S12 ; Mensuration - III

Mensuration & Geometry - III : Mensuration & Geometry - III

Q.1: The number of triangles with integral sides that can be made which have a perimeter of 14, are (CAT2000) 1.6 2.5 3.4 4.3 : Q.1: The number of triangles with integral sides that can be made which have a perimeter of 14, are (CAT2000) 1.6 2.5 3.4 4.3

Slide 3 : Answer is 3rd option

Q.2 :The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will (CAT 2006)1.Remain the same 2.Dec. by 13.64% 3.Dec.by15%4.Dec.by18.75% 5. Dec. by 30% : Q.2 :The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will (CAT 2006)1.Remain the same 2.Dec. by 13.64% 3.Dec.by15%4.Dec.by18.75% 5. Dec. by 30%

Slide 5 : Answer is 5th option

Q.3: 2 sides of plot measure 32 mt. & 24 mt. & angle between them is 90°. The other two sides measure 25 mt. each & the other 3 s are not 90°. What is the area of the plot in m2 (CAT 2001)?1.768 2.534 3.396.5 4.684 : Q.3: 2 sides of plot measure 32 mt. & 24 mt. & angle between them is 90°. The other two sides measure 25 mt. each & the other 3 s are not 90°. What is the area of the plot in m2 (CAT 2001)?1.768 2.534 3.396.5 4.684

Answer is 4th option : Answer is 4th option

Q.4 : The volume of a sphere is increased by 119.7%. What is the percentage increase in its surface area? : Q.4 : The volume of a sphere is increased by 119.7%. What is the percentage increase in its surface area?

Slide 9 : Answer is 69%.

Q.5: Three solid hemispheres having radii of 1 cm, 1 1/3 cm and 1 2/3 cm respectively are melted together and thus a new hemisphere is made. What is the radius of the hemisphere made? : Q.5: Three solid hemispheres having radii of 1 cm, 1 1/3 cm and 1 2/3 cm respectively are melted together and thus a new hemisphere is made. What is the radius of the hemisphere made?

Slide 11 : Answer is 2 cm.

Slide 12 : Q.6: The volume of a cylinder is decreased by 36%, when its radius is decreased by x%. What is the value of x?

Slide 13 : Is the answer 60%. No, it is wrong. It is 20%.

Q.7 : A 3 cm edge cubical hole is drilled in the centre of each face of a solid cube of volume 3375 cc. What is the total surface area of the solid left ? : Q.7 : A 3 cm edge cubical hole is drilled in the centre of each face of a solid cube of volume 3375 cc. What is the total surface area of the solid left ?

Slide 15 : Is the answer 1296. No it is wrong. The answer is 1566.

Q.8 : There r 2 concentric circles such that area of outer circle is 4 times the area of inner circle. Let A, B & C be 3 distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 cm2 then the area (in cm2) of the triangle ABC would be (CAT NOV 2003)1.  2. 9/ 3. 93/ 4. 63/ : Q.8 : There r 2 concentric circles such that area of outer circle is 4 times the area of inner circle. Let A, B & C be 3 distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 cm2 then the area (in cm2) of the triangle ABC would be (CAT NOV 2003)1.  2. 9/ 3. 93/ 4. 63/

Slide 17 : Answer is 3rd option.

Q.9:The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The area covered by the circle, triangle, and square are c, t, and s, respectively. Then, (CAT FEB 2004) 1. s > t > c 2. c > t > s 3. c > s > t 4. s > c > t : Q.9:The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The area covered by the circle, triangle, and square are c, t, and s, respectively. Then, (CAT FEB 2004) 1. s > t > c 2. c > t > s 3. c > s > t 4. s > c > t

Slide 19 : Answer is 3rd option

Q.10 : A piece of string is 40 cm long. It is cut into 3 pieces. The longest piece is 3 times as long as the middle-sized piece & the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece (in cm) (CAT 2002).1. 27 2.5 3. 4 4. 9 : Q.10 : A piece of string is 40 cm long. It is cut into 3 pieces. The longest piece is 3 times as long as the middle-sized piece & the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece (in cm) (CAT 2002).1. 27 2.5 3. 4 4. 9

Slide 21 : Answer is 3rd option

A rectangle PRSU is divided into 2 smaller rectangles PQTU & QRST by the line TQ. PQ = 10, QR = 5 , RS = 10. Points A, B, F are within the rectangle PQTU & points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are 103 cm apart. (CAT1999) : A rectangle PRSU is divided into 2 smaller rectangles PQTU & QRST by the line TQ. PQ = 10, QR = 5 , RS = 10. Points A, B, F are within the rectangle PQTU & points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are 103 cm apart. (CAT1999)

Q.11: Which of the following statements is necessarily true?1. The closest pair of points among the 6 given points cannot be (F, C).2. Distance between A & B is greater than distance between F & C.3. The closest pair of points among 6 given points is (C,D), (D,E) or (C,E).4. None of the above : Q.11: Which of the following statements is necessarily true?1. The closest pair of points among the 6 given points cannot be (F, C).2. Distance between A & B is greater than distance between F & C.3. The closest pair of points among 6 given points is (C,D), (D,E) or (C,E).4. None of the above

Slide 24 : Answer is 1st option.

Q.12 : AB > AF > BF; CD > DE > CE, BF = 65 cm. Which is the closest pair of points among all 6 given points? 1. B, F 2. C, D 3. A, B 4. None of these : Q.12 : AB > AF > BF; CD > DE > CE, BF = 65 cm. Which is the closest pair of points among all 6 given points? 1. B, F 2. C, D 3. A, B 4. None of these

Slide 26 : Answer is 4th option

Q.13 : From the top of a light house 60 metres high, two ships are observed. The angles of depression of these ships as seen from the the light house, are found to be of 45 and 30. Find the distance between the two ships. (assuming they all are in a line and are also on the same side of the light house) : Q.13 : From the top of a light house 60 metres high, two ships are observed. The angles of depression of these ships as seen from the the light house, are found to be of 45 and 30. Find the distance between the two ships. (assuming they all are in a line and are also on the same side of the light house)

Slide 28 : Answer is 43.92 metres.