32581 + Interview Questions in Mathematics Page 220 InterviewSolution

10951.	In ∆ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ \|\| BC and PQ divides ∆ABC into two parts equal in area. Find BPAB.
Answer» In ∆ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ \|\| BC and PQ divides ∆ABC into two parts equal in area. Find $\frac{BP}{AB}$ .

Discussion

10952.	Solve the following systems of equations:x3+y4=115x6-y3=-7
Answer» Solve the following systems of equations: $\frac{x}{3} + \frac{y}{4} = 11 \frac{5 x}{6} - \frac{y}{3} = - 7$

Discussion

10953.	Which of the following expressions is a polynomial?
Answer» Which of the following expressions is a polynomial?

Discussion

10954.	Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
Answer» Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

Discussion

10955.	Fill In the Blanks If the mean of the data x1,x2,...,xn is X¯, then the mean of ax1 + b,ax2+b,...,axn + b is ____________ .
Answer» Fill In the Blanks If the mean of the data x₁,x₂,...,x_n is $\bar{X}$ , then the mean of ax₁ + b,ax₂+b,...,ax_n+ b is ____________ .

Discussion

10956.	In Figure 3. ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)
Answer» In Figure 3. ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)

Discussion

10957.	Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.
Answer» Find a quadratic polynomial with $\frac{1}{8}$ as the sum and 2 as product of its zeroes.

Discussion

10958.	The HCF of two numbers is 16 and their product is 3072. Find their LCM?
Answer» The HCF of two numbers is 16 and their product is 3072. Find their LCM?

Discussion

10959.	Each interior angle of a regular hexagon is ____
Answer» Each interior angle of a regular hexagon is ____

Discussion

10960.	The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there? Plz explain it in detail
Answer» The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there? Plz explain it in detail

10960.

The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there? Plz explain it in detail

Answer»

The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there?

Plz explain it in detail

Discussion

10961.	Construct a triangle ABC in which AB=5 cm,BC=6 cm and ∠ABC=60∘.Now construct another triangle whose sides are57 times the corresponding sides of △ABC.
Answer» Construct a triangle ABC in which AB=5 cm,BC=6 cm and $∠ A B C = 60^{\circ}$ .Now construct another triangle whose sides are $\frac{5}{7}$ times the corresponding sides of $△ A B C$ .

Discussion

10962.	For each of the following statements state whether true(T) or false(F).(i) Two circles with different radii are similar.(ii) Any two rectangles are similar.(iii) If two traingles are similar, the their corresponding angles are equal and their corresponding sides are equal.(iv) The length of the line segment joining the mid points of any two sides of a trinagle is equal to the half the length of the third side.(v) In △ABC, AB = 6 cm, ∠A = 450 and AC = 8 cm and in △DEF, DF = 9 cm, ∠D = 450 and DE = 12 cm, then △ABC ∼ △DEF.(vi) The polygon formed by joining the mid points of the sides of a quadrilateral is a rhombus.(vii) The ratio of areas of two similar triangles is equal to the ratio of their corresponding angle-bisector segments.(viii) The ratio of the perimeters of two similar triangles is same as the ratio of their corresponding medians.(ix) If O is any point inside a rectangle ABCD then OA2 + OC2 = OB2 + OD2(x) The sum of the squares on the sides of a rhombus is equal to the sum of the squares on its diagonals.
Answer» For each of the following statements state whether true(T) or false(F). (i) Two circles with different radii are similar. (ii) Any two rectangles are similar. (iii) If two traingles are similar, the their corresponding angles are equal and their corresponding sides are equal. (iv) The length of the line segment joining the mid points of any two sides of a trinagle is equal to the half the length of the third side. (v) In △ABC, AB = 6 cm, ∠A = 45⁰ and AC = 8 cm and in △DEF, DF = 9 cm, ∠D = 45⁰ and DE = 12 cm, then △ABC ∼ △DEF. (vi) The polygon formed by joining the mid points of the sides of a quadrilateral is a rhombus. (vii) The ratio of areas of two similar triangles is equal to the ratio of their corresponding angle-bisector segments. (viii) The ratio of the perimeters of two similar triangles is same as the ratio of their corresponding medians. (ix) If O is any point inside a rectangle ABCD then OA² + OC² = OB² + OD² (x) The sum of the squares on the sides of a rhombus is equal to the sum of the squares on its diagonals.

Discussion

10963.	what is special property about element 115?
Answer» what is special property about element 115?

Discussion

10964.	Find the HCF of 55 and 210 by prime factorization and Express it as a linear combination of 55 and 210
Answer» Find the HCF of 55 and 210 by prime factorization and Express it as a linear combination of 55 and 210

Discussion

10965.	Find the equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0.
Answer» Find the equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0.

