Can I crack CLAT (Common Law Admission Test) and get into NLSIU or NALSAR after taking Science in 12th?

If you want to appear for CLAT, it does not matter what stream you were following in your higher secondary years. CLAT does not check your knowledge about a particular stream but it tests your aptitudes.

• If you work hard then you will definitely be able to get the admission nod from NLSIU or NALSAR. 
• Since you are in your 10(+2), manage your time carefully between preparing for your board exams and preparing for CLAT.
• You must have a strong foundation in general knowledge, legal aptitude, English, mathematics or quantitative aptitude, and logical reasoning if you want to appear for the CLAT.

The exams tend to be very competitive and they are not as easy as they look. Try to take mock exams and solve the questions of the previous years to get acquainted with the pattern in which the exams are held.