Csat---math Questions
#1
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden [ U.P.S.C ( 2014 ) Pre. ]
#2
A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is : [ U.P.S.C ( 2016 ) Pre. ]
#3
An agricultural field is in the form of a rectangle having length X1 meters and breadth X2 meters (X1 and X2 are variable). If X1 + X2 = 40 meters, then the area of the agricultural field will not exceed which one of the following values ? [ U.P.S.C ( 2016 ) Pre. ]
#4
AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is : [ U.P.S.C ( 2016 ) Pre. ]
#5
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is : [ U.P.S.C ( 2016 ) Pre. ]
#6
A cylindrical overhead tank of radius 2 m and height 7 m is to be filled from an underground tank of size 5.5m x 4m x 6m. How much portion of the underground tank is still filled with water after filling the overhead tank completely ? [ U.P.S.C ( 2016 ) Pre. ]
#7
The outer surface of a 4 cm × 4 cm × 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty four 1 cm × 1 cm × 1 cm small cubes. How many small cubes do not have painted faces? [ U.P.S.C ( 2017 ) Pre. ]
#8
Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling ? [ U.P.S.C ( 2017 ) Pre. ]
#9
A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces ? [ U.P.S.C ( 2018 ) Pre. ]
#10
Twelve equal squares are placed to fit in at rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square? [ U.P.S.C ( 2018 ) Pre. ]
#11
How many diagonals can be drawn by joining the vertices of an octagon ? [ U.P.S.C ( 2018 ) Pre. ]
#12
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ? [ U.P.S.C ( 2019 ) Pre. ]
#13
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is [ U.P.S.C ( 2019 ) Pre. ]
#14
Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P and mass of Q is two times that of P . Let u = m/x and v = n /y . Which one of the following is correct ? [ U.P.S.C ( 2020 ) Pre. ]
#15
Consider the following statements : 1. The minimum number of points of intersection of a square and a circle is 2 . 2. The maximum number of points of intersection of a square and a circle is 8 . Which of the above statements is/are correct ? [ U.P.S.C ( 2020 ) Pre. ]
#16
There are three points P , Q and R on a straight line such that PQ : QR = 3 : 5 . If n is the number of possible values of PQ : QR , then what is n equal to ? [ U.P.S.C ( 2020 ) Pre. ]
#17
A cubical vessel of side 1 m is filled completely with water . How many millimetres of water is contained in it ( neglect thickness of the vessel ) ? [ U.P.S.C ( 2021 ) Pre. ]
#18
There are eight equidistant points on a circle. How many right-angled triangles can be using these drawn points as vertices and taking the diameter as one side of the triangle? [ U.P.S.C ( 2022 ) Pre. ]
#19
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm : 1. It is possible to cut the sheet exactly into 4 square sheets . 2. It is possible to cut the sheet into 10 triangular sheets of equal area . Which of the above statements is / are correct ? [ U.P.S.C ( 2022 ) Pre. ]
#20
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ? [ U.P.S.C ( 2023 ) Pre.]
#21
125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each side ? [ U.P.S.C ( 2023 ) Pre.]
#22
A cuboid of dimensions 7cm × 5cm × 3cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7cm × 5cm × 5cm, 5cm × 3cm, 7cm × 3cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1cm. Which of the following statements is/are correct ? 1. 1.There are exactly 15 small cubes with no paint on any face . 2. 2.There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green . Select the correct answer using the code given below : [ U.P.S.C ( 2023 ) Pre.]
#23