent Paid salary ₹ 50,000 2,00,000 50,000 15,000 12,000 40,000 10,000 22,400 28,000 50,000 CGST and SGST 6% each is levied on Intra-state sale and purchase.

Answer»

With Goods and Services Tax (GST)

Journalise the following transactions of Singh Enterprises, Delhi:

2017

June 1

June 2

June 3

June 4

June 11

June 13

June 17

June 20

June 27

June 30

Started business with cash

Deposited cheque from Savings Account in firm's account

Received cash from Ram

Purchased goods for cash

Sold goods to M/s. Hari Sales, Delhi

Paid to Ramavtar

Received from M/s. Hari Sales

Bought furniture from S.R. Furnishers against Cash (including CGST and SGST)

Paid rent

Paid salary

₹

50,000

2,00,000

50,000

15,000

12,000

40,000

10,000

22,400

28,000

50,000

CGST and SGST 6% each is levied on Intra-state sale and purchase.

Discussion

24.	Question 16 A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
Answer» Question 16 A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

Discussion

25.	A and B both have some pencils. if A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have?
Answer» A and B both have some pencils. if A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have?

Discussion

26.	Mark the correct alternative in the following question:The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is(a) 191 (b) 193 (c) 211 (d) none of these
Answer» Mark the correct alternative in the following question: The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is (a) 191 (b) 193 (c) 211 (d) none of these

Discussion

27.	The volume of a rectangular box (or cuboid) whose length, breadth and height are 7 cm, 3 cm and 3 cm respectively, is.
Answer» The volume of a rectangular box (or cuboid) whose length, breadth and height are 7 cm, 3 cm and 3 cm respectively, is.

Discussion

28.	In a right ∆ABC, right-angled at B, if tanA=1, then verify that 2sinA·cosA=1.
Answer» In a right $∆ ABC$ , right-angled at $B$ , if $tanA = 1$ , then verify that $2 sinA \cdot cosA = 1$ .

Discussion

29.	Which of the following are sure events?
Answer» Which of the following are sure events?

Discussion

30.	Mark the correct alternative in each of the following:Three biased coins were tossed 800 times simultaneously. The outcomes are given in the following table : Outcome : No head One Head Two Head Frequency : 120 280 xIf the probability of occurrence of two heads is thrice that of all heads, then the value of x.(a) 150(b) 240(c) 300(d) 340
Answer» Mark the correct alternative in each of the following: Three biased coins were tossed 800 times simultaneously. The outcomes are given in the following table : Outcome : No head One Head Two Head Frequency : 120 280 x If the probability of occurrence of two heads is thrice that of all heads, then the value of x. (a) 150 (b) 240 (c) 300 (d) 340

Discussion

31.	Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = ________.
Answer» Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = ________.

Discussion

32.	Let Xn = {1,2,3,….n) and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3. (For example, if n = 5, A can be ϕ, {2} or {1,5} among others). When n = 10, let the probability that 1ϵA be p and let the probability that 2ϵA be q. Then
Answer» Let $X_{n}$ = {1,2,3,….n) and let a subset A of $X_{n}$ be chosen so that every pair of elements of A differ by at least 3. (For example, if n = 5, A can be $ϕ$ , {2} or {1,5} among others). When n = 10, let the probability that $1 ϵ A$ be p and let the probability that $2 ϵ A$ be q. Then

Discussion

33.	In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find x
Answer» In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find x

Discussion

34.	In the following figure, If ABC is an equilateral triangle, then shaded area is equal to(a) π3-34r2(b) π3-32r2(c) π3+34r2(d) π3+3r2Figure
Answer» In the following figure, If ABC is an equilateral triangle, then shaded area is equal to (a) $(\frac{π}{3} - \frac{\sqrt{3}}{4}) r^{2}$ (b) $(\frac{π}{3} - \frac{\sqrt{3}}{2}) r^{2}$ (c) $(\frac{π}{3} + \frac{\sqrt{3}}{4}) r^{2}$ (d) $(\frac{π}{3} + \sqrt{3}) r^{2}$ Figure

Discussion

35.	Question 8 If 3 cot A = 43, check whether (1−tan2A)(1+tan2A)=cos2A−sin2A or not.
Answer» Question 8 If 3 cot A = $\frac{4}{3}$ , check whether $\frac{(1 - t a n^{2} A)}{(1 + t a n^{2} A)} = c o s^{2} A - s i n^{2} A$ or not.