Discussion

10966.	If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =(a) 1(b) 0(c) −1(d) 2
Answer» If α, β are the zeros of the polynomial f(x) = x² − p(x + 1) − c such that (α +1) (β + 1) = 0, then c = (a) 1 (b) 0 (c) −1 (d) 2

Discussion

10967.	If the mean of the following frequency distribution is 54, find the value of p. Class0−2020−4040−6060−8080−100Frequency7p10913
Answer» If the mean of the following frequency distribution is 54, find the value of p. $\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 7 & p & 10 & 9 & 13 \end{matrix}$

Discussion

10968.	State the mid point theorem.
Answer» State the mid point theorem.

Discussion

10969.	Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.
Answer» Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.

Discussion

10970.	Question 2 (iii) Simplify : (√5+√2)2 .
Answer» Question 2 (iii) Simplify : ${(\sqrt{5} + \sqrt{2})}^{2}$ .

Discussion

10971.	Let →a=^i+^j−^k and →b=^i−^j+^k.Then the unit vector in the direction of →a+→b is [2 marks]
Answer» Let $\to a =^i +^j -^k$ and $\to b =^i -^j +^k .$ Then the unit vector in the direction of $\to a + \to b$ is [2 marks]

Discussion

10972.	In the formula X¯ = a+Σ fidiΣ fi , for finding the mean of grouped data di's are derivations from a of(a) lower limits of classes (b) upper limits ofclasses (c) mid-points of classes (d) frequency of the class marks
Answer» In the formula $\bar{X} = a + \frac{Σ f_{i} d_{i}}{Σ f_{i}}$ , for finding the mean of grouped data ${d_{i}}^{'^{s}}$ are derivations from $a$ of (a) lower limits of classes (b) upper limits ofclasses (c) mid-points of classes (d) frequency of the class marks

Discussion

10973.	The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by the x-axis is ___.
Answer» The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by the x-axis is ___.

Discussion

10974.	A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of copper used in making the pipe.
Answer» A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of copper used in making the pipe.

Discussion

10975.	Which of the following vector(s) is(are) perpendicular to the vector ^i−2^j+3^k ?
Answer» Which of the following vector(s) is(are) perpendicular to the vector $^i - 2^j + 3^k ?$

Discussion

10976.	Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Answer» Father is aged three times more than his son Ronit. After $8$ years, he would be two and a half times of Ronit's age. After further $8$ years, how many times would he be of Ronit's age?

Discussion

10977.	The perimeters of two similar triangles ABC and PQR are respectively 36cm and 24cm. If PQ=10cm, find AB
Answer» The perimeters of two similar triangles ABC and PQR are respectively 36cm and 24cm. If PQ=10cm, find AB

Discussion

10978.	Find the zero of the polynomial:(i) p(x) = x − 5(ii) q(x) = x + 4(iii) r(x) = 2x + 5(iv) f(x) = 3x + 1(v) g(x) = 5 − 4x(vi) h(x) = 6x − 2(vii) p(x) = ax, a ≠ 0(viii) q(x) = 4x
Answer» Find the zero of the polynomial: (i) p(x) = x − 5 (ii) q(x) = x + 4 (iii) r(x) = 2x + 5 (iv) f(x) = 3x + 1 (v) g(x) = 5 − 4x (vi) h(x) = 6x − 2 (vii) p(x) = ax, a ≠ 0 (viii) q(x) = 4x

Discussion

10979.	The difference of two natural numbers is 3 and the difference of their reciprocals is 328. Find the numbers.
Answer» The difference of two natural numbers is 3 and the difference of their reciprocals is $\frac{3}{28}$ . Find the numbers.

Discussion

10980.	The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.Calculate the length of AP.
Answer» The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ. Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm. Calculate the length of AP.

10980.

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.Calculate the length of AP.

Answer»

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.

Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.

Calculate the length of AP.

Discussion

10981.	Area of a circle is related to its radius by the relation __________?
Answer» Area of a circle is related to its radius by the relation __________?

Discussion

10982.	Is it possible we can not use AAS rule and by this rule that if any triangle two angle are equal then third angle is also be equal so there is no need for apply AAS rule
Answer» Is it possible we can not use AAS rule and by this rule that if any triangle two angle are equal then third angle is also be equal so there is no need for apply AAS rule

Discussion

10983.	31. If n positive integers are taken at random and multiplied together, then find the chance that the last digit of the product would be 1,3,5,7 or 9.
Answer» 31. If n positive integers are taken at random and multiplied together, then find the chance that the last digit of the product would be 1,3,5,7 or 9.

