Maths

Question: In a classroom of 30 students, 18 are boys and 12 are girls. If one student is chosen at random, what is the probability that the student is a girl?(A) 3⁄5(B) 2⁄5(C) 4⁄5(D) 1⁄3 Solution: Total students = 30, girls = 12.Thus, the probability is:P(girl)= 12⁄30 = 2⁄5 Our Social Media Presence –https://youtube.com/@rankmadeeasyhttps://www.facebook.com/groups/rankmadeeasyhttps://www.facebook.com/RankMadeEasyhttps://www.instagram.com/rankmadeeasy1https://twitter.com/rankmadeeasy

Question: A cylinder has a volume of 200π cm³ and a base radius of 5 cm. What is the height of the cylinder?(A) 8 cm(B) 10 cm(C) 12 cm(D) 15 cm Solution: Use the volume formula for a cylinder:V=πr²hGiven V=200π cm³ and r=5 cm:200π=π×5² ×h200π=25π×hh= 200⁄25h=8 cm Our Social Media Presence –https://youtube.com/@rankmadeeasyhttps://www.facebook.com/groups/rankmadeeasyhttps://www.facebook.com/RankMadeEasyhttps://www.instagram.com/rankmadeeasy1https://twitter.com/rankmadeeasy

Question: A rectangular prism has a volume of 384 cm³, a length of 8 cm, and a height of 12 cm. What is the width of the prism?(A) 4 cm(B) 6 cm(C) 8 cm(D) 10 cm Solution: Use the volume formula for a rectangular prism:V=l×w×hGiven V=384 cm³, l=8 cm, and h=12 cm:384=8×w×12384=96ww= 384⁄96w= 4 cm Our Social Media

Question: A factory produces 1000 items, of which 950 are good and 50 are defective. If one item is chosen at random, what is the probability that it is defective?(A) 1/2(B) 1/25(C) 1/30(D) 1/40 Solution: Total items = 1000.Number of defective items = 50.Thus, the probability of choosing a defective item:P(defective) = 50⁄1000 = 1⁄20

Question: A rectangular box has a length of 8 cm, width of 6 cm, and height of 5 cm. What is the total surface area of the box?(A) 184 cm²(B) 188 cm²(C) 236 cm²(D) 216 cm² Solution: The total surface area A of a rectangular box is given by:A=2(lw+lh+wh)where l is the length, w is

Question: Two triangular gates each have angles of 45°, 45°, and 90°, and side lengths of 10 meters, 10 meters, and 14.1 meters. The second gate is identical but installed on the opposite side of the park entrance. Which congruence criterion can be used to prove that the two triangular gates are congruent?(A) SSS(B) ASA(C)

Question: What is the next number in the series?2, 5, 10, 17, 26, ?(A) 36(B) 37(C) 38(D) 39 Solution: The differences are:5 – 2 = 310 – 5 = 517 – 10 = 726 – 17 = 9The differences are: 3, 5, 7, 9 (which increase by 2 each time).Next difference: 9+2 =11.Next term: 26+11

Question: Two cars start from the same point and travel in the same direction at 50 km/h and 70 km/h. How long will it take for the faster car to be 40 km ahead?(a) 1 hour(b) 2 hours(c) 3 hours(d) 4 hours Solution: Relative speed:70−50=20 km/hTime required:40/20 = 2 hours Our Social Media Presence –https://youtube.com/@rankmadeeasyhttps://www.facebook.com/groups/rankmadeeasyhttps://www.facebook.com/RankMadeEasyhttps://www.instagram.com/rankmadeeasy1https://twitter.com/rankmadeeasy

Question: Two triangular doors each have side lengths of 8 meters, 15 meters, and 17 meters. The second door is identical but installed on the opposite side of the hallway. Which congruence criterion can be used to prove that the two triangular doors are congruent?(A) SSS(B) ASA(C) RHS(D) SAS Solution: Both triangular doors have identical

Question: Two triangular pieces of a ceiling design each have side lengths of 9 meters, 40 meters, and 41 meters. The second piece is identical but located on the opposite side of the ceiling. Which congruence criterion can be used to prove that the two triangular pieces of the ceiling design are congruent?(A) SSS(B) ASA(C)