32581 + Interview Questions in Mathematics

1.	If A(7,5) , B(4,3) and C(-2,-3) are the vertices of a triangle, then find the slope angle, θ of side BC.
Answer» If A(7,5) , B(4,3) and C(-2,-3) are the vertices of a triangle, then find the slope angle, $θ$ of side BC.

Discussion

2.	If one of the zeroes of a quadratic polynomial of the form x2+ax+b is the negative of the other , then it (a) has no linear term and constant term is negative.(b) has no linear term and the constant term is positive.(c) can have a linear term but the constant term is negative .(d) can have a linear term but the constant term is positive .
Answer» If one of the zeroes of a quadratic polynomial of the form $x^{2} + a x + b$ is the negative of the other , then it (a) has no linear term and constant term is negative. (b) has no linear term and the constant term is positive. (c) can have a linear term but the constant term is negative . (d) can have a linear term but the constant term is positive .

Discussion

3.	Write the correct alternative answer for each of the following questions. (i) Which of the following is a polynomial ?(A) xy (B) x2 - 3x (C) x-2 + 7 (D) 2x2 + 12(ii) What is the degree of the polynomial 7?(A) 12 (B) 5 (C) 2 (D) 0(iii) What is the degree of the 0 polynomial ?(A) 0 (B) 1 (C) undefined (D) any real number(iv) What is the degree of the polynomial 2x2 + 5x3 + 7?(A) 3 (B) 2 (C) 5 (D) 7(v) What is the coefficient form of x3 - 1 ?(A) (1, - 1) (B) (3,-1) (C) (1, 0, 0, -1) (D) (1, 3, - 1)(vi) p(x) = x2 - 77x + 3 then p77 = ?(A) 3 (B) 77 (C) 42 7 + 3 (D) 497(vii) When x = - 1 , what is the value of the polynomial 2x3 + 2x ?(A) 4 (B) 2 (C) -2 (D)-4(viii) If x-1 , what is a factor of the polynomial 3x2 + mx then find the value of m.(A) 2 (B) -2 (C) -3 (D) 3(ix) Multiply ( x2-3) (2x - 7x 3 + 4) and write the degree of the product.(A) 5 (B) 3 (C) 2 (D) 0(x) Which of the following is a linear polynomial ?(A) x + 5 (B) x2 + 5 (C) x3 + 5(D) x4 + 5
Answer» Write the correct alternative answer for each of the following questions. (i) Which of the following is a polynomial ? (A) $\frac{x}{y}$ (B) $x^{\sqrt{2}} - 3 x$ (C) $x^{- 2} + 7$ (D) $\sqrt{2} x^{2} + \frac{1}{2}$ (ii) What is the degree of the polynomial $\sqrt{7}$ ? (A) $\frac{1}{2}$ (B) 5 (C) 2 (D) 0 (iii) What is the degree of the 0 polynomial ? (A) 0 (B) 1 (C) undefined (D) any real number (iv) What is the degree of the polynomial 2x²+ 5x³+ 7? (A) 3 (B) 2 (C) 5 (D) 7 (v) What is the coefficient form of $x^{3} - 1$ ? (A) (1, $-$ 1) (B) (3, $-$ 1) (C) (1, 0, 0, $-$ 1) (D) (1, 3, $-$ 1) (vi) $p (x) = x^{2} - 7 \sqrt{7} x + 3$ then $p (7 \sqrt{7}) = ?$ (A) 3 (B) $7 \sqrt{7}$ (C) $42 \sqrt{7} + 3$ (D) $49 \sqrt{7}$ (vii) When $x = - 1$ , what is the value of the polynomial 2x³+ 2x ? (A) 4 (B) 2 (C) $- 2$ (D) $- 4$ (viii) If $x - 1$ , what is a factor of the polynomial $3 x^{2} + m x$ then find the value of m. (A) 2 (B) $-$ 2 (C) $- 3$ (D) 3 (ix) Multiply ( x² $-$ 3) (2x $-$ 7x³+ 4) and write the degree of the product. (A) 5 (B) 3 (C) 2 (D) 0 (x) Which of the following is a linear polynomial ? (A) x + 5 (B) x²+ 5 (C) x³+ 5 (D) x⁴ + 5

Discussion

4.	If x=√7−√6 and y=√7+√6, find the value of x2+y2−xy ? 25
Answer» If $x = \sqrt{7} - \sqrt{6}$ and $y = \sqrt{7} + \sqrt{6}$ , find the value of $x^{2} + y^{2} - x y$ ? 25

Discussion

5.	Question 1 (v)Which of the following form an AP? Justify your answer.12,13,14,⋯
Answer» Question 1 (v) Which of the following form an AP? Justify your answer. $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots$

Discussion

6.	The sum of prime factors of 4620 is:
Answer» The sum of prime factors of 4620 is:

Discussion

7.	In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding outer concentric circle. What is the probability that the dart hits the smallest circle?
Answer» In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding outer concentric circle. What is the probability that the dart hits the smallest circle?