Discussion

10984.	A bag contains 4 red and 8 blue marbles. A marble is drawn at random. The probability of drawing red is
Answer» A bag contains 4 red and 8 blue marbles. A marble is drawn at random. The probability of drawing red is

Discussion

10985.	Question 2 (i)On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.5x - 4y + 8 = 07x + 6y - 9 = 0
Answer» Question 2 (i) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x - 4y + 8 = 0 7x + 6y - 9 = 0

Discussion

10986.	Let A,B be two events such that probability of occurrence of any one is 35, probability of occurrence of only B is 210. Then the probability of occurrence of A is
Answer» Let $A, B$ be two events such that probability of occurrence of any one is $\frac{3}{5},$ probability of occurrence of only $B$ is $\frac{2}{10} .$ Then the probability of occurrence of $A$ is

Discussion

10987.	The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π=227) [2 MARKS]
Answer» The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $π = \frac{22}{7}$ ) [2 MARKS]

10987.

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π=227) [2 MARKS]

Answer»

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $π = \frac{22}{7}$ ) [2 MARKS]

Discussion

10988.	Solve the following quadratic equations by factorization:9x2-6b2x-a4-b4=0
Answer» Solve the following quadratic equations by factorization: $9 x^{2} - 6 b^{2} x - (a^{4} - b^{4}) = 0$

Discussion

10989.	Deposits of money which cannot be withdrawn before the stipulated period of time are
Answer» Deposits of money which cannot be withdrawn before the stipulated period of time are

Discussion

10990.	Question 1 (i)Evaluate the following:(i) sin60∘cos30∘+sin30∘cos60∘
Answer» Question 1 (i) Evaluate the following: (i) $s i n 60^{\circ} c o s 30^{\circ} + s i n 30^{\circ} c o s 60^{\circ}$

Discussion

10991.	State with reason, whether the Proprietary Ratio will improve, decline or will not change because of the following transactions if Proprietary Ratio is 0.8 : 1:(i) Obtained a loan of ₹ 5,00,000 from State Bank of India payable after five years.(ii) Purchased machinery of ₹ 2,00,000 by cheque.(iii) Redeemed 7% Redeemable Preference Shares ₹ 3,00,000.(iv) Issued equity shares to the vendor of building purchased for ₹ 7,00,000.(v) Redeemed 10% redeemable debentures of ₹ 6,00,000.
Answer» State with reason, whether the Proprietary Ratio will improve, decline or will not change because of the following transactions if Proprietary Ratio is 0.8 : 1: (i) Obtained a loan of ₹ 5,00,000 from State Bank of India payable after five years. (ii) Purchased machinery of ₹ 2,00,000 by cheque. (iii) Redeemed 7% Redeemable Preference Shares ₹ 3,00,000. (iv) Issued equity shares to the vendor of building purchased for ₹ 7,00,000. (v) Redeemed 10% redeemable debentures of ₹ 6,00,000.

Discussion

10992.	If a line makes angles 90∘, 135∘,45∘ with the x,y and z axes respectively, find its direction cosines.
Answer» If a line makes angles $90^{\circ}, 135^{\circ}, 45^{\circ}$ with the $x, y and z$ axes respectively, find its direction cosines.

Discussion

10993.	Solve the following word problems.(1) A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.(2) Kantabai bought 112 kg tea and 5 kg sugar from a shop. She paid Rs 50 as return fare for rickshaw. Total expense was Rs 700. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2 kg tea and 7 kg sugar. She paid Rs 880 for that. Find the rate of sugar and tea per kg.(3) To find number of notes that Anushka had, complete the following activity.(4) Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages.(5) In a factory the ratio of salary of skilled and unskilled workers is 5 : 3. Total salary of one day of both of them is Rs 720. Find daily wages of skilled and unskilled workers.(6) Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.
Answer» Solve the following word problems. (1) A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number. (2) Kantabai bought $1 \frac{1}{2}$ kg tea and 5 kg sugar from a shop. She paid Rs 50 as return fare for rickshaw. Total expense was Rs 700. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2 kg tea and 7 kg sugar. She paid Rs 880 for that. Find the rate of sugar and tea per kg. (3) To find number of notes that Anushka had, complete the following activity. (4) Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages. (5) In a factory the ratio of salary of skilled and unskilled workers is 5 : 3. Total salary of one day of both of them is Rs 720. Find daily wages of skilled and unskilled workers. (6) Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.

Discussion

10994.	Question 7If the 2nd term of an AP is 13 and 5th term is 25, what is its 7th term?A) 30B) 33C) 37D) 38
Answer» Question 7 If the $2^{n d}$ term of an AP is 13 and $5^{t h}$ term is 25, what is its $7^{t h}$ term? A) 30 B) 33 C) 37 D) 38

Discussion

10995.	The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 9.5 m away from the wall. Find the length of the ladder.
Answer» The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 9.5 m away from the wall. Find the length of the ladder.

