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A roller coaster is designed such that riders experience “weightlessness” as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill should be between

Solution: The speed of the car at the top of the hill should be between 14 and 15.... View Article

Light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains.

Solution: We know that white light is composed of a band of colours arranged in red, orange, yellow, green, blue, indigo, and violet. When the... View Article

In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English. How many speak at least one of these two languages?

Solution: Let n(H) be the number of people speaking Hindi and n(E) be the number of people speaking English. n(H) = 50 n(E) = 20 n(H⋂E)... View Article

In a class there are 35 girls and 20 boys and the total average weight of class is 38 kg. Total average weight of boys is 52 kg. Find the approximate average weight of girls ?

Solution: Total number of boys and girls = 35+20 = 55 Total average weight of class=38 kg Total weight of students = 38×55 =... View Article

Angle between vectors a and b where a, b and c are unit vectors satisfying a + b + √3c = 0 is

Solution: Given a + b + √3c = 0 a + b = -√3c Squaring both sides |a|2+|b|2+2|a||b| cos θ = 3|c|2 1+1+2 cos θ = 3... View Article

If one zero of the polynomial p(x) = (a²+9)x² +45x + 6a is reciprocal of the other, find the value of a

Solution: Given p(x) = (a2+9)x2 +45x + 6a Let k and 1/k be the zeros of the polynomial. Product of the roots = k(1/k) = c/a => 1 =... View Article

In given figure ABC is a right-angled triangle at B. Let D and E be any points on AB and BC respectively. Prove that (AE)² + (CD)² = (AC)² + (DE)².

Solution: ABE is a right angled triangle. (AE)2 = (AB)2 + (BE)2…(i) DBC is a right angled triangle. (DC)2 = (BD)2 + (BC)2…(ii) Adding (i)... View Article

If A = { a, b, c, d, e }, B = { a, c, e, g } and C = { b, e, f, g }, verify that:

(a) A⋂(B-C) = (A⋂B) - (A⋂C) (b) A- (B⋂C) = (A - B) ∪ (A - C) Solution: Given A = { a, b, c, d, e } B = { a, c, e, g } C = { b, e,... View Article

If the x-intercept of some line L is double as that of the line, 3x+4y = 24 and the y-intercept of L is half as that of the same line, then the slope of L is

Solution: Given line is 3x+4y = 24 Converting to intercept form, (3x/24) + (4y/24) = 1 => (x/8) + (y/6) = 1 Here x intercept is 8... View Article

If a point C lies between two points A and B such that AC = BC, then prove that AC = ½ AB. Explain by drawing the figure.

Solution: Given that we have a point C on AB such that AC = BC. Add AC on both sides AC + AC = AC + BC 2AC = AC + BC 2AC = AB(since AC+BC... View Article

A man had a certain amount with him. He spent 20% of that to buy an article and 5% of the remaining on the transport. Then he gifted Rs. 120. If he is left with Rs. 1400, the amount he spent on transport is:

(a) Rs. 380 (b) Rs. 61 (c) Rs. 95 (d) Rs. 80 Solution: Let x be the amount with the man. He spent 20% of that to buy an article 20%x =... View Article

The degree of a monomial x²y²z² is

(a) 6 (b) 2 (c) 3 (d) 8 Solution: The degree of a monomial is the sum of the exponents of all its variables. Given... View Article

Consider the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, …. Then 1025th term is

(A) 29 (B) 210 (C) 211 (D) 28 Solution: Let m = Number of times a number n is repeated in the given sequence {n} Given... View Article

Find the locus of the middle point of the portion of the line x cos α + y sin α = p which is intercepted between the coordinate axes is, given that p remains constant.

(a) 1/x2 + 1/y2 = 1/p2 (b) 1/x2 + 1/y2 = 1/2p2 (c) 1/x2 + 1/y2 = 4/p2 (d) none of these Solution: Given line is x cos α + y sin α = p At... View Article

In a group of 15 people, 7 read French, 8 read English while 3 of them read none of them. How many read French and English both?

(a) 3 (b) 4 (c) 5 (d) 6 Solution: Let F denote the number of people who read French and E denote the number of people who read English. Let... View Article

There are three clubs A, B, C in a town with 40, 50, 60 members respectively 10 people are members of all the three clubs, 70 members belong to only one club. A member is randomly selected. Find the probability that he has a membership of exactly two clubs.

Solution: From the venn diagram a+e+g+d = 40 ..(i) b+e+g+f = 50 ..(ii) c+d+g+f = 60 ..(iii) g = 10 a+b+c = 70 Add (i), (ii) and (iii)... View Article

Number of 5 digit numbers which are divisible by 5 and each number containing the digit 5, digits being all different is equal to k(4!), then the value of k is

(a) 84 (b) 168 (c) 188 (d) 208 Solution: For the number to be divisible by 5, the digit at units place should be 5 or... View Article

Which of the following statements is false?

(a) All isosceles triangles are similar. (b) All equilateral triangles are similar. (c) All circles are similar. (d) None of the above.... View Article

A shopkeeper bought 10 fans for Rs.1250 each. He sold 6 fans for Rs.1375 each and remaining 4 fans for Rs.1200 each. Find his total loss or profit.

Solution: The cost price of 10 fans = 1250×10 = Rs.12500 The selling price of 6 fans = 6×1375 = Rs.8250 The selling price... View Article

The price of petrol was Rs. 65. The price was first increased by 4% and then reduced by 5%. What is the price of petrol now?

Solution: Price of petrol = Rs. 65 4% of 65 = (4/100)×65 = 2.6 Increased price = 65+2.6 = 67.6 Now price is reduced by 5%.... View Article