The expediture of a household for a certain month is INR 20000, out of which INR 8000 is spent on education, INR 5900 on food, INR 2800 on shopping and the rest on personal care. What percentage of expediture is spent on personal care

Outside a meeting room, Madhukar was told by a person that each meeting takes place after 13/4 hours. The last meeting has been over just 45 minutes ago and the next meeting will take place at 2 p.m. At what time did Madhukar receive this information

If m and n are distinct natural numbers, then which of the following is/are integer/integers

1. m/n+n/m
2. mn(m/n+n/m)(m²+n²)-1
3. mn/m²+n²

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Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR×SQ = OS×RP. Which of the following statements is/are correct

1. If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y.
2. ∠POC+∠QCO = 90⁰

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Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?

1. L is a straight line passing through A and in-centre of triangle ABC is on L.
2. L is a straight line passing through A and orthocentre of triangle ABC is a point on L.
3. L is a straight line passing through A and centroid of triangle ABC is a point on L.

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Consider a circle with centre at O and radius 7 cm. Let QR be a chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct

1. ∠QPD = 135⁰
2. If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x²-10x+1 = 0.
3. The ratio of the area of triangle OPR to the area of triangle OMP is 1:2√2.

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