List of practice Questions

The slope of the tangent to the hyperbola 2x²-3y²=6 at (3,2) is

4(x+(π)/(6))\cos2x((5π)/(6)+x)dx

If Im=₀¹ ( x)ᵐ dx, where mN, then I₁₀+10I₉ is equal to

The area of the region bounded by the curve y=x|x|, x-axis and the ordinates x=1, x=-1 is given by

Let E=1,2,3,4 and F=1,2. Then the number of onto functions from E to F is

If f(x)=x√(1+x²), then (f f)(x) is

The value of ⁻¹x+⁻¹((x)/(2)+(1)/(2)√(3-3x²)); \frac12 x\le1 is

If A=bmatrix1&3
3&2
2&5bmatrix and B=bmatrix-1&-2
0&5
3&1bmatrix and A+B-D=0 (zero matrix), then D matrix will be

The value of vmatrix 1 & 2 & 3
-4 & 3 & 6
2 & -7 & 9 vmatrix is

Let f(x)=cases ax²+1, & x>1
x+a, & x\le1 cases Then f(x) is derivable at x=1, if

The line ax+by=1 cuts ellipse cx²+dy²=1 only once if

Find the equation of chord of the circle x²+y²=8x bisected at the point (4,3).

Find the value of ₓₒ₀√(1+x²)-√(1-x²)x².

Mean of 25 observations was found to be 78.4. But later it was found that 96 was misread as 69. The correct mean is

If the mean, mode and S.D. of a frequency distribution are 41.45 and 8 respectively, then its Pearson’s coefficient of skewness is

A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die.

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70, then the number of diagonals of the polygon is

With 17 consonants and 5 vowels, the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

The coefficient of x³² in the expansion of (x⁴-1x³)¹5 is

If arithmetic means are inserted between 1 and 31 so that the ratio of the 7th and (m-1)th means is 5:9, then find the value of m.

The reflection of the point (4,-13) in the line 5x+y+6=0 is

If the equations of the opposite sides of a parallelogram are x²-5x+6=0 and y²-6y+5=0, then equations of its diagonals are

If the line 2x-1=0 is the directrix of the parabola y²-kx+6=0, then one of the values of k is

Experiment to study kinetics of the dissociation of hydrogen peroxide must be performed by group of two or three so that

Let A=\x:x R, |x|<1 B=\x:x R, |x-1| 1 and A B=R-D, then the set D is