List of practice Questions

The simple interest on a certain sum of money for \(2\frac{1}{2}\) years at 12% per annum is RS.40 less than the simple interest on the same sum for \(3\frac{1}{2}\) years at 10% per annum. Find the sum

Instead of walking along two adjacent sides of a rectangular field, a boy took a short-cut along the diagonal of the field and saved a distance equal to half of the longer side. Find the ratio of the length of the shorter side to that of the longer side of the field.

By selling an electric iron for ₹700, a shopkeeper incurred a loss of 30%. At what price should he have sold the electric iron to gain 40% ?

A water tank can be filled by two pipes P and Q in 60 minutes and 30 minutes respectively. How many minutes will it take to fill the empty tank if pipes P and Q are opened for first half of the time, after which only pipe Q is opened for next half of the time?

Calculate the value of median from the given data:
2.90, 3.57, 3.73, 2.98, 3.64, 3.75
3.30, 3.62, 3.76, 3.38, 3.66, 3.76

A sum of money doubles itself on simple interest in 10 years. Find the rate of interest per annum.

An athlete takes as much time in running 200 m as a car takes in covering 500m. The distance covered by the athlete during the time the car covers 2 km is:

If \(cot^2 45\degree-sin^2 45\degree = K sin^2 30\degree x tan^2 45\degree xsec^2 45\), then the value of K is

The area of a rhombus is 120 cm² and length of its one diagonal is 24 cm. Find the perimeter of the rhombus (in cm).

The monthly income and expenditure of a person were ₹10,000 and ₹6,000 respectively. Next year, his income increased by 15% and his expenditure increased by 8%. Then the percentage increase in his savings is:

If A, B and C are acute positive angles such that A + B + C = π and cot A cot B cot c = K, then

The two adjacent sides of a cyclic QUADRILATERAL are 2 and 5 and the angle between them is 60°. If the third side is 3, the remaining fourth side is -

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is -

Given below are two statements :
Statement I: If the roots of the quadratic equation \(x^2-4x-log_3a=0\) are real, then the least value of a is 1/81.
Statement II: The harmonic mean of the roots of the equation \((5+ \sqrt2)x^2 - (4+\sqrt5)x + (8+2\sqrt5) = 0\) is 2.
In the light of the above statements, choose the correct answer from the options given below:

The mean deviation from the mean of the AP a, a+d, a+2d,..... a + 2nd is

Match List-I and List-II

LIST I		LIST II
A.	Addition Theorem on probability	I.	\(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\)
B.	Binomial distribution	II.	\(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\)
C.	Baye's rule	III.	\(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\)
D.	Multiplication theorem on prob	IV.	\(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\)

Choose the correct answer from the options given below:

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If the A.M. and G.M. between two numbers are in the ratio m : n, then the numbers are in the ratio \(m+\sqrt{m^2-n^2}:m-\sqrt{m^2-n^2}\)
Reason R: If each term of a G.P. be raised to the same power, the resulting sequence also forms a G.P.
In the light of the above statements, choose the correct answer from the options given below:

Let E be the ellipse\(\frac{x^2}{9}+\frac{y^2}{4}=1\) and C be the circle x² + y² = 9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

If a Chord which is normal to the parabola y² = 4ax at one end subtends a right angle at the vertex, then its slope is -

A straight line has equation y=-x+6 which of the following line is parallel to it?

Match List-I and List-II

LIST I		LIST II
A.	Value of\(\lim\limits_{x\rightarrow0}\left(\frac{sinx}{x}\right)^{\frac{sinx}{x-sinx}}\)	I.	e3
B.	Value of \(\lim\limits_{x\rightarrow0}\int\limits_0^x\frac{sint^2dt}{x^2}\)is	II.	0
C.	Value of \(\lim\limits_{x\rightarrow0}(e^{2x}+x)^{\frac{1}{x}}\)is	III.	1
D.	Value \(\lim\limits_{x\rightarrow a}\frac{log(x-a)}{log(e^x-e^a)}\)of	IV.	e-1

Choose the correct answer from the options given below:

Match List-I and List-II

LIST I		LIST II
A.	The angle between the straight lines, 2x2+ 3y2-7xy=0 is	I.	\(\tan^{-1}\frac{3}{5}\)
B.	The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle	II.	25π
C.	The area of circle centered at (1,2) and passing through (4,6) is	III.	π/4
D.	The parabola y2=4x and x2 =32y intersect at point (16,8) at angle	IV.	π/2

Choose the correct answer from the options given below:

Match List-I and List-II

LIST I		LIST II
A.	8 : 81 :: 64 : ?	I.	290
B.	182 : ? :: 210 : 380	II.	132
C.	42 : 56 :: 110 : ?	III.	342
D.	48 : 122 :: 168 : ?	IV.	625

Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An elevator starts with m passengers and stops at n floors (m \(\leq\) n). The probability that no two passengers alight at the same floor is \(\frac{^np_m}{m_n}\)
Reason R: If (n + 1) p is an integer, say m, then\(p(x=r)= ^nC_rp^Ω(1-p)^{n-Ω} \)is maximum when r = m or r = m -1
In the light of the above statements, choose the most appropriate answer from the options given below :

Consider the adjoining diagram: What is the minimum number of different colours required to paint the figure such that no two adjacent regions have same colour?