Discussion

36.	The value of tan 10° tan 15° tan 75° tan 80° is(a) −1(b) 0(c) 1(d) None of these
Answer» The value of tan 10° tan 15° tan 75° tan 80° is (a) −1 (b) 0 (c) 1 (d) None of these

Discussion

37.	In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+ML=PN+MN.
Answer» In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+ML=PN+MN.

Discussion

38.	In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30o. The tangent at C intersects AB produced at D. Find /BDC.
Answer» In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30^o. The tangent at C intersects AB produced at D. Find /BDC.

38.

In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30o. The tangent at C intersects AB produced at D. Find /BDC.

Answer»

In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30^o. The tangent at C intersects AB produced at D. Find /BDC.

Discussion

39.	11. Prove that the tangent drawn at the mid point of an arc is parallel to the chord joining the mid points of the arc.
Answer» 11. Prove that the tangent drawn at the mid point of an arc is parallel to the chord joining the mid points of the arc.

Discussion

40.	19. Determine the height of a mountain, if the elevation of its top at unknown distance from the base is 45^° and at a distance 10km further off from the mountain along the same line , the angle of elevation is 30^° .
Answer» 19. Determine the height of a mountain, if the elevation of its top at unknown distance from the base is 45^° and at a distance 10km further off from the mountain along the same line , the angle of elevation is 30^° .

Discussion

41.

Question 106 State whether the statement is True or False. [(−32)÷8]÷2=−32÷[8÷2]

Answer»

Question 106

State whether the statement is True or False.

$[(- 32) \div 8] \div 2 = - 32 \div [8 \div 2]$

Discussion

42.	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.
Answer» 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

43.	If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.
Answer» If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

Discussion

44.	44. Find the maximum volume of a cone that can be fitted in a sphere of radius 7cm?
Answer» 44. Find the maximum volume of a cone that can be fitted in a sphere of radius 7cm?

Discussion

45.	Prove the following trigonometric identities.1-tan2 Acot2 A-1=tan2 A
Answer» Prove the following trigonometric identities. $\frac{1 - \tan^{2} A}{\cot^{2} A - 1} = \tan^{2} A$

Discussion

46.

Question 9 (iii)A right circular cylinder just encloses a sphere of radius r (see figure). Find:(iii) the ratio of the areas obtained in (i) and (ii).

Answer»

Question 9 (iii)

A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(iii) the ratio of the areas obtained in (i) and (ii).

Discussion

47.	Find the nature of the roots of the following quadratic equation. If the real roots exist, find them;2x2−6x+3=0
Answer» Find the nature of the roots of the following quadratic equation. If the real roots exist, find them; $2 x^{2} - 6 x + 3 = 0$

Discussion

48.	The value of cos 1° cos 2° cos 3° ..... cos 180° is(a) 1(b) 0(c) −1(d) None of these
Answer» The value of cos 1° cos 2° cos 3° ..... cos 180° is (a) 1 (b) 0 (c) −1 (d) None of these

Discussion

49.	When a = 0, b = -1, find the value of the given expression:2a2+b2+1
Answer» When a = 0, b = -1, find the value of the given expression: $2 a^{2} + b^{2} + 1$

Discussion

50.	If X¯1,X¯2,...,X¯k are the means of n group with n1,n2,...,nk number of observations respectively, then the mean X¯ of all the groups taken together is govern by (a) ∑i=1kni X¯i(b) 1n2∑i=1k ni X¯i(c) ∑i=1k ni X¯i∑i=1k ni(d) ∑i=1k ni X¯i2n
Answer» If ${\bar{X}}_{1}, {\bar{X}}_{2}, . . ., {\bar{X}}_{k}$ are the means of n group with n1,n2,...,nk number of observations respectively, then the mean $\bar{X}$ of all the groups taken together is govern by $(a) \sum_{i = 1}^{k} n_{i} {\bar{X}}_{i} (b) \frac{1}{n^{2}} \sum_{i = 1}^{k} n_{i} {\bar{X}}_{i} (c) \frac{\sum_{i = 1}^{k} n_{i} {\bar{X}}_{i}}{\sum_{i = 1}^{k} n_{i}} (d) \frac{\sum_{i = 1}^{k} n_{i} {\bar{X}}_{i}}{2_{n}}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?