Discussion

8.	A tangent PQ at a point P on a circle of radius 5 cm meets a line through the center O at a point Q such that OQ =13 cm. Find the length of PQ.
Answer» A tangent PQ at a point P on a circle of radius 5 cm meets a line through the center O at a point Q such that OQ =13 cm. Find the length of PQ.

Discussion

9.	Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.
Answer» Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00 Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.

Discussion

10.	Find whether - 150 is a term of the AP 17, 12, 7, 2 .......?
Answer» Find whether - 150 is a term of the AP 17, 12, 7, 2 .......?

Discussion

11.	f(x)=1/x^2-3x+2 +1/x find domain
Answer» f(x)=1/x^2-3x+2 +1/x find domain

Discussion

12.	If x is a negative integer, then(a) x + \|x\| = 0 (b) x − \|x\| = 0 (c) x + \|x\| = 2x (d) x − \|x\| = − 2x
Answer» If x is a negative integer, then (a) x + \|x\| = 0 (b) x − \|x\| = 0 (c) x + \|x\| = 2x (d) x − \|x\| = − 2x

Discussion

13.	A circular disc of radius 6 cm is divided into three sectors with central angles 90°,120° and 150°. What part of the whole circle is the sector with central angle 150°? Also, calculate the ratio of the areas of the three sectors.
Answer» A circular disc of radius 6 cm is divided into three sectors with central angles 90°,120° and 150°. What part of the whole circle is the sector with central angle 150°? Also, calculate the ratio of the areas of the three sectors.

Discussion

14.	A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill.
Answer» A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as $60^{\circ}$ , and the angle of depression of the base of the hill as $30^{\circ}$ . Find the distance of the hill from the ship and the height of the hill.

Discussion

15.	Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.
Answer» Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.

Discussion

16.	Question 5 (vi)Prove the following identities, where the angles involved are acute angles for which the expressions is defined.sec A + tan A = √(1+sin A1−sin A)
Answer» Question 5 (vi) Prove the following identities, where the angles involved are acute angles for which the expressions is defined. sec A + tan A = $\sqrt{(\frac{1 + s i n A}{1 - s i n A})}$

Discussion

17.	A cylinder has a diameter of 20 cm. The area of the curved surface is 100 cm2(sq.cm). Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.
Answer» A cylinder has a diameter of 20 cm. The area of the curved surface is $100 c m^{2}$ (sq.cm). Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.

17.

A cylinder has a diameter of 20 cm. The area of the curved surface is 100 cm2(sq.cm). Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.

Answer»

A cylinder has a diameter of 20 cm. The area of the curved surface is $100 c m^{2}$ (sq.cm).

Find:

(i) the height of the cylinder correct to one decimal place.

(ii) the volume of the cylinder correct to one decimal place.

Discussion

18.	Solve each of the following systems of equations by the method of cross-multiplication :axb-bya=a+bax-by=2ab
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $\frac{a x}{b} - \frac{b y}{a} = a + b a x - b y = 2 a b$

Discussion

19.	If A and B are symmetric matrices and AB = BA, then A−1B is a
Answer» If A and B are symmetric matrices and AB = BA, then $A^{- 1} B$ is a

Discussion

20.	In the given figure, DE \|\| BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. Find the value of ME & DM.
Answer» In the given figure, DE \|\| BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. Find the value of ME & DM.

20.

In the given figure, DE || BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. Find the value of ME & DM.

Answer»

In the given figure, DE || BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. Find the value of ME & DM.

Discussion

21.	In a trapezium ABCD, if AB \|\| CD then (AC2+BD2) = ? (a) BC2+AD2+2BC.AD (b) AB2+CD2+2AB.CD (c) AB2+CD2+2AD.BC (d) BC2+AD2+2AB.CD
Answer» In a trapezium ABCD, if AB \|\| CD then $(A C^{2} + B D^{2})$ = ? (a) $B C^{2} + A D^{2} + 2 B C . A D$ (b) $A B^{2} + C D^{2} + 2 A B . C D$ (c) $A B^{2} + C D^{2} + 2 A D . B C$ (d) $B C^{2} + A D^{2} + 2 A B . C D$

21.

