List of practice Questions

If y=x+√(1+x²), then (1+x²)dfracd²ydx²+x(dy)/(dx) is
If limₓtₒᵢₙfty xsin((1)/(x))=A and limₓ\to0 xsin((1)/(x))=B, then which one of the following is correct?
If a,b are non-zero roots of x²+ax+b=0, then the least value of x²+ax+b is
If \( 0 < x < \dfrac{\pi}{2} \), then
The number of real roots of the equation eˣ-1+x-2=0 is
A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is
Let M be a 3×3 non-singular matrix with det(M)=α. If |M⁴operatornameadj(M)|=K, then the value of K is
Tangents are drawn from the origin to the curve y=cos x. Their points of contact lie on
The slope of the tangent to the curve y=eˣcos x is minimum at x=α,0≤α\le2π. The value of α is
The total number of 4-digit numbers in which the digits are in descending order, is
The line which is parallel to the X-axis and crosses the curve y=√(x) at an angle 45^∘, is
In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
The arithmetic mean of the data 0,1,2,…,n with frequencies 1,1,1,…,1 is
The mean square deviation of a set of n observations about points -2 and 2 are 18 and 10 respectively. The standard deviation of the set is
Let S be the common focus of the circle x²+y²-2x-4y=0 and the parabola y²=8x. The area of quadrilateral APQS is
If fraceˣ+e⁵xe³x=a₀+a₁x+a₂x²+a₃x³+⋯ then the value of 2a₁+2³a₃+2⁵a₅+⋯ is
Let a, b, c be three vectors satisfying a × b = ( a × c), | a|=| c|=1, | b|=4 and | b × c|=√(15). If a · b = ?, then λ equals
The value of
\( \dfrac{3}{4} + \dfrac{15}{16} + \dfrac{63}{64} + \cdots \)
up to \( n \) terms is
The period of tan 3θ is
If g is the inverse of function f and f'(x)=sin x, then g'(x) is equal to
A bag contains (2n+1) coins. It is known that n of these coins have a head on both sides, whereas the remaining (n+1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is (31)/(42), then n is equal to
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is
The average age of 8 men is increased by 2 years when one of them whose age is 20 yr is replaced by a new man. What is the age of the new man?
Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. How is Shikha related to Ankit?
In a queue of children, Arun is fifth from the left and Suresh is sixth from the right. When they interchange their places, Arun becomes thirteenth from the left. Then, what will be Suresh's position from the right?