25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1:2 and the amount of lead and tin in the alloy Y is in the ratio 2:3, then what is the ratio of lead to tin in the mixture?
Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a
Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is
Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is
ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to
In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?
In the figure given below, ∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C respectively. What are the values of x and y respectively?
In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT= PT, then what is ∠RLM equal to?
In the figure given below, PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35° and ∠UST = 70°, then what is ∠MPQ equal to?
In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.
Consider the following statements:
Which of the above statements are correct?
In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by
ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:
Which of the above statements are correct?
ABC is an isosceles triangle such that AB = BC = 8 cm and ∠ABC = 90°. What is the length of the perpendicular drawn from B on AC?
What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?
If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to?
A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is
The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?
An automobile financer claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging the interest at the rate of 10%, the effective rate of interest becomes:
A certain sum at simple interest amounts to Rs.1350 in 5 years and to Rs.1620 in 8 years. What is the sum?
The principal on which a simple interest of Rs. 55 will be obtained after 9 months at the rate of 3⅔% per annum is
A sum of money becomes 3 times in 5 years at simple interest. In how many years will the same sum become 6 times at the same rate of simple interest?
A sum of money on compound interest amounts to Rs. 9680 in 2 yr and Rs. 10648 in 3 yr. What is the rate of interest per annum?
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest on Rs. 12,000 after 3 years at the same rate of interest?
What is the least number of complete years in which a sum of money at 20% compound interest will be more than doubled?
The difference between compound interest and the simple interest at the same rate of interest R percent per annum on an amount of Rs. 15,000 for two years is Rs. 96. What is the value of R?
If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to?
Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are
If the roots of the equation Ax2 + Bx + C = 0 are -1 and 1, then which one of the following is correct?
If a - b = 4 and a2 + b2 = 40 where a and b are positive integers, where a and b are positive integers, then a3 + b6 is equal to
The sign of the quadratic polynomial ax2 + bx + c is always positive if
In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:
If α and β are the roots of the equation x2 - x - 1 = 0, then what is (α2 + β2)/((α2 - β2)(α - β))
If the roots of the equation (a2 - bc)x2 + 2(b2 - ac)x + (c2 - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?
Rajendra bought a mobile with 25% discount on the selling price. If the mobile cost him Rs. 4,875, what is the original selling price of the mobile?
A fruit-seller buys lemons at 2 for a rupee and sells them at 5 three rupees. What is his gain percent?
A man buys a television set which lists for Rs 5000 at 10% discount. He gets an additional 2% discount (after the first discount) for paying cash. What does he actually pay for the set?
A man sold two watches, each for Rs. 495. If he gained 10% on one watch and suffered a loss of 10% on the other, then what is the loss or gain percentage in the transaction?
A person sold an article for Rs. 3600 and got a profit of 20%. Had he sold the article for Rs. 3150, how much profit would he have got?
A person selling an article for Rs. 96 finds that his loss percent is one-fourth of the amount of rupees that he paid for the article. What can be the cost price?
A person sold an article for Rs.136 and got 15% loss. Had he sold it for Rs.x, he would have got a profit of 15%. Which one of the following is correct?
A merchant earns a profit of 20% by selling a basket containing 80 apples which cost Rs 240 but he gives one-fourth of it to his friend at cost price and sells the remaining apples. In order to earn the same profit, at what price must he sell each apple?
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