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?

- 1:2
- 2:3
- 3:5
- 7:11

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

- Square
- Rectangle, but need not be a square
- Rhombus, but need not be a square
- Parallelogram, but need not be a rhombus

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

- 5/3 square units
- 5/2√2 square units
- 5/4 square units
- 1 square unit

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

- 5.5 cm
- 5 cm
- 3.5 cm
- 3 cm

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

- 5 cm
- 6 cm
- 8 cm
- 9 cm

In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

- 60°
- 75°
- 90°
- 100°

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?

- 10 and 130
- 10 and 125
- 20 and 130
- 20 and 125

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?

- ∠PQT
- ∠LRM
- ∠RML
- ∠QPT

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?

- 55°
- 70°
- 75°
- 80°

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:

- Triangle ADC is an isosceles triangle.
- D is the centroid of the triangle ABC.
- Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

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

- SAS rule
- SSS rule
- ASA rule
- AAA rule

ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:

- Triangles ADX and BAY are congruent
- ∠DXA = ∠AYB
- DX is inclined at an angle 60° with AY
- DX is not perpendicular to AY

Which of the above statements are correct?

- 2, 3 and 4 only
- 1, 2 and 4 only
- 1, 3 and 4 only
- 1 and 2 only

How many degrees are there in an angle which equals two-third of its complement?

- 60°
- 48°
- 45°
- 36°

In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?

- 26°
- 28°
- 38°
- 52°

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?

- 4√2 cm
- 4 cm
- 2 cm
- 2√2 cm

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?

- r/4
- r/2
- √2r
- r

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?

- 0
- 1
- 2
- 4

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

- 5√3 cm
- 5 cm
- 10√3 cm
- 10 cm

In the figure given, LM is parallel to QR. If LM divides the triangle PQR such that area of trapezium LMRQ is two times the area of triangle PLM, then what is PL/PQ equal to?

- 1/3
- 1/√2
- 1/√3
- 1/2

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?

- Rs. 5,500
- Rs. 6,000
- Rs. 6,250
- Rs. 7,500

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:

- 11%
- 10.75%
- 10.5%
- 10.25%

What is the compound interest on ₹1600 at 25% per annum of 2 year compounded annually

- ₹ 900
- ₹ 800
- ₹ 750
- ₹ 700

A certain sum at simple interest amounts to Rs.1350 in 5 years and to Rs.1620 in 8 years. What is the sum?

- Rs.900
- Rs.800
- Rs.700
- Rs.1000

The principal on which a simple interest of Rs. 55 will be obtained after 9 months at the rate of 3⅔% per annum is

- Rs. 1000
- Rs. 1500
- Rs. 2000
- Rs. 2500

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?

- 10.5 years
- 12 years
- 12.5 years
- 10 years

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?

- 5%
- 10%
- 15%
- 20%

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?

- Rs. 6,240
- Rs. 2,160
- Rs. 3,972
- Rs. 3,120

What is the least number of complete years in which a sum of money at 20% compound interest will be more than doubled?

- 4
- 5
- 6
- 7

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?

- 8
- 10
- 12
- Cannot be determined due to insufficient data

If α and β are the roots of the equation x^{2} + px + q = 0, then what is α^{2} + β^{2} equal to?

- p
^{2}– 2q - q
^{2}– 2p - p
^{2}+ 2q - q
^{2}– q

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

- -4, -3
- 6, 1
- 4, 3
- -6, -1

The value of x2 - 4x + 11 can never be less than

- 7
- 8
- 11
- 22

If the roots of the equation Ax^{2} + Bx + C = 0 are -1 and 1, then which one of the following is correct?

- A and B are both positive
- A and C are both negative
- A and C are of opposite sign
- A and C are both zero

If a - b = 4 and a^{2} + b^{2} = 40 where a and b are positive integers, where a and b are positive integers, then a^{3} + b^{6} is equal to

- 264
- 280
- 300
- 324

The sign of the quadratic polynomial ax^{2} + bx + c is always positive if

- a is positive and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≥ 0. - a is positive and b
^{2}- 4ac ≥ 0.

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:

- x
^{2}+ 10x + 9 = 0 - x
^{2}- 10x + 16 = 0 - x
^{2}- 10x + 9 = 0 - x
^{2}+ 10x + 16 = 0

The expression 2x^{3} + x^{2} - 2x - 1 = 0 is divisible by

- 2x - 1
- 2x + 1
- x + 2
- x - 2

If x^{2} = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values of x equal to?

- 3
- 4
- 5
- 6

If α and β are the roots of the equation x^{2} - x - 1 = 0, then what is (α^{2} + β^{2})/((α^{2} - β^{2})(α - β))

- 2/5
- 4/5
- 3/5
- 1/5

If the roots of the equation (a^{2} - bc)x^{2} + 2(b^{2} - ac)x + (c^{2} - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

- a
^{3}+ b^{3}+ c^{3}= 0 - a
^{3}+ b^{3}+ c^{3}= 3abc - a
^{2}+ b^{2}+ c^{2}= 0 - a + b + c = abc

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?

- Rs. 6,300
- Rs. 6,400
- Rs. 6,500
- Rs. 6,600

A fruit-seller buys lemons at 2 for a rupee and sells them at 5 three rupees. What is his gain percent?

- 10%
- 15%
- 20%
- 25%

On a 20% discount sale, an article costs Rs. 596. What was the original price of the article?

- Rs. 720
- Rs. 775
- Rs. 745
- Rs. 735

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?

- Rs. 4000
- Rs. 4400
- Rs. 4410
- Rs. 4500

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?

- No gain, no loss
- 1% gain
- (100/99)% loss
- 1% loss

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?

- 10%
- 6%
- 5%
- 4%

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?

- Rs. 160 only
- Rs. 240 only
- Rs. 160 or Rs. 240
- Neither Rs. 160 nor Rs. 240

A cloth store is offering Buy 3, Get 1 free. What is the net percentage discount being offered by the store?

- 20%
- 25%
- 30%
- 33.33%

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?

- 170 < x < 180
- 160 < x < 170
- 180 < x < 190
- 190 < x < 200

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?

- Rs. 4.00
- Rs. 3.60
- Rs. 3.00
- Rs. 3.80