Discussion

10996.	Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
Answer» Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.

Discussion

10997.	From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?
Answer» From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

Discussion

10998.	9. A vertical lamp post is located at one corner of a level ground. The ground is in the shape of a regular hexagon. A man walks from the foot of the post to the next three corners of the ground in clockwise direction and notices that the angles of elevation of the top of the post from each of these corners are α, β and γ respectively, where α > β > γ. Then
Answer» 9. A vertical lamp post is located at one corner of a level ground. The ground is in the shape of a regular hexagon. A man walks from the foot of the post to the next three corners of the ground in clockwise direction and notices that the angles of elevation of the top of the post from each of these corners are α, β and γ respectively, where α > β > γ. Then

Discussion

10999.	If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C 32,52, find x, y.
Answer» If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C $(\frac{3}{2}, \frac{5}{2})$ , find x, y.

Discussion

11000.	Question 32How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?
Answer» Question 32 How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?

Discussion

Explore topic-wise InterviewSolutions in .

In ∆ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ || BC and PQ divides ∆ABC into two parts equal in area. Find BPAB.

Solve the following systems of equations:x3+y4=115x6-y3=-7

Which of the following expressions is a polynomial?

Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.

Fill In the Blanks If the mean of the data x1,x2,...,xn is X¯, then the mean of ax1 + b,ax2+b,...,axn + b is ____________ .

In Figure 3. ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)

Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.

The HCF of two numbers is 16 and their product is 3072. Find their LCM?

Each interior angle of a regular hexagon is ____

The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there? Plz explain it in detail

Construct a triangle ABC in which AB=5 cm,BC=6 cm and ∠ABC=60∘.Now construct another triangle whose sides are57 times the corresponding sides of △ABC.

what is special property about element 115?

Find the HCF of 55 and 210 by prime factorization and Express it as a linear combination of 55 and 210

Find the equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0.

If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =(a) 1(b) 0(c) −1(d) 2

If the mean of the following frequency distribution is 54, find the value of p. Class0−2020−4040−6060−8080−100Frequency7p10913

State the mid point theorem.

Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.

Question 2 (iii) Simplify : (√5+√2)2 .

Let →a=^i+^j−^k and →b=^i−^j+^k.Then the unit vector in the direction of →a+→b is [2 marks]

In the formula X¯ = a+Σ fidiΣ fi , for finding the mean of grouped data di's are derivations from a of(a) lower limits of classes (b) upper limits ofclasses (c) mid-points of classes (d) frequency of the class marks

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by the x-axis is ___.

A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of copper used in making the pipe.

Which of the following vector(s) is(are) perpendicular to the vector ^i−2^j+3^k ?

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

The perimeters of two similar triangles ABC and PQR are respectively 36cm and 24cm. If PQ=10cm, find AB

Find the zero of the polynomial:(i) p(x) = x − 5(ii) q(x) = x + 4(iii) r(x) = 2x + 5(iv) f(x) = 3x + 1(v) g(x) = 5 − 4x(vi) h(x) = 6x − 2(vii) p(x) = ax, a ≠ 0(viii) q(x) = 4x

The difference of two natural numbers is 3 and the difference of their reciprocals is 328. Find the numbers.

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.Calculate the length of AP.

Area of a circle is related to its radius by the relation __________?

Is it possible we can not use AAS rule and by this rule that if any triangle two angle are equal then third angle is also be equal so there is no need for apply AAS rule

31. If n positive integers are taken at random and multiplied together, then find the chance that the last digit of the product would be 1,3,5,7 or 9.

A bag contains 4 red and 8 blue marbles. A marble is drawn at random. The probability of drawing red is

Question 2 (i)On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.5x - 4y + 8 = 07x + 6y - 9 = 0

Let A,B be two events such that probability of occurrence of any one is 35, probability of occurrence of only B is 210. Then the probability of occurrence of A is

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π=227) [2 MARKS]

Solve the following quadratic equations by factorization:9x2-6b2x-a4-b4=0

Deposits of money which cannot be withdrawn before the stipulated period of time are

Question 1 (i)Evaluate the following:(i) sin60∘cos30∘+sin30∘cos60∘

If a line makes angles 90∘, 135∘,45∘ with the x,y and z axes respectively, find its direction cosines.

Question 7If the 2nd term of an AP is 13 and 5th term is 25, what is its 7th term?A) 30B) 33C) 37D) 38

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 9.5 m away from the wall. Find the length of the ladder.

Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.

From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C 32,52, find x, y.

Question 32How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?