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Find the number of divisors and the sum of divisors of number 1400.

Solution: 1400 = 2×2×2×5×5×7 = 23×52×71 Let the number n = paqbrc, (p,q, r are prime numbers... View Article

Prime factors of 231.

Solution: To find the prime factors of a number, divide the given number by the smallest prime number. Again, divide the quotient by the... View Article

Convert 192 to binary.

Solution: Given number is 192. To convert a decimal number to binary, we divide it successively by 2, until quotient is 0. Keep the whole part... View Article

Factors of 675

Solution: To find the factors of 675, we have to find the list of numbers that would divide 675 without leaving any remainder. 675/3 = 225... View Article

A, P, R, X, S and Z are sitting in a row. S and Z are in the centre. A and P are at the ends. R is sitting to the left of A. Who is to the right of P?

(a) A (b) X (c) S (d) Z Solution: Given S and Z are in the centre. A and P are at the ends. The seating arrangement is as follows:... View Article

2 power 24 equals

Solution: 224 = 210× 210 × 24 = 1024 × 1024 × 16 = 16777216 Hence 2 power 24 equals 16777216.... View Article

Vertex of a quadratic equation

Solution: The vertex of a quadratic equation of parabola is the highest or the lowest point of the quadratic equation. Following are the steps... View Article

22 in binary is equal to

Solution: Given number is 22. To convert a decimal number to binary, we divide it successively by 2, until quotient is 0. Keep the whole part... View Article

In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they be selected such that at least one boy should be there

(a) 109 (b) 128 (c) 138 (d) 209 Solution: Total number of children = 6+4 = 10 Out of 10, 4 children are to be selected. Number of ways of... View Article

In figure below, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

(a) 66.5 cm2 (b) 66 cm2 (c) 65 cm2 (d) 67.5 cm2 Solution: Area of shaded region = area of smaller circle with diameter OD + area of semi... View Article

To conduct sports day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each.

To conduct sports day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m... View Article

What is 1 mod 3?

Solution: Modulo is the operation of finding the remainder when you divide two numbers. We divide the dividend by the divisor. Then multiply... View Article

Locus of trisection point of any arbitrary double ordinate of the parabola x² = 4by, is

(a) 9x2 = 4by (b) 3x2 = 2by (c) 9x2 = by (d) 9x2 = 2by Solution: Given x2 = 4by Double ordinate of the parabola is perpendicular to the... View Article

At each point (x, y) of a curve, the intercept of the tangent on the y-axis is equal to 2xy². Find the equation of the curve.

(a) (x/y) = x2+c (b) y/x = y2+c (c) x/y = y2+c (d) y/x = x2+c Solution: Equation of the tangent is y = mx+c Given that c = 2xy2 Slope m =... View Article

In the figure PQ, PR and BC are the tangents to the circle. BC touches the circle at X. If PQ = 7 cm, find the perimeter of ∆PBC.

Solution: Given PQ = 7 cm We know that the tangents from an external point to a circle are equal. So PQ = PR (tangents from point P) XC = CR... View Article

A Carnot engine absorbs 2000 J of heat energy from a reservoir at 127⁰C and rejects 800 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be respectively

Answer: Solution: Efficiency of Carnot cycle is η = (Q1 - Q2)/Q1 = [(2000 - 800)/2000] x 100 = [1200/2000] x 100 = 60% Also,... View Article

A particle of mass 0.1kg executes SHM under a force F=(−10x)N. The speed of particles at the mean position is 6m/s. Then amplitude of oscillations is

a) 0.6 m b) 0.2 m c) 0.4 m d) 0.1 m Answer: a) 0.6 m Solution: From conservation fo mechanical energy. (1/2)KA2 = (1/2)mv2 A =... View Article