List of practice Questions

For the data

The weighted price index number is:

If in a 200 m race. A beats B by 31 m and C by 18 m, then in a 350 m race. C will beat B by

If the present value of a perpetuity of ₹600 payable at the end of every six months is ₹18000, then the rate of interest is:

The present value (in ₹.) of a perpetuity of ₹.3600 payable at the end of each quarter, if the interest rate is 9% per annum compounded quarterly, is:

If \(\vec x\) and \(\vec y\) are two collinear vectors, then which of the following are incorrect?

The value of \(∫\frac{dx}{x^2-6x+13}\)is:

The points of non differentiability of \(f(x) = |x-2| + |x - 3|\)
A. 1
B. 2
C. 3
D. 4
E. 5
Choose the correct answer from the options given below:

Match the reactions in List-I with the features of their products in List-II and choose the correct option 

	List-I		List-II
(P)	(-)-1-Bromo-2-ethylpentane (single enantiomer)	(1)	Inversion of configuration
(Q)	(-)-2-Bromopentane (single enantiomer)	(2)	Retention of configuration
(R)	(-)-3- Bromo-3-methylhexane (single enantiometer)	(3)	Mixture of enantiomers
(S)	(single enantiometer)	(4)	Mixture of structural isomers
		(5)	Mixture of diastereomers

Match List I with List II

Choose the correct answer from the options given below:

Let \(f: \R → \R\) be defined by \(f(x) = x^2\), for every \(x∈\R\). Then \(f\) is:

If A and B are events such that \(P(A'UB')=\frac{1}{3}\) and \(P(AUB) = \frac{4}{9}\) then the value of \(P(A') + P(B')\) is:

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and second is white is:

For the LPP, Min \(Z= 5x + 7y\) subject to \(x≥0, y≥0; 2x+y≥8, x+2y≥ 10,\) the basic feasible solutions are:

The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:

The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}= \frac{y+17}{4}= \frac{z-6}{2} \space and \space \frac {x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:

The angle between the straight lines \(\frac{x+4}{2}=\frac{y+5}{5}=\frac{z+6}{3} \space and \space \frac{x-4}{10}=\frac{y-5}{2}=\frac{z-6}{-10}\) is.

If\(|\vec {a}+\vec {b}|=15, |\vec {a}-\vec{b}| =10,|\vec a|=\frac{11}{2}\) then the value of |\(\vec b\)| is/are:

If |\(\vec{a}\)| = 5, |\(\vec{b}\)| = 2 and |\(\vec{a}\) · \(\vec{b}\) | = 8 then the value of |\(\vec{a} \)×\(\vec{b} \)| is:

The solution of the differential equation \(\frac{dy}{dx}=-\frac{x}{y}\) is:

The integrating factor of \(sinx \frac{dy}{dx}+2ycosx=4\) is:

Area lying in first quadrant and bounded by the circle \(x^2+ y^2 = 9\) and the lines x = 1 and x = 3 is:

Area lying between the curves \(y^2 = 9x\) and y = 3x is:

The function \(f(x)= \frac{x^4}{4}-\frac{x^2}{2}\) has

The equation of the normal to the curve y = 2sinx at (0, 0) is:

The values of b for which the function f(x) = cos x + bx+ a decreases on R are