In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27∘ then ∠QAR equals [CBSE 2012](a) 63∘(b) 117∘(c) 126∘(d) 153∘

The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is __________.

If the angles A B and C are in AP then find the value of cosB

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

An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°.Find the height of the chimney. [CBSE 2013C]

If y=12(3x+7) is rewritten in the form ax + by + c = 0, which of the following is/are true regarding the values of a, b and c?

3I DHTV1I1Aright triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm.Find the volume of the solid so obtained.

If 3cotθ=4, show that 1-tan2θ1+tan2θ=cos2θ-sin2θ.

The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharma is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Find the number of terms of the AP 18,1512,13,....,−4912 and find the sum of all its terms.

Which among the following can be called as identity matrix/matrices.

Prove that the ratio of the perimeters of two similar triangles in the same as the ratio of their corresponding sides.

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z=0 and parallel to x axis isA) y-3z+6=0 B)3y-z+6=0C)y+3z+6=0 D) 3y-2z+6=0

If α, β are the zeros of a polynomial such that α + β = 6 and αβ = 4 the write the polynomial. [CBSE 2010]

13.In an AP, a and b are first and last term resp.if AP has n+2 term, find the common difference af the AP.

[[{{x}}]] is equal to (x€R)

The area of a circle is 49 π cm2. Its circumference is (a) 7 πcm (b) 14 πcm (c) 21 πcm (d) 28 πcm

D and E are points on equal sides AB and AC of isosceles triangle respectively and B,C,E and D are concyclic points. If O is point of intersection of CD and BE,then prove that AO bisects the line segment DE

Question 16 A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

A and B both have some pencils. if A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have?

Mark the correct alternative in the following question:The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is(a) 191 (b) 193 (c) 211 (d) none of these

The volume of a rectangular box (or cuboid) whose length, breadth and height are 7 cm, 3 cm and 3 cm respectively, is.

In a right ∆ABC, right-angled at B, if tanA=1, then verify that 2sinA·cosA=1.

Which of the following are sure events?

Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = ________.

Let Xn = {1,2,3,….n) and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3. (For example, if n = 5, A can be ϕ, {2} or {1,5} among others). When n = 10, let the probability that 1ϵA be p and let the probability that 2ϵA be q. Then

In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find x

In the following figure, If ABC is an equilateral triangle, then shaded area is equal to(a) π3-34r2(b) π3-32r2(c) π3+34r2(d) π3+3r2Figure

Question 8 If 3 cot A = 43, check whether (1−tan2A)(1+tan2A)=cos2A−sin2A or not.

The value of tan 10° tan 15° tan 75° tan 80° is(a) −1(b) 0(c) 1(d) None of these

In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+ML=PN+MN.

In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30o. The tangent at C intersects AB produced at D. Find /BDC.

11. Prove that the tangent drawn at the mid point of an arc is parallel to the chord joining the mid points of the arc.

19. Determine the height of a mountain, if the elevation of its top at unknown distance from the base is 45^° and at a distance 10km further off from the mountain along the same line , the angle of elevation is 30^° .

Question 106 State whether the statement is True or False. [(−32)÷8]÷2=−32÷[8÷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.

If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

44. Find the maximum volume of a cone that can be fitted in a sphere of radius 7cm?

Prove the following trigonometric identities.1-tan2 Acot2 A-1=tan2 A

Question 9 (iii)A right circular cylinder just encloses a sphere of radius r (see figure). Find:(iii) the ratio of the areas obtained in (i) and (ii).

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them;2x2−6x+3=0

The value of cos 1° cos 2° cos 3° ..... cos 180° is(a) 1(b) 0(c) −1(d) None of these

When a = 0, b = -1, find the value of the given expression:2a2+b2+1

If X¯1,X¯2,...,X¯k are the means of n group with n1,n2,...,nk number of observations respectively, then the mean X¯ of all the groups taken together is govern by (a) ∑i=1kni X¯i(b) 1n2∑i=1k ni X¯i(c) ∑i=1k ni X¯i∑i=1k ni(d) ∑i=1k ni X¯i2n