In a trapezium ABCD, if AB || CD then (AC2+BD2) = ? (a) BC2+AD2+2BC.AD (b) AB2+CD2+2AB.CD (c) AB2+CD2+2AD.BC (d) BC2+AD2+2AB.CD

Answer»

In a trapezium ABCD, if AB || CD then $(A C^{2} + B D^{2})$ = ?

(a) $B C^{2} + A D^{2} + 2 B C . A D$

(b) $A B^{2} + C D^{2} + 2 A B . C D$

(c) $A B^{2} + C D^{2} + 2 A D . B C$

(d) $B C^{2} + A D^{2} + 2 A B . C D$

Discussion

22.	Find the area of equirateral triangle whose side is 20
Answer» Find the area of equirateral triangle whose side is 20

Discussion

23.	If f(x) = √x and g(x) = x , then (fg) (x) equals to ( x ≠ 0 )
Answer» If f(x) = $\sqrt{x}$ and g(x) = x , then $(\frac{f}{g})$ (x) equals to ( x $\neq$ 0 )

Discussion

24.	Prove the following: cos(3π2+x)cos(2π+x)[cot(3π2+x)+cot(2π+x)] = 1
Answer» Prove the following: $c o s (\frac{3 π}{2} + x) c o s (2 π + x)$ $[c o t (\frac{3 π}{2} + x) + c o t (2 π + x)]$ = 1

24.

Prove the following: cos(3π2+x)cos(2π+x)[cot(3π2+x)+cot(2π+x)] = 1

Answer»

Prove the following:

$c o s (\frac{3 π}{2} + x) c o s (2 π + x)$ $[c o t (\frac{3 π}{2} + x) + c o t (2 π + x)]$
= 1

Discussion

25.	Let in a △ABC, x,y,z are the lengths of perpendicular drawn from the vertices of the triangle to the opposite sides a,b,c. Then the value of csinB+bsinCx+asinC+csinAy+bsinA+asinBz is equal to
Answer» Let in a $△ A B C,$ $x, y, z$ are the lengths of perpendicular drawn from the vertices of the triangle to the opposite sides $a, b, c .$ Then the value of $\frac{c sin B + b sin C}{x} + \frac{a sin C + c sin A}{y} + \frac{b sin A + a sin B}{z}$ is equal to

Discussion

26.	The sum of a natural number and its square is 156. Find the number.
Answer» The sum of a natural number and its square is 156. Find the number.

Discussion

27.	Find the number of rational roots of the quadratic equation (x2−2)2×(x3−8)2×(x2−16)2=0
Answer» Find the number of rational roots of the quadratic equation $(x^{2} - 2)^{2} \times (x^{3} - 8)^{2} \times (x^{2} - 16)^{2} = 0$

Discussion

28.	If x=a sin A cos C,y=a sin A sin C,z=a cos A shwo that a2=x2+y2+z2 [4 MARKS]
Answer» If $x = a s i n A c o s C, y = a s i n A s i n C, z = a c o s A$ shwo that $a^{2} = x^{2} + y^{2} + z^{2}$ [4 MARKS]

Discussion

29.	Solve each of the following quadratic equations:2x2+7x+52=0 [CBSE 2013]
Answer» Solve each of the following quadratic equations: $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$ [CBSE 2013]

Discussion

30.	A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
Answer» A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?

Discussion

31.	Question 2 (i) Are the following statements ‘True’ or False’? Justify your answer. i) If the zeroes of a quadratic polynomial ax2+bx+c are positive then a, b and c all have the same sign.
Answer» Question 2 (i) Are the following statements ‘True’ or False’? Justify your answer. i) If the zeroes of a quadratic polynomial $a x^{2} + b x + c$ are positive then a, b and c all have the same sign.

Discussion

32.	A sprinter goes off the starting block for 100 m run and at that instant the second- hand of a stopwatch hadpointed towards North. He touches the finishing line exactly after 12 seconds. In which direction did thesecond hand point when he just crossed the finishing line?
Answer» A sprinter goes off the starting block for 100 m run and at that instant the second- hand of a stopwatch hadpointed towards North. He touches the finishing line exactly after 12 seconds. In which direction did thesecond hand point when he just crossed the finishing line?

Discussion

33.	50.Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.
Answer» 50.Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.

Discussion

34.	A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.
Answer» A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.

Discussion

35.	In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability thatn the drawn ticket bears a prime number.
Answer» In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability thatn the drawn ticket bears a prime number.

