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What is the equation of a line, in general form, with a point (-3, 0) and an undefined slope?

(a) x + 3 = 0 (b) y + 3 = 0 (c) x - 3 = 0 (d) y - 3 = 0 Solution: If slope is undefined, the line is parallel to y axis. Given point... View Article

If x³+1 is divided by x²+ 5, then the possible degree of quotient is

(a) 0 (b) 1 (c) 2 (d) none of these Solution: Given dividend is x3+1. Divisor is x2+5. First we divide x3 by x2.... View Article

If tan α + cot α = 2, then tan²⁰α + cot²⁰α =

(a) 0 (b) 2 (c) 20 (d) 220 Solution: Given tan α + cot α = 2 => tan α + 1/tan α = 2 =>... View Article

The sum of the exponent of the prime factors in the prime factorisation of 3240 is

Solution: Prime factorization of 3240 = 23 × 34 × 51 Here the exponents are 3, 4 and 1 The sum of the exponent of the prime... View Article

The area of a square field is 9 hectares. A man cycles along its boundary at 18 km/h. In how much time will he return to starting point?

Solution: Area of square field = 9 hectare = 90000 m2 Let a be the side of square. a2 = 90000 So a = 300 m Perimeter of square = 4a = 1200m... View Article

Which number is missing in the following series? 2, 5, 10, 17, 26, 37, 50, __

(a) 65 (b) 55 (c) 70 (d) 57 Solution: 2, 5, 10, 17, 26, 37, 50, __ Observe the series. The numbers are obtained by adding 3,... View Article

The sum of first three common multiples of 4, 5 and 6 is

(a) 20 (b) 80 (c) 360 (d) 120 Solution: LCM of 4, 5 and 6 = 60 Common multiples are 60, 120, 180. Sum of common multiples = 60... View Article

Write number names for the following decimal numbers (a) 18.312 (b) 22 .05 (c) 0.987

Solution: (a) 18.312 = eighteen point three one two (b) 22 .05 = twenty two point zero five (c) 0.987 = zero point nine eight seven... View Article

The area bounded by the curve y = x² + 4x + 5, the axes of co-ordinates and the minimum ordinate is

Solution: Given y = x2 + 4x + 5 dy/dx = 2x+4 dy/dx = 0 => x = -2 When x = -2, y = 1 When x = 0, y = 5 Required area = ∫-20 (x2 + 4x... View Article

An article was purchased for Rs. 1239 including GST of 18%. Find the price of the article before GST was added?

Solution: Let the price of the article before adding GST be x. So x + (18/100)x = 1239 => x + 0.18x = 1239 => 1.18x = 1239 => x =... View Article

The number of non-negative integral solutions to the system of equations x+y+z+u+t = 20 and x+y+z = 5.

(a) 336 (b) 246 (c) 346 (d) none of these Solution: Given x+y+z+u+t = 20 ..(i) x+y+z = 5 ..(ii) Put (ii)in (i) => 5 + u + t = 20... View Article

Let x₁, x₂, x₃,…, x_n, be n observations and a be the arithmetic mean. then the formula for the standard deviation is given by

Solution: We know that the standard deviation of n observations x1, x2, …xn is given by the formula σ = √[(1/n)∑i=1n (xi... View Article

If a and b are two numbers such that a²+b² = 7 and a³+b³ = 10, then which is the wrong statement.

(a) greatest value of |a+b| is 5 (b) greatest value of a+b is 4 (c) greatest value of a+b is 1 (d) least value of |a+b| is 1 Solution: Given... View Article

Which of the following is the correct formula for the sum and products of the zeroes of a quadratic polynomial p(x) = ax² + bx + c = 0.

(a) -b/a, c/a (b) -b/c, a/c (c) a/b, -c/b (d) none of these Solution: Given polynomial is ax2+bx+c = 0 We know the roots of quadratic... View Article

Find the product of all the prime factors of 616.

(a) 154 (b) 300 (c) 144 (d) none of the above Solution: Prime factorisation of 616 = 23 × 71 × 111 Prime factors are 2, 7, and 11. Product... View Article

Find the value of x, if the two lines, through a = (5, 6) and b = (2, -3) and through c = (-3, 3) and d = (6, x) are perpendicular.

(a) 1 (b) 3 (c) 0 (d) 2 Solution: Given a(5, 6), b(2, -3), c(-3, 3) and d(6, x). When lines are perpendicular, the product of slopes = -1... View Article

Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

(a) 1 (b) 4 (c) -4 (d) 2 Solution: Let the point be A(-2, 6) and B(4, 8). Other two points be C(8,12) and D(x, 24). When lines are... View Article

A piece of wire 7/8 metre long broke into two pieces. One-piece was 1/4 metre long. How long is the other piece?

Solution: Total length of wire = 7/8m Length of one piece = 1/4m Length of remaining piece = 7/8 - ¼ = (7-2)/8 = 5/8m Hence the... View Article

In the figure shown neglecting friction and mass of pulleys, what is the acceleration of mass B?

a) g/3 b) 5g/2 c) 2g/2 d) 2g/5 Answer: d) 2g/5 Solution: aA = (aB + 0)/2 2aA = aB ------(1) From A, mg - TA = maA mg = maA + TA... View Article

The moments of inertia of two freely rotating bodies A and B are I_A and I_B respectively. I_A>I_B and their angular momenta are equal. If K_A and K_B are their kinetic energies, then.

a) KA = KB b) KA ≠ KB c) KA < KB d) KA = 2KB Answer: b.c Solution: Kinetic energy E=L2/2I If angular momenta are equal,... View Article