Discussion

36.	Question 2 (iv)Verify that each of the following is an AP and then write its next three terms.a + b, (a + 1) + b, (a + 1) + (b + 1) . . . .
Answer» Question 2 (iv) Verify that each of the following is an AP and then write its next three terms. a + b, (a + 1) + b, (a + 1) + (b + 1) . . . .

Discussion

37.	If a, b, c are in A.P. and a2, b2, c2 are inGP. such that a < b < c and a + b +c=3/4then the value of a is
Answer» If a, b, c are in A.P. and a2, b2, c2 are inGP. such that a < b < c and a + b +c=3/4then the value of a is

Discussion

38.	P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]
Answer» P is the centre of the circle . Prove that $∠ X P Z = 2 (∠ X Z Y + ∠ Y X Z)$ . [3 MARKS]

38.

P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]

Answer»

P is the centre of the circle . Prove that $∠ X P Z = 2 (∠ X Z Y + ∠ Y X Z)$ . [3 MARKS]

Discussion

39.

Draw an ogive by less than method for the following data: No. of rooms: 1 2 3 4 5 6 7 8 9 10 No. of houses: 4 9 22 28 24 12 8 6 5 2

Answer» Draw an ogive by less than method for the following data:

No. of rooms:	1	2	3	4	5	6	7	8	9	10
No. of houses:	4	9	22	28	24	12	8	6	5	2

Discussion

40.	Ramela bought Shirts worth ₹ 2000 , Bags worth ₹ 1800 and miscellaneous items worth ₹ 2850. If the sales tax is charged 5 % on shirts , 12 % on bags and 4 % on the miscellaneous items. Find the total amount spent by Ramela.
Answer» Ramela bought Shirts worth ₹ 2000 , Bags worth ₹ 1800 and miscellaneous items worth ₹ 2850. If the sales tax is charged 5 % on shirts , 12 % on bags and 4 % on the miscellaneous items. Find the total amount spent by Ramela.

Discussion

41.	The speed of a train increases at a constant rate from zero to v, and then remainsconstant for an interval, and finally decreases to zero at a constant rate B. If L be the totaldistance travelled, then the total time taken isL(A)1L 21 1(B)V2 aL1+2v1(C)(D)P.
Answer» The speed of a train increases at a constant rate from zero to v, and then remainsconstant for an interval, and finally decreases to zero at a constant rate B. If L be the totaldistance travelled, then the total time taken isL(A)1L 21 1(B)V2 aL1+2v1(C)(D)P.

Discussion

42.	Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
Answer» Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).

Discussion

43.	A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : (i) the production in the 1st year (ii) the production in the 10th year (iii) the total production in first 7 years
Answer» A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : (i) the production in the $1^{s t}$ year (ii) the production in the $10^{t h}$ year (iii) the total production in first $7$ years

Discussion

44.	sin θ1-cot θ+cos θ1-tan θ is equal to(a) 0(b) 1(c) sin θ + cos θ(d) sin θ − cos θ
Answer» $\frac{\sin θ}{1 - \cot θ} + \frac{\cos θ}{1 - \tan θ}$ is equal to (a) 0 (b) 1 (c) sin θ + cos θ (d) sin θ − cos θ

Discussion

45.	Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x. [CBSE 2014]
Answer» Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x. [CBSE 2014]

Discussion

46.	Prove that 3 - 3√7 is an irrational number
Answer» Prove that 3 - 3√7 is an irrational number

Discussion

47.	What is the mean of position vector ?
Answer» What is the mean of position vector ?

Discussion

48.	10. If the squared differences of the zeros of the quadratic polynomial p(x)=xsqaure+3x+k is 3 ,find k
Answer» 10. If the squared differences of the zeros of the quadratic polynomial p(x)=xsqaure+3x+k is 3 ,find k

Discussion

49.	What is the probability that a number selected from the numbers 1, 2, 3,........... 25 is a prime number, when each of the given numbers is equally likely to be selected?
Answer» What is the probability that a number selected from the numbers 1, 2, 3,........... 25 is a prime number, when each of the given numbers is equally likely to be selected?

Discussion

50.	Find the roots of the following quadratic equations (if they exist) by the method of completing the square.2x2 + x + 4 = 0
Answer» Find the roots of the following quadratic equations (if they exist) by the method of completing the square. 2x² + x + 4 = 0

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If A(7,5) , B(4,3) and C(-2,-3) are the vertices of a triangle, then find the slope angle, θ of side BC.

If x=√7−√6 and y=√7+√6, find the value of x2+y2−xy ? 25

Question 1 (v)Which of the following form an AP? Justify your answer.12,13,14,⋯

The sum of prime factors of 4620 is:

In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding outer concentric circle. What is the probability that the dart hits the smallest circle?

A tangent PQ at a point P on a circle of radius 5 cm meets a line through the center O at a point Q such that OQ =13 cm. Find the length of PQ.

Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.

Find whether - 150 is a term of the AP 17, 12, 7, 2 .......?

f(x)=1/x^2-3x+2 +1/x find domain

If x is a negative integer, then(a) x + |x| = 0 (b) x − |x| = 0 (c) x + |x| = 2x (d) x − |x| = − 2x

A circular disc of radius 6 cm is divided into three sectors with central angles 90°,120° and 150°. What part of the whole circle is the sector with central angle 150°? Also, calculate the ratio of the areas of the three sectors.

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill.

Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.

Question 5 (vi)Prove the following identities, where the angles involved are acute angles for which the expressions is defined.sec A + tan A = √(1+sin A1−sin A)

A cylinder has a diameter of 20 cm. The area of the curved surface is 100 cm2(sq.cm). Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.

Solve each of the following systems of equations by the method of cross-multiplication :axb-bya=a+bax-by=2ab

If A and B are symmetric matrices and AB = BA, then A−1B is a

In the given figure, DE || BC, AE = 15cm, EC = 9cm, NC = 6 cm &amp; BN = 24 cm. Find the value of ME &amp; DM.

In a trapezium ABCD, if AB || CD then (AC2+BD2) = ? (a) BC2+AD2+2BC.AD (b) AB2+CD2+2AB.CD (c) AB2+CD2+2AD.BC (d) BC2+AD2+2AB.CD

Find the area of equirateral triangle whose side is 20

If f(x) = √x and g(x) = x , then (fg) (x) equals to ( x ≠ 0 )

Prove the following: cos(3π2+x)cos(2π+x)[cot(3π2+x)+cot(2π+x)] = 1

Let in a △ABC, x,y,z are the lengths of perpendicular drawn from the vertices of the triangle to the opposite sides a,b,c. Then the value of csinB+bsinCx+asinC+csinAy+bsinA+asinBz is equal to

The sum of a natural number and its square is 156. Find the number.

Find the number of rational roots of the quadratic equation (x2−2)2×(x3−8)2×(x2−16)2=0

If x=a sin A cos C,y=a sin A sin C,z=a cos A shwo that a2=x2+y2+z2 [4 MARKS]

Solve each of the following quadratic equations:2x2+7x+52=0 [CBSE 2013]

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?

Question 2 (i) Are the following statements ‘True’ or False’? Justify your answer. i) If the zeroes of a quadratic polynomial ax2+bx+c are positive then a, b and c all have the same sign.

A sprinter goes off the starting block for 100 m run and at that instant the second- hand of a stopwatch hadpointed towards North. He touches the finishing line exactly after 12 seconds. In which direction did thesecond hand point when he just crossed the finishing line?

50.Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.

A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.

In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability thatn the drawn ticket bears a prime number.

Question 2 (iv)Verify that each of the following is an AP and then write its next three terms.a + b, (a + 1) + b, (a + 1) + (b + 1) . . . .

If a, b, c are in A.P. and a2, b2, c2 are inGP. such that a < b < c and a + b +c=3/4then the value of a is

P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]

Draw an ogive by less than method for the following data: No. of rooms: 1 2 3 4 5 6 7 8 9 10 No. of houses: 4 9 22 28 24 12 8 6 5 2

Ramela bought Shirts worth ₹ 2000 , Bags worth ₹ 1800 and miscellaneous items worth ₹ 2850. If the sales tax is charged 5 % on shirts , 12 % on bags and 4 % on the miscellaneous items. Find the total amount spent by Ramela.

The speed of a train increases at a constant rate from zero to v, and then remainsconstant for an interval, and finally decreases to zero at a constant rate B. If L be the totaldistance travelled, then the total time taken isL(A)1L 21 1(B)V2 aL1+2v1(C)(D)P.

Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : (i) the production in the 1st year (ii) the production in the 10th year (iii) the total production in first 7 years

sin θ1-cot θ+cos θ1-tan θ is equal to(a) 0(b) 1(c) sin θ + cos θ(d) sin θ − cos θ

Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x. [CBSE 2014]

Prove that 3 - 3√7 is an irrational number

What is the mean of position vector ?

10. If the squared differences of the zeros of the quadratic polynomial p(x)=xsqaure+3x+k is 3 ,find k

What is the probability that a number selected from the numbers 1, 2, 3,........... 25 is a prime number, when each of the given numbers is equally likely to be selected?

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.2x2 + x + 4 = 0

In the given figure, DE || BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. Find the value of ME & DM.